of ABSTRACT
Title Document:
THE IMPACT OF TEACHER INTERACTION ON THE ACHIEVEMENT AND SELF-EFFICACY OF STUDENTS WITHIN A COMPUTER-BASED, DEVELOPMENTAL MATHEMATICS COURSE Kristy M. Vernille Blocklin, Ph.D., 2008
Directed By:
Dr. James T. Fey Dr. Anna O. Graeber Education Curriculum and Instruction
A concern of our nations universities and colleges is the number of students entering with what are considered to be sub-standard mathematics skills. According to the National Center for Education Statistics (NCES, 2001), in the fall of 2000, 24% of entering freshmen in 4-year institutions, and 53% of entering freshmen at 2-year institutions were enrolled in a developmental mathematics course. Since developmental educators are increasing their use of technology to reteach this population of students, understanding the role of the instructor in such a setting can inform developmental educators about the needs of the students, thereby potentially increasing the success rate in such courses. Success in developmental mathematics courses could lead to an increase in college-level retention rates and increase students learning and achievement in credit-bearing mathematics courses.
The purpose of this study was to examine if teacher initiated interaction with developmental mathematics students studying in a computer-based classroom has an effect on their achievement or self-efficacy in mathematics. The study seeks to explore whether the role the instructor assumes is a factor in student success. Many theorists and researchers believe that teacher-student interaction and support/motivation provided by teachers are critical to students mathematical achievement. Through the use of a quantitative, experimental design, the researcher attempted to gain insight into the role of a developmental mathematics teacher, the achievement of students enrolled in a computerized class, as well as their feelings of self-efficacy toward mathematics. Six sections of an existing computer-based developmental mathematics course was the setting at a four-year research university in the mid-Atlantic area. The treatment provided by the teacher included: conducting brief initial interviews to obtain background information; initiating interaction and encouragement in every session; monitoring student progress; setting intermediate goals; e-mailing about absences; and verbalizing feedback on tests. The repeated measure ANOVA results of this study indicated that there were significant improvements in student achievement, confidence, and attitude toward teacher when pre- and post- scores were compared in both the control and treatment group. However, no statistically significant difference occurred in achievement or self-efficacy when the classes were analyzed between groups; treatment group vs. control group.
THE IMPACT OF TEACHER INTERACTION ON THE ACHIEVEMENT AND SELF-EFFICACY OF STUDENTS WITHIN A COMPUTER-BASED, DEVELOPMENTAL MATHEMATICS COURSE
By
Kristy M. Vernille Blocklin
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2008
Advisory Committee: Dr. James Fey, Co-Chair Dr. Anna Graeber, Co-Chair Dr. Sharon Fries-Britt Dr. William Sedlacek Dr. Elizabeth Shearn
Copyright by Kristy M. Vernille Blocklin 2008
ACKNOWLEDGEMENTS
Over the past seven years, many people have guided me to the completion of this dissertation. Although I would like to thank every one of them individually, I cannot do so here. Instead I would like to thank those individuals who helped me the most. I wish to begin by thanking Allison Bell, Aimee Felts, Paulina Nusinovich, Tony Smith, and Amber Rust for helping me carry out this study. I am so grateful for all of your time and efforts. Allison Butler, my dear friend, I thank you not only for your contributions to the study, but for also being a source of strength for so many years. You are my rock. You picked me up at my lowest and gave me reasons to continue. You are a beautiful person and I cherish you so very much. I wish to thank Grace Benigno, my first Maryland friend. You guided me through my tough beginning years of graduate school and always made sure I was okay. Your selflessness and kindness I will always appreciate, and I thank you for helping me through this journey. Alycia Marshall and Ming Tomayko, I thank you both for paving the way for me and providing me with constant guidance and support. You made me see that there is an end to all of the hard work and you believed in me every step of the way. From our classes together, to our long lunches and phone conversations, I thank you for all of your love and support and truly treasure our friendship. Dr. Gregory Hancock and Jaewha Choi, I thank you for taking the time to help me with my statistical questions and analysis. I appreciate every minute you set aside for me. Also, I wish to thank Dr. Sharon Fries-Britt for taking the time and energy to serve on my committee. I enjoyed having you as a professor and thank you for your willingness to see me through my defense. To Dr. William Sedlacek, it was an honor working with you at the counseling center and to have you as one of my committee members. I am grateful for your endless knowledge, support, and encouragement and I thank you for the time you took to meet with me and provide me with feedback.
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To Dr. Jim Fey, thank you so much for helping me mold this study into what it has become. Your wisdom, kindness, gentle prodding, and encouragement helped me through many difficult times and helped me to achieve this goal. I thank you for all of your time and advice and wish to say it is a true honor to have had you as a professor and as a co-chair of my dissertation. Dr. Elizabeth Shearn, you are the reason I am where I am today. You have been such a wonderful mentor and helped me discover a passion I never knew existed. Working with you and learning from you from my very first day in graduate school has been remarkable, and I am so lucky to have you in my life. Your love and wisdom has helped me overcome so many obstacles, and I am a better person today because of you. I love you dearly! Thank you for the honor of serving on my committee. Dr. Anna Graeber, I think I can honestly say that I would have never finished this dissertation without you. You have helped me grow so much over the last seven years and were with me every single step of the way. I cannot thank you enough for the uncountable meetings and endless feedback you have provided for me. I wanted to give up so many times, but you always made me focus on the ultimate goal. Thank you for your wisdom, kindness, endless support and motivation, and for seeing me through to the very end. I am so lucky to have had you for an advisor. I dont know how I would ever repay you for helping me achieve something I never knew was possible. It is such an honor to have worked with you and I am forever indebted to you. Finally, I wish to thank my family. I want to thank my brother, Jim, and my sisters, Karrie, Lori, Selina, and Yen. Your constant love and support over the last seven years has been such a motivator and comfort. I thank you for your touching cards, encouraging words, and supportive phone calls. I love you all so very much! To my parents, Dave and Bronia, thank you for helping me to become the person I am today. You provided me with constant love and support that helped me to persevere especially through the most difficult challenges. Your endless encouragement and faith in my abilities motivated me to keep persisting and helped me achieve this remarkable accomplishment. Thank you for being the best and most loving parents
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and for helping me through my entire academic career. I love you both so much. And last by not least, thank you to my wonderful husband Daniel. You had to put up with me every single day and helped me to continue even when I thought I had hit rock bottom. I thank you for your love, support, encouraging words, and for never letting me give up. I love you more than you ever know and thank you from the bottom of my heart.
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DEDICATION
I dedicate this dissertation to Elizabeth Shearn and Anna Graeber for seven years of mentoring, guidance, and support. I could have never done this without both of you.
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TABLE OF CONTENTS
List of Tables ............................................................................................................. viii List of Figures .............................................................................................................. ix Chapter 1: Introduction ................................................................................................. 1 Background and Rationale ........................................................................................ 2 Remedial vs. Developmental ................................................................................ 3 Characteristics of the Students Enrolled in Developmental Courses.................... 4 The Goals of Developmental Education ............................................................... 6 Who Will Teach These Students? ......................................................................... 8 Statement of Purpose .............................................................................................. 10 Overall Methodology .............................................................................................. 11 Research Questions ................................................................................................. 12 Theoretical Framework ........................................................................................... 13 Self-Efficacy Theory........................................................................................... 13 Attribution Theory .............................................................................................. 13 Self-Regulation Theory....................................................................................... 14 Significance............................................................................................................. 15 Limitations .............................................................................................................. 15 Definition of Terms................................................................................................. 16 Chapter 2: Review of Literature ................................................................................. 18 Theoretical Framework ........................................................................................... 21 Self-Efficacy Theory........................................................................................... 22 Attribution Theory .............................................................................................. 28 Self-Regulation ................................................................................................... 32 Instrumentation ....................................................................................................... 36 The Influence of a Teacher ..................................................................................... 37 Chapter 3: Methodology ............................................................................................. 40 Setting and Participants........................................................................................... 41 Computer Program and Class Policies................................................................ 44 Procedures ............................................................................................................... 47 Treatment Group ................................................................................................. 48 Control Group ..................................................................................................... 53 Data Sources ........................................................................................................... 55 Data Analysis .......................................................................................................... 59 Timeline .................................................................................................................. 60 Chapter 4: Results ....................................................................................................... 62 Observation Results ................................................................................................ 62 Research Question 1 ............................................................................................... 65 Overall Test Score Results .................................................................................. 66 Arithmetics Score Results ................................................................................... 66 Elementary Algebra Score Results ..................................................................... 67 Intermediate Algebra Score Results.................................................................... 68
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Research Question 2 ............................................................................................... 70 Total Attitude Survey.......................................................................................... 74 Total Survey Results ........................................................................................... 74 Dimension Results .............................................................................................. 75 Attitude Toward Success Dimension .................................................................. 75 Effectance Motivation Dimension ...................................................................... 76 Confidence in Learning Mathematics Dimension .............................................. 76 Usefulness of Mathematics Dimension .............................................................. 76 Teacher Scale Dimension ................................................................................... 77 Additional Questions .......................................................................................... 77 Chapter 5: Summary and Discussion of Results ........................................................ 79 Overview of Treatment ........................................................................................... 79 Summary and Discussion of Findings .................................................................... 81 Research Question 1 ........................................................................................... 81 Research Question 2 ........................................................................................... 82 Understanding the Results ...................................................................................... 83 Implications............................................................................................................. 89 Directions for Future Research ............................................................................... 91 Appendix A: Distribution of the Four Modules .......................................................... 93 Appendix B: Pilot Study Results ................................................................................ 94 Appendix C: Interview Questions ............................................................................... 98 Appendix D: Observer Checklist ................................................................................ 99 Appendix E: Background Information and Career Aspirations Form ...................... 100 Appendix F: Fennema-Sherman Mathematics Attitude Survey ............................... 102 Appendix G: Attendance Patterns of Study Population............................................ 106 Appendix H: Module Results for Part III of Achievement Test ............................... 107 Appendix I: Statistical Analysis for the Five Dimensions ........................................ 108 Appendix J: IRB Approval and Consent Form ......................................................... 109 References ................................................................................................................. 113
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LIST OF TABLES
Table 1. Student Demographic Information ............................................................... 42 Table 2. Purposes of Data Sources ............................................................................. 58 Table 3. Timeline of Study ......................................................................................... 60 Table 4. Rate of Classroom Interaction ...................................................................... 63 Table 5. Descriptive Statistics for Total Score ........................................................... 66 Table 6. ANOVA for Pre- and Post-Total Scores....................................................... 66 Table 7. Descriptive Statistics for Part One Scores .................................................... 67 Table 8. ANOVA for Pre- and Post-Test Scores (Part One) ...................................... 67 Table 9. Descriptive Statistics for Part Two Scores ................................................... 68 Table 10. ANOVA for Pre- and Post-Test Scored (Part Two) ................................... 68 Table 11. Module Distribution of Students Analyzed in Achievement ...................... 69 Table 12. Descriptive Statistics for Part Three Scores ............................................... 70 Table 13. ANOVA for Pre- and Post-Test Scores (Part Three) .................................. 70 Table 14. Attitude Toward Success in Mathematics Survey Items ............................ 71 Table 15. Effectance Motivation Survey Items .......................................................... 72 Table 16. Confidence in Learning Mathematics Survey Items ................................... 72 Table 17. Mathematics Usefulness Survey Items ....................................................... 73 Table 18. Teacher Scale Survey Items ........................................................................ 73 Table 19. Descriptive Statistics for Total Attitude Survey ......................................... 74 Table 20. ANOVA Results for Total Attitude Survey................................................ 74 Table 21. Descriptive Statistics for the Five Attitude Dimensions ............................. 75 Table 22. Comparing Means of Additional Questions Added to Attitude Survey ..... 78 Table 23. Independent t-test Results for Additional Questions .................................. 78 Table 24. Results of Open-Ended Question (What was most helpful?) ..................... 78 Table 25. Previous Course Experience ....................................................................... 85 Table A. Distribution of Students Across the Four Course Modules ......................... 93 Table B-1. Fall 2006 Pilot Study Outcomes ............................................................... 94 Table B-2. Spring 2007 Pilot Study Outcomes ........................................................... 95 Table H. Module Results for Part III of Achievement Test ...................................... 107 Table I-1. Attitude Toward Success.......................................................................... 108 Table I-2. Effectance Motivation .............................................................................. 108 Table I-3. Confidence in Learning Mathematics ...................................................... 108 Table I-4. Mathematics Usefulness........................................................................... 108 Table I-5. Teacher Scale ........................................................................................... 108
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LIST OF FIGURES
Figure 1. Rate of Classroom Interaction ..................................................................... 64 Figure 2. Total Test Score Comparison ...................................................................... 86 Figure B-1. Fall 2006 Pilot Study Attendance Pattern (Treatment) ........................... 96 Figure B-2. Fall 2006 Pilot Study Attendance Pattern (Control)................................ 96 Figure B-3. Spring 2007 Pilot Study Attendance Pattern (Treatment) ....................... 97 Figure B-4. Spring 2007 Pilot Study Attendance Pattern (Control) ........................... 97 Figure G-1. Attendance Pattern (Treatment) ............................................................ 106 Figure G-2. Attendance Pattern (Control) ................................................................ 106
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CHAPTER ONE: INTRODUCTION
This study seeks to understand whether enhanced teacher initiated interaction within a developmental, computer-based mathematics classroom plays a significant role in student achievement or student sense of self-efficacy in mathematics. Since developmental educators are increasing their use of technology to re-teach this population of students, understanding the role of the teacher in such a setting can inform developmental educators about the needs of the students, thereby potentially increasing the success rate in such courses. Success in developmental mathematics courses could lead to an increase in college-level retention rates and increase students learning and achievement in credit-bearing mathematics courses. This study addresses an issue, of national concern, identified by the National Research Council (2003) for improving the effectiveness of instruction in lower-division college courses in science, technology, engineering, and mathematics. According to the Council, pressures are mounting from within and beyond academe (e.g., state boards of regents and legislatures, business and industry) to improve learning, particularly in introductory and lower-division courses. These calls also request accountability in academic departments, including a new emphasis on improved teaching and enhanced student learning through curriculum revision and collegial peer mentoring (p. XI).
