Unformatted text preview: CI 401 M&M2 Fall 2011 Final Exam Directions: There are four sections of this final that encompass questions concerning material covered at different points throughout the semester. You are to choose one question from each section and answer it thoughtfully and completely. Responses should synthesize material covered throughout the course and make connections between key pedagogical and mathematical ideas. When suggesting specific teaching actions, you should justify your decisions by drawing on the rubrics on specific activities of teaching, NCTM documents, and the Brahier text. Your exam needs to be submitted prior to 5:00 pm on Wednesday, Dec. 14th, in the appropriate forum on our class Moodle Site. Please save your exam as a single .doc or .docx document with a title that contains your last name (ex: LastName_401Final.doc). Please write your full name in the header of all pages. Your exam should not exceed 5 single
spaced pages. Section One: Explaining a Concept & Teaching a Procedure (Choose One) 1. You are teaching an introductory lesson on the concept of (CHOOSE A. Exponential Functions in an algebra one class or B. Surface Area of Spheres in a geometry class) a. What is the relevant prior knowledge that students would need to understand this concept? b. What would be one way that you could problematize this concept? Be specific. c. Script 3
5 lines detailing how you might summarize the core principles of this concept to students. d. Choose two different representations (be specific) that you might use to illustrate some of the core principles of this concept. State in which order you would show these representations. Explain the reasoning behind your choices. € 2. You are teaching the procedure of (CHOOSE A. Solving a system of linear equations by substitution in an algebra one class or B. Graphing simple rational functions (ex: x +1
) in an Algebra II class) f ( x) =
2x − 4
a. What is the relevant prior knowledge that would be helpful for students to have in order to successfully perform and understand this procedure? b. Script 3
5 lines detailing how you could focus the procedure to explain what this procedure is for and when we might choose to use it. c. Choose 3 examples (different than the ones above) you might use to demonstrate how to apply procedure to different cases. Explain what you hope students will learn about the procedure from each different example. d. What are means of control that students could use to check whether they have performed the procedure correctly? 3. You are teaching a lesson on (CHOOSE A. The Golden Ratio or B. The number e) in your Algebra II class. a. How could you use history of mathematics to help problematize the concept? b. Script 3
5 lines about what you would say to your class about references to the history of this concept. c. What specific question/scenario could you use to problematize the concept? d. Script 3
5 lines about what would you say to introduce this problem. Section Two: Problem Solving & Lesson Planning (Choose One) 4. It is the first day of your Algebra II class and you want to give your students a problem to begin developing certain habits and dispositions when working on problems. You know that students have experience with linear, quadratic, and exponential functions from their Algebra I class and you want to use some of this prior knowledge. a. What problem would you choose? Why? b. Anticipate two different ways that students might choose to solve the problem, using two different representations. c. Choose one habit of mind or disposition that you can teach with this problem. Explain your choice. d. Script 3 – 5 lines of what you would say at the end of class to show how this problem illustrates expectations for them to develop this habit of mind or disposition throughout the year. 5. You are planning a lesson for your Geometry Class on either A: Properties of parallel lines cut by a transversal; or B: Reflections. a. Write 3 sample objectives that may be used to guide your lesson plan that incorporate different cognitive processes of Bloom’s Revised Taxonomy. b. Write a “Hook” that might be used to capture student attention towards the beginning of your lesson. Explain what you hope to accomplish through your choice c. Describe two assessment techniques that you could incorporate in your lesson plan to check for student understanding throughout your lesson. Explain your choices. d. State which Common Core Math Standards (ex: A
SSE.1 ….. ) this lesson would cover. Also choose one of the Common Core Practice Standards that you think could be promoted in a lesson on this material and explain your choice. Section Three: Teaching with Student Participation & Classroom Norms (Choose One) 6. It’s your first week of school and you want to establish clear expectations for your freshmen algebra class about participating in classroom discussions. Your want to begin establishing the norms for sharing their ideas in class and listening to the ideas of others. Frame your explanation drawing from key ideas from the NCTM Principles and Standards about teaching and learning in math classrooms. Script an explanation to your class about what you want to accomplish using language and terminology that your students will understand. Communicate to your students the importance of having a safe environment and learning from errors. Explain to them what they should expect from you as a teacher when you are leading classroom discussions. Set a positive tone that would encourage your students to actively participate in class activities and discussions. 7. Create your own fictional classroom script in which a high school teacher is using discursive moves to guide a class discussion about a problem or mathematical concept. Your script should incorporate at least 5 different discursive moves performed by the teacher and have a maximum of 10 teacher lines. At the end of the script, identify which discursive moves were used at various points in the dialogue. Choose two of the moves and share your reasoning as to why you had the teacher use those moves at their defined locations in the script. Section Four: Equity & “Hot Topics” Presentations 8. The NCTM Principles and Standards book states that equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students. One of the goals of this semester’s “Hot Topic” presentations” was to investigate what “reasonable and appropriate” accommodations may look like for students of different backgrounds. Reflect on two specific “best practices” that you learned about from the hot topics presentations that relate to providing reasonable and appropriate accommodations for students in the classroom. Explain your choices and why you feel they would help to promote equity in your math classroom. Honor Code • You may discuss these questions with others from the class but your final written answers should be completed individually and in your own words. To certify that you followed these guidelines, write the statement below at the end of your exam. • Ex: “I certify that my final written answers were completed individually and in my own words. Adam Poetzel 12/14/2011” ...
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