Mathematics
Introduction
and
Chapter DRAFT
Communicating 1 (WHS User Guide) Part 1
Paul Eakin, Carl Eberhart, K.K. Kubota University of Kentucky
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Chapter 0: Introduction
Chapter 0: Introduction ................................................................................................... 2 Chapter 1: A Guide to WHS ........................................................................................... 5 1.1 WHS Students ........................................................................................................... 5 1.1.1 Logging In Or Creating an Account ........................................................... 6 If You Have an Account ........................................................................................ 6 If You Dont Already Have an Account ............................................................... 6 If You Dont Have An Email Address.................................................................... 7 Exercises: ................................................................................................................ 9 1.1.2 Adding or Dropping a Class ............................................................................. 9 The Differences between Browsing and Registration .......................................... 11 Exercises: .............................................................................................................. 12 1.1.3 Checking the Class Announcements and Home Pages ................................... 12 Exercises: .............................................................................................................. 13 1.1.4 Doing an Assignment...................................................................................... 13 Version Numbers .................................................................................................. 14 Individual Homework, Version Number, and Expiration Dates........................... 15 Printing Out WHS Assignments vs Working at the Co ........................................ 15 Video/Audio Hints From Server and Local Machine ........................................... 16 Importance of Properly Logging Out and Timeouts ............................................ 17 Upload Submissions .............................................................................................. 19 Feedback following Assignment Submissions. .................................................... 19 1.1.5 Checking Homework Results Later ................................................................ 20 Exercises: .............................................................................................................. 23
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This is a course for current and prospective teachers of mathematics-intensive subjects to study creation of mathematical exercises. These exercises may contain supplemental material in text or audio- visual from and must in general include deterministic mechanisms for evaluating student responses and assessing mastery of the underlying content. This is a very high level problem solving activity requiring the practitioner to marshal his or her full repertoire of mathematical knowledge, and teaching, and communications skills. Beyond a certain level of creativity or style, the development of a coherent problem set requires: 1. Understanding of the instructional objectives for the problem set and targeted student population, 2. Mastery of the underlying mathematical content and its technical vocabularies, 3. Knowledge of some of the principal natural or human systems the underlying content can be used to model, and 4. Language fluency and precision of expression in a vocabulary and style appropriate to the targeted students. An experienced teacher can readily evaluate and constructively criticize student problems relative to these attributes. Moreover they are areas in which students can improve with guidance and practice. This means that such a course is feasible but defines it far too broadly to be practical in a general educational setting because it implies too much work for the teacher. The biggest problem is item 3 and the requirement for a means to evaluate student responses. In a general setting these makes the teacher responsible for analyzing not only the problem but also the accompanying solution, key, answer, etc. a terribly labor-intensive task. To avoid this difficulty we restrict the types of problems considered to those which can be expressed in a format compatible with a web-based instructional support system which auto-checks student responses. We employ a system called WHS (Web Homework System) which has been (and continues to be) developed by the authors at the University of Kentucky, concurrently with the Communicating Mathematics course and other applications. Although it is used in a production capacity to support instruction for thousands of students, WHS was developed concurrently with this course specifically: to address the formatting and graphics problems of mathematics, to provide a research and development model for technology-assisted instructional support in mathematics, and to provide an inexpensive (hopefully free) environment for those who complete it to actually employ what they learn in their own teaching. The latter group includes practicing teachers, graduate students, and faculty as well as undergraduate students who may become graduate teaching assistants, teachers, or faculty in the future. To guarantee future access the