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Background and Rationale A concern of our nations colleges and universities is the number of students entering with what are considered to be sub-standard mathematics skills. According to the National Center for Education Statistics (NCES, 2001), in the fall of 2000, 24% of entering freshmen in 4-year institutions, and 53% of entering freshmen at 2-year institutions were enrolled in a remedial mathematics course. At the research university where this study was conducted, approximately 16% of admitted students in the fall registration were placed into a remedial-level mathematics course (W. Schildknecht, personal communication, May 29, 2008). All students at this university are required to take at least one mathematics credit-bearing course, regardless of the major they select. Students who are required to take a remedial, sometimes referred to as a developmental, mathematics courses do not meet the college pre-requisites or agreed upon standards for credited mathematics courses (Merisotis & Phipps, 2000). These students are lacking the foundation and skills required for rigorous college curriculum (Smittle, 2003, p. 10). As a consequence, these students are required to pass a developmental, usually non-credit bearing, course before registering for a mathematics course required for their major or university credit. Higher-education institutions have recognized the need for developmental programs for almost 200 years. They have accepted the fact that some students do not meet their standards, and the institutions attempt to find ways of meeting the needs of their diverse learners (Casazza, 1999). Today, individuals taking developmental courses include students who have taken Advanced Placement (AP) courses in high school, are returning adults, have disabilities, took the minimum
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number of mathematics courses required for high school graduation, are of both genders, and represent all ethnicities. There is no stereotype for a developmental student. A developmental student can be a student who scored over a 1200 on their SATs or a student for whom English is a second language (Hardin, 1988, 1998). Remedial vs. Developmental It has been argued that the meaning of the word remedial is not the same as that of developmental (Ross, 1970). Since the term remedial has tended to have a negative connotation, or implies a deficiency (Spann & McCrimmon, 1998), some people might think it is merely a matter of political correctness to say developmental (Maxwell, 1979). However, at least according to Ross (1970), remedial instruction refers to the teaching of pre-requisite skills necessary to successfully complete a course. Non-credit courses teaching pre-college material are usually referred to as remedial courses (Boylan & Bonham, 2007). Developmental instruction, on the other hand, assists a student in obtaining a stated objective. Therefore, according to the definitions and Ross (1970), we can label a course as remedial or developmental but we can only label a student as developmental, not as remedial. For the purposes of this study, students will be referred to as developmental students, in a developmental course, receiving developmental instruction. This term has been adopted because the interaction within the classes will encompass more than just the teaching of mathematics skills. The following section will offer additional reasons why the term developmental was adopted for this study.
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Characteristics of the Students Enrolled in Developmental Courses Developmental education is often thought of as courses designed exclusively for underprepared students. This idea can be thought of as a nave one. Students placed or enrolled in a developmental course generally have the ability to achieve, but they are lacking in some fundamental skills, understandings, or dispositions, that lead to high achievement in mathematics. Developmental theorists, such as Hardin (1998), suggest that most students in developmental courses may be underprepared, [but] this does not equate to being incapable or ineducable (p. 22). Students in developmental courses often have been found to have low motivation, lack of confidence, or do not know or how to use proper study skills (Higbee & Thomas, 1999; Yaworski, Weber, & Ibrahim, 2000). It is not because they do not have the intelligence to be in a regular class; these students need to learn certain content or adopt more productive learning attitudes or skills in order to be successful and ultimately achieve a college degree. Affective variables such as motivation, anxiety, self-esteem, and cognitive variables such as learning styles and critical thinking skills, must be considered when trying to identify the specific skills, concepts, or attitudes developmental students must learn (Higbee & Thomas, 1999). Some behavioral patterns are also commonly found in this student population. Sagher, Siadat, and Hagedorn (2000) summarized the findings of multiple researchers as examples of behaviors that were destructive to learning. These behaviors were: short attention spans, little or no attention to assigned homework, procrastination, failure to learn from mistakes, passivity, poor attendance patterns, and low selfesteem.
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There are multiple reasons why a student might be placed in developmental courses. For example, a student might never have received a consistent and proper foundation in mathematics. Alternatively, if an individual had to move several times throughout elementary and/or secondary school, the material covered in mathematics classes might have been drastically different from one school to the next. Therefore, a student might have missed very important concepts that are considered building blocks from one topic to another, or even from one year to another. Mathematics is often referred to as hierarchical, meaning, one must have certain knowledge and skills to be able to move onto the next topic or stage of mathematics. If a student is not exposed to a basic skill early on, their later success can be compromised. Another reason that a student might be on a path to developmental mathematics courses is that the teachers they have had in some of their K-12 mathematics classes may have been ineffective. Unfortunately, not all mathematics teachers are certified for the grade or even sometimes the subject they teach. It has been reported (NCES, 2004) that in schools with a high minority enrollment, as many as 23.0% of public middle school mathematics teachers, and 10.1% of public high school mathematics teachers have neither a major nor certification in the field of mathematics (these percents tend to be lower in schools with low minority enrollment). This ultimately leads to a wide range of experience and knowledge the teachers possess, and can result in lower student achievement. Parental influence can be another explanation for a students lower mathematics achievement and negative feelings for mathematics (Wang, Wildman, & Calhoun, 1996). It is not out of the ordinary to hear a student say that their parent(s)
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claimed that they themselves were never good in mathematics so the pressure of success was never placed on them. It is often the case that a poor mathematics student can cite the exact time or event that caused them to begin to fall apart in their mathematics classes. Many participants interviewed during this study stated: I was always told that since I was a girl, I couldnt be good in mathematics. My elementary teacher liked to teach more reading than math. I lost a whole year of math because my teacher didnt teach. He told us to do whatever we wanted. I just hated Geometry. The teacher was horrible. We actually did Sudoku puzzles in math class my senior year. The schools basketball coach was our math teacher. I had the same horrible math teacher for three years. My sixth grade math teacher insulted the students. This negativity towards their mathematics teacher(s) could influence their attitudes towards the subject of mathematics and ultimately hinder the development of a productive disposition toward mathematics. The Goals of Developmental Education In order to help these students succeed, developmental education has evolved into more than just noncredit courses offered by the university. According to the National Association of Developmental Education (NADE), the goals of developmental education include developing students skills and attitudes necessary for the attainment of academic, career, and life goals (NADE, 2008).
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Developmental education also refers to services that have been developed and organized in order to retain this student population and help them achieve their educational goals (Boylan & Bonham, 2007). These services include offering study skills integrated with course material or just courses teaching only study skills, tutoring resources, workshops, learning assistance centers, as well as workshops offered to advanced students hoping to take the Graduate Record Exam (GRE) or Law School Admission Test (LSAT). Developmental education is not limited to students at risk of failing out of school (Boylan & Bonham, 2007; Casazza, 1999). If postsecondary institutions want to retain as many students as possible, these institutions need to promote both affective and cognitive growth for all learners, at all levels, and focus on both a students social and emotional development (Casazza, 1999). According to Boylan (1999, p. 5), there are principles that institutions must follow in order to promote good developmental education. He believes good developmental education: Is provided through well-educated professionals; a masters or doctoral degree does not automatically qualify a developmental educator. Is student-oriented. It encourages students to use their current knowledge as a building block for their future knowledge. Is based on stated objectives and goals that are connected to the college curriculum. Incorporates critical skills (i.e., metacognitive and study strategies) into all courses and activities.
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Who Will Teach These Students? Institutions need to have a plan of action in place for educating their population of developmental students. A major goal of most developmental education programs is to help underprepared students improve their mathematics skills so that they have the same likelihood of graduating from college as do students not required to take developmental courses (Penny & White, 1998). Therefore, a question mathematics educators should be asking themselves is: How can we make these students better mathematics learners and how can we help them to develop positive attributions, increase self-efficacy and motivation, and develop essential learning strategies toward the subject of mathematics? Another question that is pondered by college and university mathematics departments is Who is going to teach this developmental population? While most upper-level mathematics courses are taught by tenured faculty, lower-level courses are frequently assigned to graduate assistants and adjunct faculty, many of whom have neither a great deal of teaching experience nor education in pedagogy (Penny & White, 1998; Wheland, Konet, & Butler, 2003). And, as previously noted by Boylan (1999), developmental educators need to be well-educated. In addition to having content knowledge, researchers have suggested that developmental instructors must have pedagogical content knowledge (knowledge of content-specific pedagogy, general pedagogy, and student development), provide structure for the students, encourage the students, and help students to grow both personally and independently (Smittle, 2003; Wambach & Brothen, 2000). Students in developmental courses tend to have a number of characteristics that are different from, say, students in a calculus
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course, to which the instructors are rarely alerted. So that students are not put at an immediate disadvantage depending on the mathematics instructor they choose, all developmental educators need to be well informed about this population so they can bring this new understanding into the classroom (Boylan, 1999). In the past, developmental mathematics classes were taught as lecture classes. Today, because of the rapid advances in technology, colleges and universities are opting to use computers to teach their developmental students (Kinney & Robertson, 2003). There are a variety of reasons why a university might choose this option (i.e., cost, convenience, facilitation of self-paced instruction, etc.). However, this raises even more questions: What is the effectiveness of a computer-based class? and What kind of faculty-student interaction, if any, is taking place in these computerbased classes? Computer based instruction (CBI), or as others would call it computermediated instruction, is seen in many forms. Some CBI classes occur over the internet where students do not have to attend an actual mathematics class. They can do their mathematics from their dorm room or from many states away. Other CBI classes are held in a computer lab with just a computer technician present. While others, like the one in this study, are held at a specific time and location with an instructor present. The programs used can vary as well. Some CBI involves lessons, videos, and practice problems that do not change from one student to another, while other CBI can vary the presentation from one student to the next, depending on their ability level. For example, say two students were working on the same problem, but one student got it wrong, while the other got the correct solution. Some CBIs will
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present a more challenging problem to the student who answered correctly and a problem similar or easier than the original problem to the student who answered the problem incorrectly. Interaction has been identified as a critical factor in the success of developmental students (Cooper & Robinson, 1991). All students require feedback, motivation, and a sense of confidence that they can achieve their learning goals. Developmental mathematics students might, however, need a classroom environment that provides more feedback and encouragement since most of the students that make up this population have experienced more failure than most average students and have lower self-efficacy (Hall & Ponton, 2005; Higbee & Thomas, 1999; Wambach & Brothen, 2000). The negative emotions and poor classroom experiences that many of these students carry with them are often difficult to overcome (Ironsmith, Marva, Harju, & Eppler, 2003). Developmental mathematics instructors can likely help improve a students attitude, motivation, or confidence by bringing more to the classroom than just mathematics content. Explicit teaching of study skills and cognitive learning processes, as well as self-regulation training are among the techniques cited as useful for improved student achievement (Schraw, Crippen, & Hartley, 2006; Smittle, 2003; Young & Ley, 2003).
Statement of Purpose The purpose of this study is to examine if teacher initiated interaction with developmental mathematics students studying in a computer-based classroom has an effect on their achievement or self-efficacy in mathematics. The study seeks to
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explore whether the role the teacher assumed was a factor in the students success. Many theorists and researchers believe that teacher-student interaction and support/motivation provided by teachers is critical to students mathematical achievement (Cooper & Robinson, 1991). Noddings (2001) expressed the idea that a teacher should show care towards his/her students. Caring teachers provide attention, encouragement, and are receptive to the needs of the ones that are being cared-for (Noddings, 2001). According to Mayeroff (1971), to care for another person, in the most significance sense, is to help him grow and actualize himself (p. 1). Since increasing numbers of developmental classrooms are using technology to re-teach developmental students (McCoy, 1996; Wadsworth, Husman, Duggan, & Pennington, 2007), explaining the role of the instructor in such a setting can help educate developmental instructors as to the needs of the students, potentially increasing the success rate of students placed into such classes. This might then set students on the road to success in their future, credit-bearing mathematics courses.
Overall Methodology Through the use of a quantitative, experimental design, I attempted to gain insight into the role of a developmental mathematics teacher, the achievement of students enrolled in a computerized class, as well as their feelings of self-efficacy toward the field of mathematics. At a four-year research university in the midAtlantic area, data was collected using students mathematics placement test scores (pre- and post-) and a modified version of the Fennema-Sherman Mathematics Attitudes Scale (Fennema & Sherman, 1976). Three sections of an existing
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computer-based developmental mathematics course were the setting in which the teacher provided initiated interaction and encouragement, monitored student progress, set intermediate goals, responded to absences, and verbalized feedback on tests. Three other sections of the same course were provided with teacher interaction available upon student request and written feedback on corrected exams. All six sections met in the same semester, on the same days, within the middle part of the day, and accessed instruction from the same computer program. Each of the six sections had an assigned Teaching Assistant (TA) who was given instructions as to how to interact with their particular section. At each of the three time slots, one section was randomly assigned to the treatment group and one to the control group. The enrollment of the two groups was 72 and 57, respectively. (Two students assigned to the treatment group and five students in the control group declined participation in the study).
Research Questions This study is guided by two research questions. They are as follows: 1. Does teacher initiated interaction affect students mathematics achievement? 2. Does teacher initiated interaction have any effect on students sense of selfefficacy? Answering these questions could provide direction for structuring future computer-based mathematics classes and how to attend to the students needs within these classes.
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Theoretical Framework The following section will briefly outline the theories that were influential to the underlying premise of this research study. The theoretical frameworks and their related research will be discussed more in depth in Chapter Two. Self- Efficacy Theory Self-efficacy is defined as a persons confidence in their ability to perform a task (Bandura, 1986). This belief of personal competence influences the choices one makes and the course of action they pursue (Pajares, 1996). According to Pajares (1996), efficacy beliefs help determine how much effort people will expend on an activity, how long they will persevere when confronting obstacles, and how resilient they will prove in the face of adverse situations (p. 544). A mathematics student who has a lower sense of self-efficacy, which is often the case in developmental students, will tend to give less effort to a task and show less motivation or even give up when presented with a challenging problem or situation. This type of student believes that they do not have the ability to overcome difficult tasks. Therefore, a lower self-efficacy can hinder student achievement (Young & Ley, 2001). Self-efficacy theory has been explored in studies and has been identified as having a relationship with attribution theory (Schunk, 1991) and with self-regulation theory (Zimmerman, Bandura, & Martinez-Pons, 1992). Thus, the literature review also includes attention to these two theories. Attribution Theory Attribution theory states that a person (in this case student) believes that their past successes or failures will influence their future achievement (Weiner, 1980). In
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other words, they attribute a cause to a behavior or outcome. The roots of this theory date back to Heider (1958) who proposed a psychological theory of attribution. From this, Weiner and his colleagues (1974) developed a theoretical framework that indicated that students generally attribute their achievements to their ability, their effort, the difficulty of the task, or to luck. Attribution theory is related to motivation efficacy beliefs. A student who is a low achiever will often tend to avoid tasks because they doubt their ability and assume that they have bad luck. Therefore, they will show little or no motivation or perseverance toward a particular activity or subject in which they have previously failed. Attributions can also be classified along three causal dimensions. These three dimensions are locus of control (internal vs. external), stability (stable or unstable), and controllability (Weiner, 1980). Developmental mathematics students tend to have an external locus of control. This means that they tend to identify factors external to themselves as causes for their failure, for example, a poor teacher or textbook. They also tend to attribute failures to stable and uncontrollable factors. In other words, ones failure on a test would be attributed to ones ability. Self- Regulation Theory Self-regulation refers to the degree in which students are motivationally, behaviorally, and metacognitively regulators of their own learning process (Zimmerman, 1986). Zimmerman, Bandura, and Martinez-Pons (1992) state that in terms of a social cognitive perspective, self-regulated learners set challenging goals for themselves, select strategies to achieve these goals, and by enlisting selfregulative influences that motivate and guide their efforts (p. 664). A student that
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has better self-regulation skills than another can typically learn more with less effort and report higher levels of academic satisfaction (Schraw, Crippen, & Hartley, 2006, p. 111).
Significance The purpose of this study is to help inform future developmental educators, particularly those teaching within a computer-based developmental mathematics course. Theory suggests developmental students need structure, encouragement, and more attention than the average mathematics student. It is the intent of this study to investigate whether increased teacher attention to these factors can have a profound effect on students sense of self-efficacy and achievement. Improvement of instruction and increased student self-efficacy and achievement will promote both affective and cognitive growth for all learners; a goal of developmental education.
Limitations There are several obvious limitations of this study. The first is that this study is limited to the developmental mathematics program of only one university, though it seems reasonable to expect that the findings may also be typical of other similar large universities. A second important limitation is that the study was conducted in classes during the fall semester. Past experience in undergraduate teaching suggests that there are often significant differences between the students enrolled in this course in the fall and spring semesters. The majority of the students enrolled in the fall semester are typically first-semester freshmen, where as in the spring semester, there
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is an increase in the number of transfer students and those repeating the course. A third limitation of the study is that the investigator carried out the treatment. There is always a concern that an investigator who is performing the treatment can have an emotional tie to the experiment resulting in a chance of bias. A similar limitation, and maybe the most important, is the teacher. A teachers education, previous experience, knowledge of the student population, personality, and commitment to the students vary from one teacher to the next. Since the personal touch of the teacher is such an important part of the treatment being tested, those factors are a particular threat to generalizability. The same concerns can also be raised about the teaching assistants. Their experience working in the classroom and their education (number of courses taken in the mathematics and/or education department) can have a huge impact on how they handle themselves as well as interact with the students in this type of course. A final limitation is that the class sizes were not the same. One lab holds more students than the other, and since three sections were assigned to a treatment group, and the remaining three were assigned to the control group, it was impossible for equal number of students in each group.
Definition of Terms In order to have a better understanding of how data was collected, presented, and analyzed throughout the course of this study, several terms that will be used throughout this paper are defined as follows: Developmental Student a student who is placed into a non-credited mathematics class because they have not demonstrated mathematics
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skills/understandings considered sufficient for success in a university credit bearing course. Computer-Based Course students main source of information is presented to them (in a self-paced manner) through a computer, not an instructor. Placement Test a mathematics skills test required of all students before registering for classes at the university. Depending on score, students can be placed into one of five non-credit mathematics courses or one of six credit bearing mathematics courses. Module one of four curriculum tracks the developmental students at the university can follow to prepare for one of four credited mathematics courses.
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CHAPTER TWO: REVIEW OF LITERATURE
Over the last several decades, mathematics education has evolved into a distinct discipline that contains its own theoretical frameworks and research (Sowder, 1989). Previous to this evolution, mathematics educators drew on theories and research methodologies from other areas, such as developmental psychology and sociology (Lesh, Lovitts, & Kelly, 2000). Prior to the 1960s, researchers focused most of their attention on the cognitive theories and factors of students and their learning. In other words, research was more concerned with how students process information and retain it. Educators were focused on skill performance and learning procedures with understanding (Kilpatrick, Swafford, & Findell, 2001). In the 1960s, researchers began studying affective factors within cognitive theories. Such work can be traced back to the work of Schacter and Singer (McLeod, 1992). Cognitive psychologists, such as Lazarus (1982) and Mandler (1975) also included affect in their theories, and hypothesized how it might apply to the teaching and learning of mathematics (McLeod, 1992). Affective issues, such as beliefs, attitudes, and emotions, play a central role in mathematics learning and instruction (McLeod, 1992, p. 575). Emotions and attitudes, such as anxiety and frustration, and beliefs, such as self-efficacy and confidence, are all factors that play an important role in a mathematics classroom. McLeod (1992) noted three major components of the affective experience of mathematics students. These three components were: Students hold certain beliefs about mathematics and about themselves, Students will experience both positive and negative emotions as they learn mathematics, and Students will develop
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positive or negative attitudes toward mathematics (p. 578). If educators understand affective factors and the three previously stated components, they can help students to become better mathematics learners. Pintrich, Marx, and Boyle (1993), drawing on more general psychological studies, emphasized that a classroom learning community can contribute positively or negatively to students motivational beliefs and thus to conceptual change or learning. They created a conceptual framework that details how cognitive, motivational, and classroom factors can interact with one another to promote positive conceptual change. Classroom factors, such as teacher scaffolding and methods of evaluation, can contribute to a students involvement and success on a mathematical task. For example, if a classroom setting is created where there is a great deal of interaction occurring between both the students and the teacher, the students could have an increased chance of witnessing their peers struggle though more challenging mathematics. This is more likely to result in having a positive effect on the observers efficacy and learning (Pintrich, Marx, & Boyle, 1993, p. 187). Much more recently, the authors of the book, Adding It Up, identified five inter-related strands that contribute to students mathematics proficiency (Kilpatrick, Swafford, & Findell, 2001). These five strands include: conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently, and appropriately), strategic competence (ability to formulate, represent, and solve mathematical problems), adaptive reasoning (capacity for logical thought, reflection, explanation, and justification), and productive disposition (habitual inclination to see
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mathematics as sensible, useful, and worthwhile, coupled with the belief in diligence and ones own efficacy) (p. 116). The first four, conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning, are chiefly related to the cognitive domain. Productive disposition, on the other hand, can be classified under the affective domain. This strand focuses on students attitudes, beliefs, and motivation toward mathematics. Students with a productive disposition believe that mathematics is useful and worthwhile, that they can learn and complete mathematical tasks, and that effort in learning mathematics has benefits (Kilpatrick, Swafford, & Findell, 2001). By providing the student with opportunities to make sense of mathematics, encouraging them to contribute effort and perseverance in learning mathematics, and to believe that they can be an effective learner of mathematics by experiencing rewards of their efforts (Kilpatrick, Swafford, & Findell, 2001) will likely increase students sense of self-efficacy and therefore improve their academic success. Students disposition towards mathematics is related to their educational success, and teachers play a critical role in supporting students development of a productive disposition (Kilpatrick, Swafford, & Findell, 2001). It has been argued that failure to develop a productive disposition in early school years may have negative consequences for students once they get into high school and college. Such students may not choose to engage in more challenging mathematics courses (Kilpatrick, Swafford, & Findell, 2001). Students who enter high school disliking mathematics, tend to take only those mathematics courses required to graduate, and this can have an effect on their college performance and lead to enrollment in
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developmental courses. Researchers have identified mathematics as the subject most essential to students choice in determining a college major and ultimately to success in attaining a college degree (Hall & Ponton, 2005, p. 26). Therefore, developing a positive productive disposition and encountering teachers that foster such a disposition can be essential for a students mathematical success and endeavors. Acknowledgement of the role of affective factors, such as motivation, beliefs, and attitudes is reflected in research on mathematics education and developmental education. This chapter highlights previous research studies, especially those concerning the affective dimension, that have been influential to this studys theoretical perspective and research questions. The chapter will begin with a very brief overview of research involving developmental education and remedial mathematics courses. Studies involving self-efficacy, and related theories of attribution and self-regulation theory, will be explored in the theoretical framework, the second part of the chapter. A third section will discuss the instrument used in this study that analyzed some of the affective factors identified in the three theories. Finally, the last section will explore the role of discourse, faculty interaction, and caring within a classroom. The chapter will conclude by identifying how previous research influenced the present study.
Theoretical Framework Numerous studies have been performed on developmental education within both 2-year and 4-year postsecondary institutions. Studies range from investigations
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in remedial mathematics, reading, and writing classes, with comparisons between remedial and non-remedial college students (Hagedorn, Siadat, Fogel, Nora, & Pascarella, 1999; Young & Ley, 2001), supplemental instruction and its effectiveness (Wright, Wright, & Lamb, 2002), the impact of faculty (Penny & White, 1998; Wheland, Konet, & Butler, 2003), learning assistance centers and their role at the institution (Boylan, 1999; Casazza, 1999), and cooperative learning (Higbee & Thomas, 1999; Smittle, 2003). While all of these studies have important issues to reveal about developmental students and developmental education, only those few studies that pertain more specifically to this research study will be highlighted in this chapter. I will limit the studies reviewed to be those involving developmental mathematics students in a computer-based or lecture based course, and the impact and role of teachers within these settings. The findings from these studies are reported in the discussion of self-efficacy theory, attribution theory, and self-regulation theory. These studies will be categorized in the remaining sections of this chapter. The following section of this chapter details the theoretical frameworks as well as the relevant research that has been done in this area that served as a guide to this study. The theories that will be described are self-efficacy theory, attribution theory, and self-regulation theory. Although they are three separate theories, it will be apparent to the reader that they are not all independent of one another, as some concepts are common to several of these theories. Self- Efficacy Theory Self-efficacy, as defined by Bandura (1986), is an individuals personal beliefs about their abilities to perform a task. In mathematics, this could be a students
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confidence on solving a problem, succeeding in a specific mathematics course (e.g., calculus), or persistence when faced with a challenging task. Self-efficacy theory suggests that students will often appraise their own efficacy based on their performance as well as the performance of others (Schunk, 1991). According to Schunk (1991), observing similar peers perform a task conveys to observers that they too are capable of accomplishing it (p. 208). Therefore, observations of peer success and ones own success will raise ones efficacy and help develop a strong sense of self-efficacy, which will be resistant to occasional failures (Bandura, 1986). It is important to note that a high sense of efficacy will not result in a higher proficiency if there is a lack of skills and knowledge (Schunk, 1994, as cited in Young & Ley, 2001). Self-efficacy involves self-judgments of ones capabilities and, when researched, is assessed before a student is asked to perform a task (Hanlon & Schneider, 1999). Bandura (1993) believed that there are four major processes that are affected by self-efficacy beliefs. These four processes are: cognition, motivation, selection, and affective responses. Efficacy beliefs help determine the goals one might set for oneself, how much effort one will give to a certain activity, how long they will persevere if they confront a challenging task, and how resilient they are to failures (Bandura, 1993; Pajares, 1996). Researchers have found that persistence on mathematical tasks can significantly contribute to achievement (Miller, Green, Montalvo, Ravindran, & Nichols, 1996). Similarly, motivation, which has been identified as one of the most pervasive explanations for success or failure in academics (Kinney, Stottlemyer, Hatfield, & Robertson, 2004, p. 18), can be a threat
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to effort and persistence if it is too low, which can hinder success in mathematics (Kloosterman, 1997; Meyer, Turner, & Spencer, 1997). In an academic learning environment, initial self-efficacy varies depending on ones aptitude and past experiences. Factors such as goal setting, cognitive processing, and teacher feedback affect a student while they are working (Pintrich, 1994; Schunk, 1991). Self-efficacy researchers have argued that students need to have feedback on their progress and that when the feedback is positive, students will develop a greater sense of their ability in order to succeed at learning tasks (Wambach & Brothen, 2000). Positive teacher feedback has been shown to enhance selfefficacy, however, if the student was not successful on the performance, its effects are lessened (Young & Ley, 2001). Based on these factors, students will develop a sense of how they are performing, and if they are making progress, their sense of selfefficacy will heighten and thus lead to an improvement in their motivation (Schunk, 1991). Students who have a stronger sense of self-efficacy tend to participate more readily, give greater effort, and persist longer at tasks than those with low selfefficacy (Pajares, 1996; Young & Ley, 2001). Heightened self-efficacy sustains motivation and improves skill development (Schunk, 1991, p. 213). Students who believe they are capable at performing a task are more likely to exert more effort and use deeper thinking and studying strategies in order to process information (Pintrich, 1994; Schunk, 1996). Similarly Snow, Como, and Jackson (1996) note that selfefficacy is hypothesized to affect individuals activity choice and persistence along with amount of effort.
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Two other aspects of self-efficacy theory that influence academic motivation are students goal orientation and their sense of task value (Elliott & Dweck, 1988; Ray, Garavalia, & Murdock, 2003). Goal orientation describes a persons goals for learning in a specific context (Ray, Garavalia, & Murdock, 2003). There are two types of goal orientation: intrinsic and extrinsic. The first is intrinsic, or learning goal, orientation. Learning goals help students to focus on developing their ability over time and increasing their competence (Dweck & Leggett, 1988). Intrinsically motivated students engage in academic tasks because they enjoy them (Middleton & Spanias, 1999, p. 66), tend to be more confident, possess a positive affect, and are not defeated by failure (Elliott & Dweck, 1988; Middleton & Spanias, 1999). Failure might signal to them that the task may require more effort and ingenuity for mastery (Dweck & Leggett, 1988, p. 261). Dweck and Leggett (1988) found that, in general, students who adopted a learning goal orientation had a higher perception of their self-efficacy and had more success in their courses. The second goal orientation is referred to as extrinsic, or performance goals. Students with this type of goal orientation focus more on external rewards (e.g., grades), engage in academic tasks to avoid punishment (Middleton & Spanias, 1999), and are concerned with the extent of their ability. They tend to have a negative affect and succumb to failure (Elliott & Dweck, 1988; Ray, Garavalia, & Murdock, 2003). Therefore, a student with a lower sense of self-efficacy is likely to adopt a performance goal orientation. They are more likely to avoid challenging tasks that have a threat of failure (Dweck & Leggett, 1988). In a study of at-risk college
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students, Yaworski, Weber, and Ibrahim (2000) found that these students have behaviors that resembled a performance goal orientation. They tended to skip class, not complete assignments, and not take responsibility for their own learning. They believed that effort, perseverance, and good study habits were all related to academic success, they just chose not to engage in these behaviors. Task value is another aspect of motivation. Task value is defined as how one values the importance of the task (or course content), ones interest in the task, and how useful the task is perceived to be (Ray, Garavalia, & Murdock, 2003). According to Brophy (1999), students need to feel that the subject they are learning has a purpose and value for the future endeavors. Academic performance (Pintrich & Schrauben, 1992) and long term engagement in mathematics (Wigfield & Eccles, 1992) has been found to be correlated with task value. Developmental mathematics college students whose past academic achievement was low, might report low levels of interest and usefulness for mathematics tasks. This low task value could be detrimental to their future academic achievement. In a study conducted by Yaworski, Weber, and Ibrahim (2000), the researchers talked with developmental students in an attempt to assess why some students succeeded while others failed. One important finding was that low achieving students chose not to attend class or complete coursework because they had a lack of interest in their course. Therefore, they had low task value, which resulted in a decrease in their motivation and low academic achievement. Efficacy beliefs can also influence affective factors such as emotional attitudes and beliefs which influence achievement. A student with low self-efficacy
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will tend to have less confidence, more anxiety and stress, and avoid challenging tasks that they feel might lead to failure (Pajares, 1996; Schunk, 1991). According to Bandura (1993), people with a high self-efficacy attribute failure to insufficient effort or deficient knowledge and skills that are acquirable (p. 144). Research has found that a persons expectation of mathematics self-efficacy are positively correlated with mathematics ability, while being negatively correlated with mathematics anxiety (Fennema & Sherman, 1976). In other words, when a student has a positive sense of their self-efficacy, their mathematics ability will increase, therefore leading to an increase in mathematics performance. However, if a student has a low perception of their self-efficacy, the more anxious that student will become, which will hinder their mathematics achievement. Research has found significant differences between the self-efficacy of college students in credited courses compared to the students in developmental mathematics courses (Hall & Ponton, 2005). Teachers can influence the development of students efficacy especially in the developmental mathematics population. It has been suggested that teachers of developmental mathematics courses need to find a way to create a learning environment that helps foster self-efficacy, but at the same time keeps the course rigorous and comparable to other mathematics courses (Hall & Ponton, 2005). Teachers can create this environment by encouraging students to ask questions, giving students many opportunities for success, helping them to set goals for themselves, allowing them to observe the success and failure of their peers through interaction, and providing them with positive feedback (Hall & Ponton, 2005; Schunk, 1991).
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Self-efficacy theory suggests that students attitudes, beliefs about mathematics, motivation, goal orientation, and task value affects students efficacy which can influence mathematical achievement. Researchers also suggest that teachers play an influential role on fostering efficacy and improving student achievement and retention in mathematics. The treatment outlined in Chapter Three was intended to influence some aspects of developmental students self-efficacy beliefs. For example, the teacher worked with students to set short-term (weekly and semester) goals and understand students mathematical background. The teacher also provided each student with attention by giving them a progress report and some feedback at each class meeting. On the other hand, the treatment did not attempt to alter task value. The computer program used for all sections of the course provided students with explanations of why mathematical topics are important and how they can be used in life. Attribution Theory There are several theories that are related to self-efficacy theory, and one of them is attribution theory (Schunk, 1991). Attribution theory suggests that students possess attitudes and beliefs about the sources of their success or failures that affect their motivation and learning outcomes (Weiner, 1980). Since students attributions affect their motivation, attribution theory can be related to self-efficacy theory. For example, some students believe that their past performance has an influence on their future achievement. If a student has had multiple failures in past mathematics courses, they may feel that their future attempts at mathematical tasks will also lead to failure and thus be less motivated to work hard.
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Weiner (1980) had found that students tend to attribute their success or failure to their ability, effort, task difficulty, and luck. Therefore, he built off of the work of earlier researchers (e.g., Heider (1958), Rotter (1966), and Kelly (1967)) to propose a theory for the attribution of causation of success and failure. Weiners model proposed that the factors for success and failure exist on three different dimensions (Smith & Price, 1996): locus of control, stability, and controllability. The first dimension, locus of control, concerns the cause to which students assign blame or credit for their failure or success (Rotter, 1966). Pintrich (1994) argued that locus of control beliefs can be internal, external, or unknown. A student with an internal locus of control will credit or blame their success or failures on themselves. For instance, they might think they failed a test because they did not study enough. Conversely, a student with an external locus of control will credit or blame everything but themselves. They might say they failed a course because they had a poor teacher. Lastly, students that cannot say who or what is responsible for their success or failure have an unknown locus of control. Students who do not distinguish between their behavior and the outcomes are often labeled as evidencing learned helplessness. Learned helplessness is defined as a stable pattern of attributing many events to uncontrollable causes (Pintrich, 1994, p. 29). These students experience anxiety, lack of effort, lower achievement, and feel that no matter how hard they try, they will always fail (Dweck & Reppucci, 1973; Kloosterman, 1984; Pintrich, 1994). Researchers (Pascarella, Edison, Hagedorn, Nora, & Terenzini, 1996) have found that first year college students who have an internal locus of control have higher academic success and more motivation. These students
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feel that they are in control of their learning, and that their effort will lead to more success (Moore, 2007). The second dimension of Weiners (1980) model is stability. A student who attributes a success or failure to a stable factor, such as ability, will then have the same expectations for their future endeavors as they did the past ones. According to Middleton and Spanias (1999), by the time they reach college, students generally have formed stable attributions regarding their successes in mathematics (p. 70). Ability is considered an internal and uncontrollable cause. On the other hand, a student who attributes successes or failures to unstable factors, such as effort, will more easily change their expectations (Smith & Price, 1996). In order to increase academic success, teachers need to help students to stop blaming their failure on their internalized lack of ability (Weiner, 1980). Lastly, the third dimension is controllability. Controllability is whether a situation or action is in your control or not. According to Smith and Price (1996), of all of causal attributions, the only one completely under our control is effort (p. 2). Therefore, students need to associate failure with a lack of effort (Weiner, 1980). Researchers believe that attribution theory has implications for developmental education (Kloosterman, 1984; Smith & Price, 1996). Attribution theory researchers have described some of the ways locus of control, stability, and controllability play into developmental students failures. The first thing they noted was that developmental students typically have an external locus of control which can be linked to a passive learning style (Smith & Price, 1996). A student with a passive learning style does not take an active part in their learning. In a typical mathematics
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class, a passive student would simply take notes on what the teacher writes on the board and tries to restate that information on homework and exams. Not much more thought goes into learning the material and how it relates to previously taught concepts. Some (Smith & Price, 1996) speculate that passive students attribute their failure to external causes so that they can keep a positive self-perception. Developmental educators may be able to impact a students sense of control by helping them to assume responsibility for their learning (Mercer, 1991). Such students need to accept the fact that some teachers are better than others or that one textbook might have more examples and clearer explanations than others, but that these things cannot be the sole determinant of their success or failure. The student has to take control of their learning situation and motivate themselves to succeed no matter what obstacles they face. In a study conducted on students enrolled in a developmental program, the researchers found that this student population tended to blame their past high school failures on external factors. These factors included the difficulty of tasks, luck, the amount of work assigned, and the quality of their teachers (Smith & Price, 1996). Therefore, these students were not willing to accept responsibility for their past failures. Researchers have also found that developmental students attribute outcomes to stable factors as well as noncontrollable factors (Smith & Price, 1996). Again, developmental educators need to enable students to become aware and reflect on their actions and how it relates to their success or failure (Mercer, 1991), since it has been claimed that some students lack the ability to identify factors that limit their success (Hall & Ponton, 2005, p. 26). A students perception of why they succeeded or failed
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at a task can be a prediction as to how they will do on future tasks (Kloosterman, 1984). As stated previously, the only thing completely in ones control is effort. Educators need to help students understand the role of effort in their successes and failures (Smith & Price, 1996, p. 4). It has been found that students who exert a high degree of effort will have more success than students that do not (Kloosterman, 1984). Although developmental students frequently share similar characteristics, teachers must always remember that each student is unique. That is why educators should take the time to also get to know their students individually so that they know which students require a little more motivation and attention (Merisotis & Phipps, 2000). Developmental educators need to have effective teaching strategies as well as effective support services (Penny & White, 1998). In order to understand the participants involved in this study, the researcher conducted individual interviews that provided insight into the students mathematical background, including their likes and dislikes of their mathematical experiences, their motivation toward the subject, and on their short and long-term goals. Self-Regulation Self-regulation theory is another theory that is closely related to self-efficacy theory, as well as attribution theory. Self-regulated learning refers to the metacognitive, motivational, and behavioral processes a student uses when they attempt to monitor and regulate their own constructive learning process (Zimmerman, 1986). It is related to self-efficacy theory and attribution theory in that it addresses the degree of motivation a student will afford to monitoring and changing their behavior
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in order to achieve academic success. In order to attain their personal learning goals, a student will self-generate feelings, thoughts, and actions to be able to achieve their goals (Kinney, 2001; Zimmerman, 2001). A self-regulated learner is one who will analyze and set attainable goals for specific tasks, monitor and control their progress during the activity, and assess their progress and change their behavior depending on this assessment (Pape, 2002). Effective self-regulation has been said to depend on students developing a sense of self-efficacy for learning and performing well (Schunk, 1996, p. 5). Although there are many models for self-regulated learning, there are some basic assumptions that appear throughout the various models. Pintrich (2000) created a framework containing four common assumptions. The first assumption he called the active, constructive assumption (p. 452). This assumption views all learners as active, not passive recipients of information, who are constructive participants in their own learning process (Pintrich, 2000; Pintrich & Schrauben, 1992). The individual student sets their own goals and strategies from both their internal and external environment. The second assumption concerns the potential for control (Pintrich, 2000). Many models of self-regulation suggest that learners have the ability to monitor, control, and regulate certain features of their own cognition, motivation, behavior, and even their environments (Schunk, 1996; Zimmerman, 2001). There are biological, developmental, contextual, and individual difference constraints that can interfere with individual efforts of regulation (Wambach & Brothen, 2000).
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A third common assumption is the goal, criterion, or standard assumption (Pintrich, 2000, p. 452). All regulation models assume that there is some type of standard to which a student compares their present performances (Pintrich, 2000; Schunk, 1996). Students assess their performance against these criteria to determine whether if any modifications should be made in their learning. Individuals set goals, examine their progress, and modify and regulate their cognition, motivation, and behavior in order to achieve these set goals. Learning goals also allow students to focus their attention on the processes and strategies they have to endure in order to obtain their competencies (Schunk, 1996). The last assumption that most regulation models assume is that selfregulatory activities are mediators between a students personal and contextual characteristics and actual achievement or performance (Pintrich, 2000, p. 453). In other words, students self-regulation of their behavior, motivation, and cognition mediates the relationships between themselves, their environment, and their over-all achievement. Researchers (Wambach & Brothen, 2000) suggested that students who are self-regulating have more of an ability to identify areas in which their skills are weak and try to find the ways in which they can improve them. Self-regulating students also have the ability to observe aspects of their behavior and judge them against the goals in which they have set for themselves. This will then allow the students to react in a positive or negative way (Schunk, 1996). Pintrich and De Groot (1990) found that in seventh graders, goal orientation and task value were strongly related to selfregulation. They found that a student who possessed an intrinsic goal orientation and
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believed their school work was interesting were more cognitively engaged, persisted in their efforts, and were more likely to be self-regulating. Self-regulating students take responsibility for their own learning by seeking feedback on their performances, monitoring their successes and failures, predict their level of math skill, and utilize support systems when necessary (Kinney, 2001; Schoenfeld, 1987). Garcia and Pintrich (1994) found self-regulatory strategies to be closely tied with self-efficacy and attributions. They noted that lower achieving students found themselves on many occasions feeling helpless when trying to motivate themselves to regulate their academic behavior. Similarly, Zimmerman (1990) observed that self-regulated learners tended to exhibit a high degree of effort and persistence during learning, and that they reported higher self-efficacy, selfattributions, and intrinsic motivation. Finally, students who found value in the mathematical tasks they were performing, tended to become self-regulating (Miller et al., 1996). In order to help students development of self-regulation, the teacher of the treatment sections in this study modeled and enforced ideas such as goal setting, progress review, and seeking feedback with each student. It was the intent of the teacher to improve motivation, and help students become more active and responsible learners, which would have an impact on their over-all mathematics achievement and attitudes towards the subject.
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Instrumentation One of the goals of this study was to assess the impact of a treatment on students self-efficacy. The instrument that was used to assess students self-efficacy both prior to and after the treatment, was a modified version of the Fennema-Sherman Mathematics Attitudes Scale (Fennema & Sherman, 1976). Other instruments were considered for this study, however, the Fennema-Sherman was chosen because of its popularity in mathematics education research over the last 30 years (Tapia & Marsh, 2004) and because it can be answered by college-level students. For the current study, the survey was modified to gather information on five of the nine dimensions of the original instrument. The first dimension is the Attitude toward Success in Mathematics. This dimension measures the extent to which students anticipated negative or positive consequences resulting from success in mathematics. The second dimension, Confidence in Learning Mathematics, measures students confidence in one's ability to learn and be successful in mathematics. The third dimension, Effectance Motivation, measures how much students range from lack of involvement to active participation and seeking a challenge within mathematics. The fourth dimension measured on the survey is Mathematics Usefulness. This category measures students perceptions of their current and future mathematics and how useful they feel it will be in their lives. It can be argued that these dimensions are all related to self-efficacy theory, and are also influenced by attribution and selfregulation theory. As previously mentioned, self-efficacy is related to a persons confidence to perform a task (Bandura, 1986) and how resilient a person can be when confronted with obstacles or adverse situations (Pajares, 1996). Therefore, a
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students motivation to persist in difficult situations can be affected by the students level of confidence and their perception on how useful a task will be to their life. Thus, a student with low confidence, or the view that learning mathematics will have no effect on their future, could cause them to have less motivation toward achieving a goal. The fifth and final dimension measured by the Fennema-Sherman Mathematics Attitudes Scale is the Teacher Scale. These questions are intended to measure students perceptions of their teachers attitudes towards them as learners of mathematics, and includes areas such as teachers interest, encouragement, and confidence in students abilities (Fennema & Sherman, 1976). Both the domain of mother and father, as well as Mathematics as a Male Domain were omitted since they were not central to the questions intended to be investigated in this study.
The Influence of a Teacher Learning theorists and researchers have suggested that a students experience in a classroom can be one of the most important factors affecting that students growth and success (Volkwein & Cabrera, 1998). In a computer-mediated environment, teachers play a small role in the students cognitive learning since the software is the primary source of instruction. Therefore, teachers of these courses can vary considerably as to the amount of attention and support they provide their students. According to Kinney, Stottlemyer, Hatfield, and Robertson (2004), the teachers role in a computer-mediated class is to develop a course structure that promotes student success, to provide feedback to students regarding their
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understanding of the course content and progress in the class, and to provide individual or small group assistance as requested (p. 15). Researchers have found that a computer-based classroom with no teacher interaction during the learning process has been found to be less effective than computer-based classrooms where teacher interaction is a critical part of the course (Hasselbring, 1986). Therefore, the way teachers approach and interact with their students could be considered a critical element of the classroom environment, especially if it is a computer-based environment. As previously stated, the development of a productive disposition is a major factor in determining students mathematical success. A productive disposition requires a student to view mathematics as useful, to believe that effort and perseverance can pay off, and to believe that one can learn and perform mathematical tasks (Kilpatrick, Swafford, & Findell, 2001). Teachers may provide structure, encouragement, and motivate students to keep a positive attitude toward mathematics in their classroom. Teachers who are encouraging, patient, and supportive can help students feel less anxious and have positive attributions with mathematics (Middleton & Spanias, 1999). With encouragement comes the notion of care. According to Noddings (2001), the word caring can refer to an attitude or can describe a relationship. One can show that they care by encouragement, being attentive, receptive, and by showing support. Therefore a teacher that listens to his/her students, respects their interests, and shares their own wisdom with their students is thought to be a caring teacher (Noddings, 2001). Caring is not just an attitude. It is wanting what it best for your
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students and recognizing poor behavior and low achievement and conveying that message to the person (persons) you are caring for (Noddings, 2001). A caring teacher could convey this message by establishing clear and realistic expectations, and by getting to know their students on an individual basis so that they can assess where they are in their learning (Lumpkin, 2007). Noddings (2001) idea of caring is the main focus of this study. It is the intent of the investigator to try to create a warm, supportive, friendly, and safe environment to help foster student growth and achievement. It is the hope of the investigator that this caring and interactive environment will create positive attitudes, increase motivation, and show a significant increase in students asking for assistance and positive attributions toward mathematics in general. In order to establish the idea of caring, it is important that the teacher learn what each students individual attributions are, since developmental students often have more failures and negative feelings toward mathematics in their past than nondevelopmental college students (Higbee & Thomas, 1999; Ma & Kishor, 1997). Chapter Three outlines the methodology of this study and one aspect of the study was to interview some of the students individually and obtain an over-all sense of their feelings towards mathematics. Once the teacher can show this initial response of caring through an individual interview, this notion of caring can be carried through the rest of the semester. Giving positive feedback, motivating students, and setting personal goals, are teacher behaviors that might enhance students self-efficacy, allow students to have more positive and internal attributions, and develop the use of selfregulation.
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CHAPTER THREE: METHODOLOGY
The overall purpose of this study was to explore the effects of enhancing computer-based developmental mathematics classes with teacher initiated practices that provide a more caring and supportive experience for students. A quantitative experimental design was used to compare the effects of several specific instructional interventions on students achievement and self-efficacy in mathematics. These comparisons were analyzed in two ways: comparing pre- and post- mathematics test scores, and comparing responses to a survey of student attitudes and beliefs that was administered at both the beginning and the end of the semester Three sections of a developmental algebra course were assigned to a treatment involving monitoring, structure, feedback, and enhanced interaction, while the other three sections received the standard structure of the course, which did not involve regular daily check-ins, due-dates on homework, or one-on-one sessions with the teacher. The researcher was the teacher of record for all six sections. The data collected over a period of one semester included mathematics placement test scores, final test scores, two sets of responses on one attitude survey, and twelve sets of observation data on the amount and type of interaction that occurred in each class. The research setting, participants, and procedures are described in the first section of this chapter, while the data sources and data analysis are explained in the second half of the chapter.
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Setting and Participants The study took place in a computerized developmental mathematics course at a large university in the mid-Atlantic region. All of the participants involved in the study placed into this remedial mathematics course. The mathematics department at the university assigned students to this course based on their score on a mathematics placement test. The students who did not score well enough on the placement test for enrollment in a credited mathematics course were instructed to register for this developmental course. Slightly more than 96% of the students involved in this study took the placement test before the semester began. Almost all of the remaining enrollees were students whose self-assessment was that they would test into this course given the number of years that had passed since their last mathematics class. University policy specified that students who elect not to take the placement test be placed in this developmental course. Students chose which section of the course they wanted to enroll, based on their semester schedule. The students had no prior knowledge of the instructor teaching their class, unless they registered within a week of the beginning of the semester. In this particular semester, over 87% of the students involved in this study registered for their mathematics course prior to the date on which instructors names were released. Total enrollment for all sections of this course was 357 students. The enrollment of the six study sections was 129, where 72 were assigned to the treatment classes and 57 were assigned to the control classes. Only two students in the treatment and five students in the control classes declined participation in the study.
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The students enrolled in this course can be classified as a heterogeneous mix when considering their gender, age, class standing, race, and major. The student demographics of the study population as well as the other course population are summarized in the following table: Table 1: Student Demographic Information Other Population N = 204
Study Population Treatment group N = 70 Control group N = 52 28.8% 71.2%
Gender Male Female Class Standing Freshmen Sophomore Junior Senior Age Under 18 18-20 21-23 24+ Race/Ethnicity African American Asian Caucasian Other Latino Puerto Rican Other Foreigna Other Information Native Student Transfer Student Repeating the Course
a
38.7% 61.3%
40.0% 60.0%
76.0% 16.7% 6.8% 0.5%
55.7% 25.7% 11.4% 7.2%
46.1% 28.9% 23.1% 1.9%
5.9% 75.5% 9.3% 9.3%
2.9% 72.8% 10.0% 14.3%
1.9% 65.4% 23.1% 9.6%
39.7% 1.5% 30.9% 7.8% 2.5% 3.4% 14.2%
38.6% 4.3% 35.7% 4.3% 1.4% 1.4% 14.3%
44.2% 5.8% 34.6% 5.8% 1.9% 1.9% 5.8%
60.8% 39.2% 8.3%b
52.9% 47.1% 12.7%
44.2% 55.8% 5.36%
b
Students in this category responded to two or more races 11.7% did not respond
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At the beginning of the semester, each student was assigned to one of four instructional modules. Depending on their major, the students can prepare for one of the following credited courses: Elementary Mathematical Models, College Algebra with Applications, Introduction to Probability, or Pre-calculus. The credited course for which they are preparing determined their module. The modules were ranked in the given order to reflect the increasing number of needed skills and understandings and thus facilitate advising. In other words, if students prepare for an Introduction to Probability module and change their major to one that only requires the completion of College Algebra with Applications, those students can move down into that class since the College Algebra module is considered less demanding. However, if students prepare with the College Algebra module and later determine that they are required to take Introduction to Probability for their major, those students are not permitted to move up to that class unless they complete the Introduction to Probability module. The distribution of students enrolled in each module in each section of the course in shown in Appendix A. Three of the participating sections, each populated by approximately 15 students, met in one computer lab, while the other three sections, each populated by approximately 30 students, met in a different computer lab. The class length was one hour and fifty minutes, and all sections met three times per week. The six sections involved in the study met during one of three time periods, 10-11:50 am, 12-1:50 pm, or 2-3:50 pm, with two sections of the course meeting at the same time. Within each time period, one of the two sections was randomly assigned to the treatment group and the other to the control group. The instructor (in this case the investigator) spent
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half of the class time with one class and then traveled to the other section where she spent the second half of the class period with the other group of students in the other section. Each participating section had its own teaching assistant (TA) present for the entire class period so assistance was always available even during the time the instructor was not present. The six teaching assistants included five undergraduates and one graduate student. Most of the teaching assistants were mathematics or mathematics education majors, however all were given the position since they had successfully completed at least two semesters of calculus and possessed good communication skills. Only two of the six teaching assistants were new to the course. The others had been teaching assistants in the course for more than two semesters. The TAs and I had an opportunity to meet as a group prior to the first day of class. This meeting gave me the opportunity to give them the background and details of the study. The meeting was also the time for me to explain their role in the study and to get a sense of how they felt about participating in it. All of the TAs were interested in the study and agreed to their assigned roles. Their roles will be discussed in greater detail later in this chapter. Computer Program and Class Policies The Lifetime Library computer program was used in all classes (Liafail, Inc., 2006). The topics ranged from basic mathematics (e.g., addition and subtraction) to concepts and skills of intermediate algebra. The computer lab was only open to students taking this particular mathematics course, so no other students from the University were permitted in the lab. The computers were equipped with only the
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Lifetime Library program, so that the use of the internet or other word processing programs was not a distracter for the students. All but one of the students in the study followed the regular progression of topics in the course elementary algebra through intermediate algebra. The one exception, a student who had a very limited mathematics background and struggled with the subject, followed the instructors advice and started with the pre-algebra section of the computer program. The computer program has instructional material organized into chapters. The students were provided with a module guide for all of the chapters they were required to master in order to complete the course. Modules contained anywhere from 41 to 57 different chapters. Each chapter included instruction, both in writing and with video segments, as well as interactive questions that provided the student with feedback as soon as a solution was entered. After a student finished a chapter, there were 10 practice problems from the chapter material that the students were required to complete before moving on to the next chapter. A student needed to obtain a score of 80% or higher in order to move on to the next chapter. If the student scored less than an 80%, they need to revisit the chapter and re-take the practice problems. There was one exception to this class standard. Some students in the class were preparing for a theoretical pre-calculus course and they were required to score 90% or higher on the computer exercises in order to progress. The computer provided the student with solutions to the practice problems so they could assess where they made their errors. After a student finished the material in what the program defined as a book (usually four chapters), and all of the associated practice problems, a book final test was given
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(five questions per chapter). The instructors focused most of their attention on monitoring the completion of book final tests, since the computer did not provide the students with hints or solutions in these tests. The instructors had access to computer records that detailed how long students spent on a test and how many times they took a test. If a student spent an extremely long amount of time on the book final test, or repeated it multiple times, an instructor would typically instruct the student to spend more time within the lessons and practice problems. Poor performance on a book final test was usually an indication that a student was not going through the program in the way that was intended. The students were required to purchase a course workbook at the beginning of the semester. The course workbook contained homework exercises, approximately 10 supplemental lessons, suggestions on study skills, and review sheets for the three written exams. All the sections of this course used the same workbook. The workbook was written to follow the computer program. Students were encouraged to complete the homework exercises corresponding to the chapters they completed during their lab time. All students must have all of the required homework completed and turned in before they were permitted to take one of the three written pencil and paper exams for each module. The module guide that the students referred to everyday indicated when a student was ready, or eligible, to take a written exam. There were three intermediate written exams throughout the semester that had to be completed before a student was eligible to take the course final exam. The grading system for all sections of this course was S (satisfactory) or F (fail). If a student completed the class with a 70% average or better, they were given
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an S for satisfactory and were granted eligibility into the credited mathematics course for which they were preparing. Final computation of grades was based on completion of all required chapters and practice tests on the computer (10%), class attendance (5%), homework completion (10%), scores on three written exams (45%), the score on a pre-final test, which was an older version of the university placement test (5%), and the score on a final written exam (25%). The class was self-paced, so some students finished the course prior to the end of the semester. After a student had completed all required computer lessons, homework, and written exams, the student was eligible to take the final exam. The students did not have to wait until the official university final exam date at the end of the semester. In fact, students were permitted to take the course final exam as early as five weeks into the semester. Other students may need to enroll in the course for multiple semesters.
Procedures Pilot studies conducted over two semesters, one in a fall semester and one in the spring, preceding the main study, helped shape the research procedures described below. It was important to conduct a pilot study in both fall and spring semesters since it has been observed that the number of students and background of the students are significantly different from one semester to the next. The studies revealed promising results. In both semesters that the pilot studies were conducted, the success rate of completing the developmental course in the treatment groups was higher than the control groups. In the spring semester pilot, it was also observed that
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the attendance rate of the treatment group at the end of the semester was more than 20% higher than that of the control group. Additional insights attained from the two pilot studies are noted in the remaining sections of this chapter and also detailed in Appendix B. The pilot findings helped shape the final procedures and the data sources that are described below. Treatment Group Within each time period, one of the two sections was randomly assigned to the treatment group and the other to the control group. For example, there were two 1011:50 am sections, a treatment group that met in one lab and the second, a control group, that met in another lab. Thus, each of the three time periods had a randomly assigned treatment group and control group. The principal difference between the treatment and control instructional approaches was the extent to which the instructor and the teaching assistants initiated contact with students. The purpose of the contact was to evidence interest in the students and help structure the pacing of their by work checking on their daily and over-all progress on the computer-based materials and homework, providing encouragement, monitoring attendance, and giving specific instructional assistance and feedback beyond that which the computer program provided. All of this additional attention and structure was an attempt to enhance the students sense of self-efficacy, foster high achievement, and help model how one might self-regulate. In the treatment sections, I attempted to create a warm and personally supportive environment in numerous ways. For example, I began the personal touch treatment early in the semester by interviewing each individual student. The
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interviews provided me with the opportunity to get to know each students mathematics background and helped me to identify any students who might need more attention than others. The interview questions (Appendix C) consisted of background information such as the types of mathematics courses previously taken and their degree of success in those courses. These questions allowed me to get an over-all impression of the students attribution and sense of self-efficacy in relation to mathematics. Each initial interview lasted approximately 5-10 minutes, depending on how much the student was willing to share with me. The students in the treatment group also received individual attention during each class period. I made sure to check-in with each individual student each day regardless of whether I was present for the first or second half of the class. In each encounter I asked how everything was going, checked their progress, gave positive feedback to those who were on track, and provided encouragement and suggestions to those who were falling behind. I also asked each student if they had any questions regarding the material they were learning or had previously learned. It has been my experience in this course that students tend to ask questions more readily when they are prompted by the instructor. Attendance was closely monitored within the treatment groups. If a student had missed two class days without giving me prior notice of their absence, I sent an email to the student to inquire about the absence. The e-mail provided me with the opportunity to let the student know that their absence did not go unnoticed and that attendance in the course was critical in order for them to complete the computer work and exams in one semester.
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In one of the pilot studies performed, only four times out of a total of 14 email contacts made after absences did a treatment student not return to class the next day or contact me after an e-mail was sent to them regarding their missed classes. This result made me realize that e-mail contact was an efficient and effective way of letting the student know that I cared about their performance, and similar observations were reported in a study by Jacobson (2005). The participants of the treatment group were also required to review each days progress with the teaching assistant or me before leaving the classroom. This gave us the opportunity to monitor the individual students progress and give a small amount of feedback to them as they left for the day. In this review, each student was given an appropriate homework assignment and reminded of any homework due dates. This check-out routine was carried out to reflect Smittles (2003) belief that developmental students need to know exactly what is expected of them and when it is due (p. 11). The guideline for assigning homework was once the student had completed the computer lessons for a book, the student had two class days to turn in the homework required for that book (a book of homework usually covered four chapters of material). If a student was struggling with a homework assignment and asked questions about it, I gave them the option of an extension until the next class period so that they could have more time to work on it. An extension was only given if the student approached us with their questions. I did not announce to the class at any time during the semester that an extension could be received. This was to benefit only the students who were working diligently on their homework, not to reward someone who simply did not do it. In general, all sections of the course required
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students to hand in all homework before they take a written exam; however, in all non-treatment sections, no due dates were given. The assignment of due dates was an attempt to provide the students with structure and give the students an opportunity to self-regulate their learning by developing the skill of pacing their work (Smittle, 2003). This same idea was used in the pilot treatment sections. In the pilot studies I gave the treatment students due dates, but did not give the control students such dates. I observed that the students who did not receive due dates, procrastinated, and turned in their homework at the very last opportunity. This resulted in more unanswered questions and lower homework averages than those of the treatment students. I provided four mini-lectures to the treatment group students on topics that experience has shown to be particularly troublesome. Each mini-lecture was presented at that point in the semester when most students had studied the material prior to the lecture so they had some exposure to the topic. These mini-lectures lasted approximately 20 minutes and were held at the chalkboard in each lab. The students were encouraged to bring questions and work through some problems with the instructor. The instructor would usually present a short 10 minute presentation on the topic while working through a problem or two. Students were then given an opportunity to work on a problem or two on their own. The students were allowed to interact with one another and shared their solutions as a group. All students had these mini-lectures lessons typed up in their course workbook. The students in the treatment group were able to view the supplemental instruction in their books as well as at the board with the instructor.
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Students were seated at a computer in a section along with students assigned to the same module. On the second day of class, seats were assigned so that those students who were placed in the same module were seated close to one another. It was the hope of the teacher that students working within the same module would interact with one another if they were seated in the same area. Some students did sit in that same area of the computer lab throughout the semester, while others moved into other areas. The seating assignment was not enforced. The students in the treatment group had the opportunity to review their written exams with me on an individual basis. Self-efficacy theory suggests that students need feedback on their learning progress and when feedback is positive, this can result in an increased sense of their ability to master learning tasks (Bandura, 1997). Since developmental students tend to doubt their skills and have a lower self-efficacy, giving immediate feedback is essential for this population (Smittle, 2003). In this review I was able to describe in detail where the student errors occurred and suggested some ways to improve their knowledge on the particular topic before they took the course final exam. The individual sessions provided me with another opportunity to discuss the students progress in the course, explore the students study habits, and give suggestions on some strategies that might be helpful to improve (if necessary). Each test review lasted approximately 5-10 minutes. The pilot studies provided me with guidance for this study. I learned that tracking interactions with over 100 students can be quite overwhelming, so I needed to keep a record of the interactions I had with each student. These records allowed me to keep track of which students had taken tests and if they did or did not review
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their test. Not all students requested the results of their exams, so for the treatment participants in particular, I had to be careful to track them down and discuss their results with them. Finally, the students in the treatment groups received feedback on their prefinal exam. Before the student took the course final exam, I sent the student an e-mail listing any topics that the student showed weakness on in the pre-final exam. This email gave the student an over-all sense of how prepared they were for the final. The role of a TA assigned to a treatment section was to mimic the strategies the instructor used. They were encouraged to initiate any kind-of contact, whether math related or not, and also instructed to maintain an open and friendly environment as much as they could. I also asked the treatment group TAs to keep me informed on any students who were struggling when I was not in the classroom. We usually had a brief meeting before or after each class to discuss any issues that were occurring in the classroom. Control Group The students in the control groups were expected to rely more heavily on the computer instruction, unless assistance from myself or the TA was requested. There were no attempts to be cold or unfriendly in any of these sections. The TAs for these groups had explicit instructions not to be unpleasant in any way. However, we did not make an effort to initiate substantive personal or academic interaction with the students beyond those the students specifically requested or were required. The TAs of a control class were instructed to walk around the classroom in order to be seen without making initial contact with the students. If a student were to ask the TA a
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question, the TA was to help the student in any way possible. The control students were responsible for initiating all contact in the class. If the student asked for assistance on a problem, we were fully responsive as requested. No student was ever denied assistance. The syllabus given out to all students on the first day of class contained my email address and the projected dates for written tests. All students were encouraged to contact me if they had to miss a class and to keep the written test dates in mind in order to complete the course within one semester. On occasion, a broadcast was sent out to the students through their computers to remind them of the upcoming test dates outlined in their syllabus. The students in this group were not interviewed individually, I simply had them fill out the standard class questionnaire. A daily check-in was not performed every day, as opposed to the treatment group. Most days I would walk around the classroom and observe which book they were working on. Only when the students were close to taking a written exam would I ask them when they intended on setting up the exam date and inquire about the amount of homework they had completed. This was the only time I initiated contact with the individual student. The students absences and tardiness were documented, but I never approached any of the students regarding any failure to attend class. The students were not contacted by e-mail about their attendance. However, if a student did contact me with a reason for an absence, this was recorded. The students were allowed to leave the class without checking out with me and showing me their days progress. I, or the TA, was always available to answer
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any questions as they left the room, but we made sure not to approach the students about their days work. They were also not given due dates for their homework. They were occasionally reminded that all homework must be turned in before a written exam and they were also reminded that they could not turn in an excessive amount of homework to the TA at one time. These groups did not have any mini-lectures during class. Every lecture that I provided to the treatment participants was written up in their course workbook. A reminder was announced several times during the semester to read the supplemental material provided in their homework book, for it might provide more insight on or a different approach to the more difficult concepts. Following the completion of a written exam, I worked out, directly on the exam paper, the questions the student had missed and allowed the student to see their errors. I did not discuss any details of the exam one-on-one unless the student asked a specific question about their errors or the corrections I had made. I also did not provide feedback on the pre-final exam unless a student asked me specifically about their results. For the majority of the students, I simply told them whether they showed improvement or not from the beginning of the semester. If the students had any more specific questions, I was more than happy to answer them.
Data Sources The pilot studies, conducted over two previous semesters, provided information about the need for additional data. The main purpose for piloting this study was to perfect the research methodology and to become aware of any
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difficulties that may arise. I learned several things from these two pilots. The most important thing I learned was the need for outside observers to come in and document any interaction that was occurring within the classroom, especially during the time I was not present. This helped for three reasons; first, it allowed me to see how much interaction was taking place. When I kept a tally of my own interactions during class (in the pilot studies), I would sometimes forget to jot down when a student asked me a question because I was so involved with the students, not thinking about the checksheet I had in my hands. Second, an outside observer was able to witness the types of interactions that were occurring. It allowed me to expand on the observer checklist (Appendix D). Finally, having an observer in my class provided feedback on my behavior as well as my TAs behavior. If the observer witnessed me initiating a great deal of interaction with my control group (or my TA), I was able to address that issue. Therefore, the first data source, observations, was to help monitor the implementation of the intended treatments. The observer checklist (Appendix D) was completed once a week over the course of the semester (for 12 of the 15 weeks) by one of three graduate research students. They observed a randomly chosen class (from among the six) for the entire duration, and kept a tally on how much interaction was involved in a specific category while I was present and while the TA was on their own. An observer recorded a tally when a student or I initiated contact. If a student or I asked multiple questions in one encounter, this was still recorded as one tally or one interaction. The observers had no contact with any of the students, they just recorded the behaviors they witnessed. The purpose of collecting this data was to help in checking the
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fidelity of implementation for the treatment, to record the amount of interaction happening in each of the classes, and to also control for TA interaction. A second data source was the students university mathematics placement test scores (generally taken before a students initial semester on campus). A students placement scores were obtained from the mathematics department once written permission was granted by the student. These placement test scores were collected in order to be compared to the pre-final exam scores, which was the third data source. The pre-final exam was merely a parallel form of the placement test, so pre- and posttest scores were comparable. The fourth data source was the student background information sheet (Appendix E). This data provided by the students on the first day of class allowed me to make comparisons within and among groups in terms of gender, race, major, math background, and class standing. I was also able to use this information to find out if a student was repeating the course or not and if they were a native student to the university. The fifth and sixth data source came from a modified version of the FennemaSherman Mathematics Attitude Survey (Appendix F) that students were asked to fill out at the beginning of the semester and once again at the end of the semester. The survey was modified to gather information on five of the nine dimensions of the original instrument. As previously mentioned in Chapter Two, the dimensions being measured in this study included the following scales: Attitude toward Success in Mathematics, Confidence in Learning Mathematics,
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Effectance Motivation, Mathematics Usefulness, and Teacher Scale. The survey was given once at the beginning of the semester and then again at the end of the semester (or when a student finished the course). The survey allowed me to explore which aspects of student attitude were affected differently by the treatment and control instructional scheme. To summarize, I have outlined the previous section in Table 2.
Table 2: Purposes of Data Sources Data Source Purpose Instructor/Student To measure the amount and types of interaction Interaction Check-list occurring between the treatment and control groups Placement Test Scores Pre-Final Exam To measure initial student achievement A parallel from the Placement Test given to measure achievement when the student had completed their required module and written exams. To document the demographics and mathematics background of the students in my sections To measure students self-efficacy at the beginning of the course and when the student has completed their required module and written exams. (Note: The end of the course survey contained six additional questions, and one open-ended question pertaining to the different aspects of this course to get an understanding of their feelings toward the teacher and class in this particular semester.)
Student Background Information Fennema-Sherman Attitude Survey
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Data Analysis The graduate research students came to the computer lab to make observations once per week over a twelve week period. The observations were intended to serve two purposes. First, the observers feedback afforded me the opportunity to check in on both my TAs, and my interaction. If an observation revealed that I was being too interactive with my control group, it allowed me to adjust my involvement. Likewise, if a TA was not providing enough interaction in a treatment group, or if a TA was initiating too much interaction in a control group, this weekly check allowed me the opportunity to consult with the TA. Second, the observations intended to document the activity being produced by the students. The observations showed that there was a clear distinction between the two treatments that were given to the participants of the study. The second and third data sources analyzed were the students pre- and postplacement test scores. The scores were analyzed using a repeated measure ANOVA design using a treatment and control factor. The design is mixed in that it has one between-subject factor (treatment vs. control) and one within-subject (or repeated measure) factor (pre-test vs. post-test). This analysis allowed me to compare the achievement gained between each group as well as observe any interactions in the pre- and post-test scores within the treatment and control groups. The scores were also analyzed taking a students module into consideration to determine whether any significant differences occurred between the two groups because of the differences in module representation. By introducing module, this created a mixed design with two between-subject factors along with the same one within-subject factor.
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The remaining data sources came from the responses on the modified version of the Fennema-Sherman survey. A test of reliability for the instrument was performed using a Pearson correlation. The survey reliability resulted with Pearson correlation of 0.599, which is significant at the 0.01 level. The survey was coded from -2 (strongly disagree) to 2 (strongly agree). Since some of the items were negatively worded, for example, Math is not important in my life, the values of these items were negated so that if a student answered strongly disagree which would normally receive a value of -2, this was negated to a +2. This way, when the results were analyzed, the answers had consistency. A mixed, repeated measure design was also conducted on this data. First the data was separated into the five dimensions (attitude, confidence, motivation, usefulness, and teacher) and dimensions scores were obtained and analyzed. Second, the total survey was analyzed using a repeated measure ANOVA. This allowed me to analyze the entire instrument and make comparisons between the two groups.
Timeline The table listed below is the actual timeline for this study: Table 3: Timeline of Study Task Assignment of sections to treatment/control Training of TAs Administer Fennema-Sherman survey Request student participation in study Obtain initial placement test scores Interview treatment students
Date 8/28 8/28 8/29 9/5 9/7 9/10 9/10 9/21
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Task (cont). Monitor implementation including observations by graduate students Administer post Fennema-Sherman and give post placement test (to obtain second placement test score)
Date (cont.) Weekly between the 3rd-14th week of classes Students second to last day of class (if they finished early); otherwise, last day of class (12/10)*
*Note: Students who did not finish course requirements (3 written exams) prior to the last day of class completed only the post-survey on the last day of class (they did not take the post-placement test)
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CHAPTER FOUR: RESULTS
The purpose of this study was to test the hypothesis that enhanced teacher interaction in a computer-based, developmental mathematics course would have a positive effect on student achievement and sense of self-efficacy in mathematics. This chapter provides evidence that the treatment with enhanced teacher interaction occurred as intended and an analysis of the impact of that treatment on student achievement and attitudes.
Observation Results In order to document the actions of the course teacher and teaching assistants, three graduate research assistants observed randomly selected treatment and control classes over a twelve week period. Each individual class was observed on two different dates for the entire length of the class. The observers did not have contact with anyone in the classroom, they simply recorded the amount and type of teacherstudent interaction on an observer checklist (Appendix D). The rate of teacher-student interaction (the number of occurrences/the number of students present) was calculated for each of six categories: (1) personal contact; (2) responding to a mathematics related question; (3) responding to a non-mathematics related question; (4) following up on mathematics understanding; (5) following up on mathematics goals; and (6) teacher initiated content questions to struggling students. The personal contact with the treatment groups occurred at the beginning of the class or when the teacher arrived to the class. This contact usually involved asking the students how they were doing (in general), and following up on personal matters (i.e.,
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winning a game, feeling better from illness, etc.). In the control groups, the teacher tried to limit such interaction by responding to a students greeting only if the student initiated it. The fourth, fifth, and sixth categories (as listed above) were also interactions that the teacher tried to utilize in the treatment groups. The teacher, along with help from the TA, made note of struggling students and the areas in which they struggled, and attempted to follow-up on their difficulties with them individually. This would include asking a student for understanding on a specific topic, and if necessary, sitting down with them at their work station for a review and a check for comprehension. All students, struggling or not, had several opportunities during the semester to re-assess their goals for the class with the teacher. Table 4 and Figure 1 detail the rates of interaction in the treatment and control classes.
Table 4: Rate of Classroom Interaction Type of Interaction Personal Contact Responding to a students content related question Responding to a students non-content related question Follow up to a students questions (Content related) Follow up to a students question (Non-content related) Teacher initiating content questions
Treatment Group Control Group 0.735 0.124 2.479 1.640 0.909 0.350 1.608 0.438 0.871 0.127 0.407 0.109
The attendance patterns of both the control and treatment group can be found in Appendix G. The patterns were very similar to each other, therefore, the number of students present in each group were consistent with one another. And taken together with the data in Table 4, the attendance suggests that comparable groups of students were present to receive the intended treatment.
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Rate of Interaction
2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Personal Contact Responding to a question (Content related) Responding to a question (Non-content related) Follow-up (Content related) Follow up (Noncontent related) Teacher initiating content questions
Treatment Control
Figure 1: Rate of Classroom Interaction
The observation data confirm that in the categories where the teacher was initiating contact (i.e., personal, follow up, content questions), the rate at which the teacher would make such contact with the students in the treatment group was three or more times that of the rate in the control group. The two categories that involved responding to a question were categories in which the students were in control of the rate of interaction. Similar to the results of the teacher-initiated interaction categories, the number of questions students asked in the treatment group was higher than the number of questions students asked in the control group. It can be argued that the students in the treatment group felt more comfortable asking questions concerning either the content of the course or other class related matters, than did the students in the control groups.
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The data provides evidence that the treatment outlined in Chapter Three was in fact enacted. The results of both the pre- and post-achievement test and attitude survey will be described in the rest of this chapter.
Research Question 1 Does teacher initiated interaction affect students mathematics achievement? The study participants had completed the universitys mathematics placement test prior to the first day of class and took a parallel form of that test at the end of the semester. Only the scores of those students who took both the placement test before the beginning of the semester and completed the course were analyzed. Therefore, the treatment group consisted of scores from 59 (of 70) students and the control group consisted of scores from 49 (of 52) students. The placement test consisted of three different sections. The first section tested students understanding and skill in arithmetic, the second section was a test on elementary algebra, and the third section consisted of intermediate algebra questions. The student scores are reported by section, so the achievement of the treatment and control groups could be compared on the three individual sections as well as on a total score. The scores were analyzed using a repeated measure ANOVA. The analysis was a mixed design with the between-subject factors being the treatment and control groups, and the within-subject factors consisting of pre-test and post-test scores.
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Overall Test Score Results The descriptive statistics show that the mean total score of the pre-test for the control group was 19.143, where the treatment groups average was 18.610. The maximum number of possible points for the entire test was 52. The mean total score of the post-test for the control group participants was 29.939, and the treatment groups mean total score was 28.864. Conducting a split-plot repeated measure ANOVA revealed, through the test of the two-way interaction, that the pre-post change did not differ statistically significantly across groups (p = 0.666). These results are shown in Tables 5 and 6.
Table 5: Descriptive Statistics for Total Scores Class Mean Std. Deviation Pre-test Total Control 19.143 5.6310 Treatment 18.610 5.4489 Post-test Total Control 29.939 5.5430 Treatment 28.864 6.7580
N 49 59 49 59
Table 6: ANOVA for Pre- and Post-Total Scores Source Sum of Squares df Pre/Post Test 5930.686 1 Pre/Post * Class 3.927 1 Error 2216.573 106
Mean Square 5930.686 3.927 20.911
F 283.615 .188
Sig. .000 .666
Arithmetic Score Results The first part of the mathematics test assessed proficiency with arithmetic procedures. Although most of the material covered in this particular course was algebraic, some arithmetic skills were taught within the computerized course material (e.g., order of operations). A maximum of 11 points could be obtained in this section of the test. The mean part one score for the control group in the pre-test was 8.082, 66
where the treatment groups mean part one score was 7.424. The mean part one score on the post-test for the control group was 8.163, and the treatment group had a mean of 8.203. Although the treatment group did have a greater gain than the control group, the difference between the pre- and post-test scores was not significant between the two groups (p = 0.107) at the = 0.05 level. Tables 7 and 8 detail the statistical results.
Table 7: Descriptive Statistics for Part One Scores Class Mean Std. Deviation P1 Pre-test Control 8.082 1.778 Treatment 7.424 2.191 P1 Post-test Control 8.163 1.841 Treatment 8.203 1.873
N 49 59 49 59
Table 8: ANOVA for Pre- and Post-Test Scores (Part One) Source Sum of Squares df Mean Square Pre-P1 vs. Post-P1 9.929 1 9.929 Pre/Post-P1 * class 6.521 1 6.521 Error 260.905 106 2.461
F 4.034 2.650
Sig. .047 .107
Elementary Algebra Score Results The second part of the mathematics placement test included 18 questions related to elementary algebra. All of the students in the course had the same exposure to the elementary algebra topics within the computer assisted material, with the exception of a few topics. Although the module A students, the students who have chosen majors not requiring mathematics beyond the university requirement, are not required to complete the lessons on some topics (e.g., completing the square, imaginary numbers), they were not at a disadvantage on the post-achievement test as these topics did not appear on the test.
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The results of the scores indicate a mean part two pre-test score of 5.837 for the control students and 5.831 for the treatment participants. For the post-test of this section, the control group had a mean score of 11.490, while the treatment group had a mean score of 11.051. The ANOVA analysis indicated that there was no significant difference between the two groups (p = 0.466) at the =0.05 level. Tables 9 and 10 detail the results of the statistical analysis.
Table 9: Descriptive Statistics for Part Two Scores Class Mean Std. Deviation P2 Pre-test Control 5.837 2.649 Treatment 5.831 2.780 P2 Post-test Control 11.490 2.161 Treatment 11.051 2.642
N 49 59 49 59
Table 10: ANOVA for Pre- and Post-Test Scores (Part Two) Source Sum of Squares df Mean Square F Pre-P2 vs. post-P2 1582.432 1 1582.432 337.760 Pre/Post-P2 * class 2.506 1 2.506 .535 Error 496.619 106 4.685
Sig. .000 .466
Intermediate Algebra Score Results The third and final section on the mathematics achievement test contained 23 questions on topics from intermediate algebra. Of the three test sections, this section contained the most variation in scores, since the exposure students had to intermediate algebra topics varied by their chosen module. A student in one of the upper modules (B, C, or D) can be expected to score higher than a student studying in module A. Therefore, it was important to compare the percent of students in the treatment and control groups by module. Table 11 details the module distribution of
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the students completing the course (the students who took the post-achievement test) and whose test scores were represented in the analysis.
Table 11: Module Distribution of Students Analyzed in Achievement Treatment Control Frequency Percent (%) Frequency Percent (%) Module A 10 16.9 13 26.5 Module B 12 20.3 13 26.5 Module C 6 10.2 4 8.2 Module D 31 52.5 19 38.8
The percent of students in module A and D had a larger difference between the two groups than those in module B and C. To make sure that the lower percent of module As did not give the treatment group an advantage and therefore result with a significant difference in test scores on this section, a 2x4x2 repeated measure ANOVA was performed to confirm any significance within the modules. The between subjects variables were the two groups (treatment vs. control) and the four modules. The within subjects variables were the pre- and post-tests. The repeated measure ANOVA confirmed that there was no significant difference on the pre- and post-test scores among the modules (p = .198) or between the two groups (p = .744) at the = .05 level. Therefore, a students module had no significant effect on the group they were in. (The results are detailed in Appendix H.) The descriptive statistics for each group indicate that on the pre-test for part three, the mean of the control population was 5.225 and the mean for the treatment population was 5.356. For the post-test, the mean of the control group was 10.286 and the mean of the treatment group was 9.610. An ANOVA analysis concluded, at
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= 0.05 level, that differences of the two group means were not statistically significant (p = 0.356). The results are represented in Tables 12 and 13.
Table 12: Descriptive Statistics for Part Three Scores Class Mean Std. Deviation P3 Pre-Test Control 5.225 4.214 Treatment 5.356 2.802 P3 Post-Test Control 10.286 3.536 Treatment 9.610 3.686
N 49 59 49 59
Table 13: ANOVA for Pre- and Post-Test Scores (Part Three) Source Sum of Squares df Mean Square Pre-P3 vs. Post-P3 1161.457 1 1161.457 Pre/Post-P3 * Class 8.716 1 8.716 Error 1076.001 106 10.151
F 114.418 .859
Sig. .000 .356
Research Question 2 Does teacher initiated interaction have any effect on students sense of self-efficacy? The participants in both groups answered a 62 question attitude survey, a modified Fennema-Sherman Attitude Scale, on the first day of the semester. Only the students who agreed to participate in the study and who were still present at the end of the semester (or took their final exam early), were asked to answer the same 62 item attitude survey along with six additional course Likert Scale type questions and one open-ended question (see Appendix F). The total number of surveys completed by the treatment participants was 58, while the total completed by the control participants was 44. However, since some of the participants left a question unanswered here and there, the number of surveys analyzed will be different in each analysis.
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The modified Fennema-Sherman Attitude Survey was coded from -2 (strongly disagree) to 2 (strongly agree). Since some of the items are negatively worded, for example, Math is not important in my life, the values assigned to responses for these items were negated so that if a student answered strongly disagree which would normally receive a value of -2, this was negated to a +2. The survey was analyzed as a whole, as well as by the five different dimensions. These dimensions included attitude toward success in mathematics, effectance motivation, confidence in learning mathematics, mathematics usefulness, and teacher. The following tables (14- 18) describe the questions and item numbers contained in each dimension.
Table 14: Attitude Toward Success in Mathematics Survey Items Item no. Statement 3 It would make me happy to be told I was an excellent math student. 7 It would make people like me less if I were a really good math student.a 8 I dont like people to think I am smart in math. 10 If I had good grades in math, I would try to hide it.a 15 It would be really great to win a prize in math. 16 If I got the highest grade in math I wouldnt want anyone to know.a 28 It would be great if other people thought I was smart in math. 29 Winning a math prize would make me feel uncomfortable.a 46 People would think that I was a student who worked too hard if I got high grades in math. 47 I would be proud to be first in a math contest. 54 Id be happy to get top grades in math. 61 Id be proud to be the outstanding student in math.
a
Statement was reverse coded (-2 = Strongly Agree, -1 = Agree, 0 = Undecided, 1 = Disagree, 2 = Strongly Disagree).
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Table 15: Effectance Motivation Survey Items Item no. Statement 1 I like mathematics. 2 Math is very interesting to me. 6 I like to work on math problems I cant understand immediately. 11 The challenge of math problems does not appeal to me.a 12 If I cant solve a math problem right away, I stick with it until I do. 23 I think about unanswered questions after math class is over. 26 I do as little work in math as possible.a 27 I dont understand how people can enjoy spending a lot of time on math.a 30 Figuring out math problems does not appeal to me.a 35 Once I start trying to work on a math puzzle, I find it hard to stop. 37 Math puzzles are boring.a 44 Math is fun and exciting. 56 I would rather have someone give me the solution to a hard math problem than to work it out for myself.a 58 I like math puzzles.
a
Statement was reverse coded (-2 = Strongly Agree, -1 = Agree, 0 = Undecided, 1 = Disagree, 2 = Strongly Disagree).
Table 16: Confidence in Learning Mathematics Survey Items Item no. Statement 4 I think I can handle more difficult mathematics. 5 I know I can do well in math. 13 I am sure that I can learn math. 24 I am sure of myself when I do math. 32 Most subjects I handle o.k., but I just cant do a good job with math.a 33 Math has been my worst subject.a 36 I can get good grades in math. 38 Math is hard for me.a 42 Im not the type to do well in math.a 43 I dont think I could do advanced math.a 50 I am sure I can do advanced work in math. 60 Im no good in math.a
a
Statement was reverse coded (-2 = Strongly Agree, -1 = Agree, 0 = Undecided, 1 = Disagree, 2 = Strongly Disagree).
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Table 17: Mathematics Usefulness Survey Items Item no. Statement 9 Doing well in math is not important for my future.a 17 Ill need a good understanding of math for my future work. 19 I dont expect to use much math when I get out of school.a 20 I will use mathematics in many ways as an adult. 25 Math is not important for my life.a 34 I see mathematics as something I wont use very often when I get out of college.a 40 I study math because I know how useful it is. 45 Ill need mathematics for my future work. 52 Taking math is a waste of time.a 53 Knowing mathematics will help me earn a living. 55 Math is a worthwhile and necessary subject. 57 Math will not be important to me in my lifes work.a
a
Statement was reverse coded (-2 = Strongly Agree, -1 = Agree, 0 = Undecided, 1 = Disagree, 2 = Strongly Disagree).
Table 18: Teacher Scale Survey Items Item no. Statement 14 I have had a hard time getting teachers to talk seriously with me about math.a 18 Its hard to get math teachers to respect me.a 21 I feel that math teachers ignore me when I talk about something serious.a 22 Math teachers have made me feel that I have the ability to go on in mathematics. 31 My teachers have been interested in my progress in math. 39 My teachers have wanted me to take all the math I can. 41 My teachers have thought that I am the kind of person who could do well in math. 48 My teachers think that advanced math will be a waste of time for me. 49 My teachers have encouraged me to study more math. 51 I would talk to my math teachers about a career which uses math. 59 My teachers would not take me seriously if I told them I was interested in a career in science and mathematics.a 62 Getting a teacher to take me seriously in math is a problem.a
a
Statement was reverse coded (-2 = Strongly Agree, -1 = Agree, 0 = Undecided, 1 = Disagree, 2 = Strongly Disagree).
The statistical results of the repeated measure ANOVA of all six analyses will follow, with an overall summary to conclude.
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Total Attitude Survey The total survey consisted of 62 questions. Twenty nine students in the control group and 36 students in the treatment group answered every question, therefore only their results were in the statistical analysis. The potential range of scores for the 62 question survey is -124 to +124. Tables 19 and 20 illustrate the results for the total 62 question survey.
Table 19: Descriptive Statistics for Total Attitude Survey Class Mean Std. Deviation Pre-Total Control 21.897 26.991 Treatment 13.694 35.950 Post-Total Control 28.862 24.839 Treatment 21.361 33.870
N 29 36 29 36
Table 20: ANOVA Results for Total Attitude Survey Source Sum of Squares df Mean Square Pre- vs. Post 1719.394 1 1719.394 Pre/Post * Class 3.948 1 3.948 Error 8360.483 63 132.706
F 12.956 .030
Sig. .001 .864
Total Survey Results The descriptive statistics for the total survey indicate that the control group had a mean score of 21.897 for the first survey and a 28.862 for the second survey. The treatment group, on the other hand, had a mean of 13.694 for the first survey and a 21.361 for the second survey. The results of the repeated measure ANOVA analysis for the total survey show that there was no statistically significant difference between the two groups. With = 0.05, the p-value was 0.864.
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Dimension Results The following section separates the total survey into five separate dimensions and shows the results for each dimension. Table 21 outlines the descriptive statistics for the five dimensions.
Table 21: Descriptive Statistics for the Five Attitude Dimensions Treatment Group Control Group Mean Std. Deviation N Mean Std. Deviation Attitude Toward Success Pre-total 8.216 4.268 51 9.659 4.794 Post-Total 8.745 4.707 9.610 4.770 Effectance Motivation Pre-Total -.922 12.23 51 -.590 9.904 Post-Total -1.510 10.314 1.026 10.579 Confidence in Learning Pre-Total -.292 11.030 48 2.341 9.611 Post-Total 2.354 9.318 4.705 8.846 Usefulness of Mathematics Pre-Total 6.377 10.685 53 7.805 9.770 Post-Total 6.623 9.161 8.000 8.062 Teacher Scale Pre-Total 5.196 6.636 51 6.262 5.700 Post-Total 5.961 7.985 8.238 5.378
N 41
39
44
41
42
The statistical repeated measure ANOVA analysis for each individual dimension can be found in Appendix I. Attitude Toward Success Dimension The 12 questions in this dimension investigated the feelings that students had toward being a successful mathematics student. The questions varied from how a student feels about being successful (e.g., getting good grades, winning a math contest, etc.) to how their peers might judge them based on their success. The range of responses could be from -24 to +24. The repeated measure AVOVA revealed that
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there was no statistical difference (p = .459) between the treatment and control groups on this dimension of attitude. Effectance Motivation Dimension The second dimension of the attitude survey focused on effectance motivation. The 14 questions in this dimension can be viewed as an assessment of a students motivation toward the field of mathematics. The different questions focused on students interest in the field of mathematics, as well as their persistence on working through challenging tasks. The responses could range from -28 to +28. The statistical repeated measure ANOVA indicated no significant difference (p=.107) between the two groups on this dimension of attitude. Confidence in Learning Mathematics Dimension The third dimension contained 12 questions aimed at investigating the students confidence in mathematics. The questions focused on students confidence in handling more difficult mathematics classes and tasks, along with their confidence on getting good grades and understanding the subject. The range of points that could occur in this dimension is from -24 to +24. The statistical ANOVA analysis indicated that there was no significant difference (p = .829) between the two groups on this dimension of attitude. Usefulness of Mathematics Dimension The fourth dimension of the attitude survey focused on students perception of how useful mathematics will be for their everyday lives. This is similar to the concept of task value that was introduced in Chapter Two. The 12 questions in this dimension probed the degree to which the student thinks mathematics is worthwhile,
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being successful in the subject is important, and that mathematics will be used in their future career and everyday living. The range of points that could occur in this dimension is -24 to +24. There was no statistically significant difference (p = .969) between the treatment and control groups on this dimension of attitude. Teacher Scale Dimension The fifth, and final dimension is the Teacher Scale. The purpose of these 12 questions was to get a better understanding of the students perception of their teachers. The questions focused on how much encouragement and interest their past teachers have had in their mathematics ability, progress, and future work. The range of points that could occur in this dimension is from -24 to +24. The statistical analysis indicated that there was no significant difference (p = .225) between the two groups on this dimension of attitude. Additional Questions The participants who filled out the end-of-the-semester survey were also asked six additional questions and one open-ended question that pertained to this specific course. Since the questions in the survey, especially those relating to teacher, can be answered with any past teacher in mind, the additional questions were specific to the teacher/TA of this course. The results indicate that the treatment group responded slightly higher compared to the control group on questions 65 and 68, however, after performing an independent t-test, no statistically significant difference between the two groups was found among the six questions The results are shown in Tables 22, 23, and 24.
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Table 22: Comparing Means of Additional Questions Added to Attitude Survey Treatment Control Question No. Mean N Mean N 63. Learning from a computer improved my 0.220 59 0.457 46 overall algebraic understanding. 64. The ability to move at my own pace 1.203 59 1.327 46 made me feel comfortable in this class. 65. The amount of interaction with the 1.000 59 0.913 46 teacher was critical to my success. 66. I feel I am prepared for my credited math 1.138 58 1.239 46 class. 67. I felt comfortable asking my teacher 1.407 59 1.413 46 questions. 68. This math class has been a good 1.339 59 1.217 46 experience.
Table 23: Independent t-test Results for Additional Questions Question No. t df Sig,(2-tailed) Mean Difference 63. .975 100.079 .332 .236 64. .715 99.679 .476 .12270 65. -.449 88.102 .654 -.087 66. .663 97.579 .509 .101 67. .042 89.376 .967 .006 68. -.719 88.247 .474 -.122
Table 24: Results of Open-Ended Question (What was most helpful?) Treatment Control Frequencya Percent Frequencya Percent Self-pacing of course 20 37.0% 18 40.9% Computer program 11 20.4% 12 27.3% Workbook/Homework 2 3.7% 3 6.8% Teacher/TA 24 44.4% 21 47.7% Lectures b 3 5.6%
a b
Some students had multiple responses that fell in 2 or more categories Lectures were only provided to the treatment group.
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CHAPTER 5: SUMMARY AND DISCUSSION
The intention of this study was to explore the effects of enhanced teacherstudent interaction in a computer-based developmental mathematics course on students achievement and self-efficacy in mathematics. This study drew on research from developmental education, self-efficacy theory, attribution theory, and selfregulation theory to identify cognitive and affective factors likely to influence learning in this particular student population. The investigator designed and developed an experimental teaching treatment to optimize application of insights from the literature. The effectiveness of the experimental treatment was tested by analyzing pre- and post-mathematics achievement scores and pre- and post-selfefficacy scores of university developmental mathematics students in treatment and control groups. This final chapter provides a summary discussion of the treatment and major findings of the study, and the relationships of those findings to the theoretical framework and prior research discussed in Chapter Two. The chapter concludes with some implications of this research for computerized developmental mathematics courses and suggestions for future research.
Overview of Treatment Six sections of a self-paced developmental mathematics course at a large university were broken into two separate groups; treatment and control. Both groups completed all of the basic requirements of the course-computer lessons, computer tests, homework from the course workbook, three written exams, and a written final
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exam. The instruction took place in a computer lab on campus with a teaching assistant present for the entire duration of each class meeting and the teacher present for half of each class period. The teacher/TA presence allowed the students to get their mathematical questions answered without having to seek outside help. Students in the treatment sections were required to have an informal interview with the teacher at the beginning of the semester and to review their progress at the end of each class meeting with either the teacher or the TA. The treatment group students were given due dates for homework assignments and were penalized points for late homework. They were prompted by an e-mail inquiry if they missed two or more consecutive classes without consulting the teacher, in order to remind them that attendance is critical to successful completion of the course. The teacher also provided treatment group students with mini-lectures on topics that are known to be difficult, and she reviewed results of each written test with individual students to discuss mathematical errors and study skills. The sections were randomly assigned to either the control group or the treatment group. When students registered for the course at the beginning of the semester, they had no knowledge of the teacher assigned to each of the sections. The classes were held during the middle part of the day and each time period had one treatment group and one control group occurring at the same time, just in two separate locations. Outside observers visited both control and treatment classes once every week for twelve weeks to monitor the type and amount of student/teacher interaction that was occurring in each class. The observations confirmed that the experimental
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treatment was indeed being delivered as intended; that there was a significant amount of special student/teacher interaction occurring in the treatment sections.
Summary and Discussion of Findings The two central research questions of the study dealt with treatment effects on student learning and attitudes toward mathematics. Research Question 1 Does instructor initiated interaction affect students mathematics achievement? The first research question pertained to the students mathematics achievement. The students took a mathematics placement test prior to the first day of class and took a similar one at the point at which they had completed their three written exams. Students who did not complete the course in one semester were not part of this analysis. The statistical test for the total test revealed the students post-test scores were significantly different from their pre-test scores when data from all students was analyzed. It can be concluded that both groups made progress in learning the material. However, when the achievement scores were separated into the two groups, treatment vs. control, the repeated measure ANOVA revealed that the gain scores of the two groups were not statistically significantly different. Likewise, the two groups did not differ significantly in gains on any of the three individual sections of the test.
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Research Question 2 Does instructor initiated interaction have any effect on students sense of self-efficacy? A modified version of the Fennema-Sherman Mathematics Attitudes Scale was given to the participants on the first day of class and before they took their final exam (some students finished the course in as little as five weeks). The survey was comprised of five different dimensions; Attitude toward Success in Mathematics, Effectance Motivation, Confidence in Mathematics, Usefulness of Mathematics, and a Teacher Scale. The first four dimensions can be argued to be aspects of selfefficacy theory. It is important to note that the results from the pre- to post-attitude surveys for the total survey (p = .001), the teacher dimension (p = .007), and the confidence dimension (p = .000), were the only domains that resulted in a statistically significant difference for students in all six sections (e.g., when group was not taken into consideration). In the domains of attitude toward success (p = .538), effectance motivation (p = .450), and usefulness (p = .732), there was no significant difference among all the students from the pre-survey to the post-survey. The repeated measure ANOVA results indicated that no statistically significant difference occurred between the treatment and control groups on the total survey responses or in any of the individual five dimensions. One can conclude that the enhanced interaction with a teacher had no special effect on the students sense of self-efficacy as measured by the scale used.
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The students pre- to post- responses on the teacher dimension should be viewed with some caution. The questions in this dimension were a little vague with respect to what teacher or teachers are being considered. A student could have taken different teachers into consideration when answering this item at the beginning and at the end of the semester. For example, one of the questions asks, My teachers have been interested in my progress in math. In the beginning of the semester it is unclear what teacher(s) the student considered when responding. However, at the end of the semester, it is likely that the student might be referring to the teacher of this course when answering the question. Therefore, their responses could be referenced to two (or more) totally different mathematics teachers. Since the attitudes toward teacher did show a significance difference pre-to-post-survey among all students, we have to make the assumption that the teacher of this course most likely did not cause this significant pre/post difference on the teacher dimension. It is to the teachers credit that their attitudes towards teacher did improve over the course of the semester.
Understanding the Results This study explored the hypothesis that increased teacher interaction with students would have a significant impact on the achievement and the attitudes of students. This hypothesis is backed by research and theory suggesting that the teacher remains an important part of a students learning experience in a computerized course (Hasselbring, 1986; Kinney & Robertson, 2003). However, results of this study suggest that exceptional efforts to provide teacher cognitive and affective support for students may not yield significant improvements in student learning or self-efficacy.
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In a computerized, developmental mathematics course at a large university, the heightened level of care, structure, involvement, and interest in the students did not have a significant effect on those receiving the extra attention. Given the existing research and theory on developmental education, it is unlikely that teacher-student interaction has no impact on students self-efficacy or achievement. Rather, the results of the current study may lead one to speculate that some minimal amount of interaction, as was provided in the control group, is in fact necessary to improve developmental students sense of self-efficacy and achievement. However, exceeding this necessary amount of the interaction will not necessarily yield greater increases in self-efficacy and achievement. The findings of this study lead us to think of alternative explanations as to why the research hypothesis was not supported, especially when two pilot studies had results that showed promise in the claim. These explanations are given in the following paragraphs. The most significant and major limitation of this study was the number of participants involved. Some students did not finish the course on time, or simply dropped out, so the number of students taking the post-achievement test at the end of the semester was small (N=108). Also, the number of students dropping out of the course and leaving a question blank here and there on the attitude survey, caused the numbers to fall. For the total survey, the number of student responses compared was 65, and in the analysis of the five dimensions, the number of responses compared ranged from 90-94, depending on the dimension. Since the ns were so small, there was significantly less power, the ability of a test to detect an effect given that the
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effect exists, in the statistical analysis and the chances for a Type II error was greater. A Type II error is defined as accepting the null hypothesis that states that no differences exists between the two groups when the null hypothesis is false (Isaac & Michael, 1981). Failure of the treatment group to achieve the expected greater mathematical achievement than the control group leads one to look for explanations of the counterintuitive results. There are several plausible factors at work in this particular test of the hypothesis which states that enhanced student/teacher interaction should yield greater student learning. The descriptive statistics describing the student achievement in the study reveal that the treatment group started out with lower means than the control group on all but one section of the pre-test. Although the differences in means were not statistically significant, one might speculate why the control group may have started the semester with a higher mean. This observation led to an investigation of the students previous mathematics experience and the results are displayed in Table 25.
Table 25: Previous Course Experience Repeating the course Took mathematics in their senior year Transferred in AP credits Last mathematics class taken At another college/university Calculus in high school Pre-Calc in high school Statistics in high school Algebra II Consumer Math/Discrete Treatment 12.68% 70.42% 7.14% 26.76% 1.41% 12.68% 16.90% 19.72% 4.23% Control 5.36% 71.43% 8.93% 35.09% 10.53% 19.30% 7.02% 15.79% 3.51%
Note: Percentages of last mathematics course taken do not add up to 100% since some students failed to answer this question
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We can observe that the experience of taking higher-level mathematics courses (i.e., a course at another college, calculus, and pre-calculus) was higher for the control population (64.92%) than it was for the treatment population (40.85%). This is a plausible explanation of why the control group had a higher mean on the total pre-test score than the treatment group. It might also explain why the control group students appeared to be able to be successful in the computer-based self-paced course without the enhanced teacher support and interaction provided in the treatment. It is possible that if the students in the treatment group did not have the enhanced faculty interaction, structure, support, and feedback that they received, their rate of achievement could have been a lot less than the control group.
Figure 2: Total Test Score Comparison
A third plausible explanation for the lack of difference between the two groups is the limited duration of the treatment. The study was only conducted over a
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15-week period. Many of the students coming to this course expressed having experienced repeated failures or had negative attitudes from previous mathematics courses. It seems improbable that a 15 week experience (and in 12.86% of the cases, 10 weeks or less) with a caring, involved teacher could make multiple years filled with feelings of anxiety, failure, and frustration change so dramatically. Referring back to the literature on productive disposition, attribution theory, and developmental education, students who develop negative feelings towards mathematics early on tend to keep these feelings throughout high school and college (Kilpatrick, Swafford, & Findell, 2001). They tend to blame external fac...