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University of Kentucky makes WHS freely available for non-profit, educational use and has heavily invested in its use in mathematics and foreign language programs at UK. This offers long-term stability and continued development and support and makes it reasonable for teachers at all levels to invest the time and effort required. To us, saying that WHS is a web-based instructional support system means that it has: (1) a problem development/editing system, and (2) a web server on which the problems are installed and through which students interact with the problems. In some systems the development tools are part of the server while in others the problems are written with standard editors and uploaded to the server. WHS is of the latter type since this form permits the developer render the problem sets as source documents in standard commercial formats such as MS-Word *.doc files or Maple *.mws worksheets. The source is exported to html which is passed to the server for formatting, organization, and presentation. The use of source documents in standard formats helps isolate the mathematics from the nuts and bolts of the technology while greatly enhancing sharing and collaboration. It gives the developer access to high level formatting and graphics capabilities of standard applications such as MS-Word and Maple and makes materials revision and maintenance simple. For instance correcting a spelling or grammar error in a WHS problem set typically takes a minute or two and involves only standard word processor or editor functions. The use of Maple to develop problems means that the entire capability of a powerful problem solving language is available to check and construct solutions and even to automate problem production. Thus in this course the instructor can (and should) exact the highest standards of presentation and grammar while, of course, expecting absolute mathematical correctness. To reiterate, this is a problem solving course in which the problem solving process is: 1. Identification of a set of standards relative to which mastery by some population is to be assessed, 2. development of coherent sets of instructional exercises which reference the chosen standards, 3. precisely and grammatically correctly stating the problems in the appropriate vocabulary (including illustrations) for the targeted students, 4. fully and correctly solving the problems, 5. implementation of the problem set as a collection of auto-corrected problems on the web-based system Steps 1-4 are by far the most important and can, of course, be carried out completely independently of technology. In the process and in the course they typically take 75% of the time and effort. In step 5 the problems, diagrams, and solutions are formatted and installed on the
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instructional support system. Formatting and installation are simple and quickly mastered. The challenging and interesting parts of this are: o The development of alternative answers, distractors, for problems with multiple choice answer formats, o The construction of high quality graphical representations of the problem diagrams Both of these require a deep understanding of the mathematics of the problem and the second requires mastery of elementary trigonometry, and analytic geometry and linear algebra of two and three dimensions. The need for clear understanding becomes more evident with the understanding that the student is expected to create not just verbatim renditions of the original problems but rather to produce problem generators which are versions in which selected parameters in the problems can be changed with the answers, alternatives, and diagrams automatically re-computed.
Chapter 1: A Guide to WHS
This chapter covers the acquisition and use of WHS student, teacher, author, and coordinator accounts. In reading it be mindful of the fact tha t WHS is a very dynamic system in which the basic functionality is stable but the interface changes frequently; new features are continually being added. Thus do not be surprised if there are details and diagrams in what follows that do not correspond exactly to what you see on your computer. The most recent WHS documentation is maintained at www.mathclass.com at For Students and For Teachers
1.1 WHS Students
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In WHS a student is simply one who has a WHS student account. In WHS students add (and drop) classes, submit assignments, and communicate with teachers of the classes they have added. Anyone can at no cost become a WHS student and as such can join (at least as an auditor or browser) any class or course on WHS. At some colleges and schools student accounts are created in advance when students register for a class. In most situations they are created by the individual. At any time an individual needs only one WHS account regardless of the number of classes in which he or she is participating. To get started with WHS connect to www.mathclass.org or www.mathclass.com to reach the mathclass.com main page. The Mathclass portal hosts WHS and other services. To get to WHS select login (if you already have an account) or Web Homework (if you need to create an account for yourself). The result will be, respectively, one of the two screens below. At this point you can log in or create your account.
1.1.1 Logging In Or Creating an Account
Creating a Student Account in WHS If You Have an Account
If you already have an account then enter your login and password.
If You Dont Already Have an Account
Pass the mouse over the Web Homework bar on the mathclass main page and press the Register (as a New User) bar which will appear near the center of the screen. This will place you in the Registration Screen. If you have an account which you did not create as a new user then you will also land in the Registration Screen when you login. The difference in the two cases is that in the latter case most of the screen will be filled in.
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Now simply fill in the information that is not there. At this time we suggest that you enter your student number or social security number as your password. You will be able change it later. For now its convenient, easy to remember, and you have it written down in several places. Once you are registered for a class the teacher of that class can create a new password for you if you lose the old one. The requested social security number is used only within the system to uniquely identify your account. If you object to providing your social security number you can enter 9digit number of your choice. However, be careful to make a note of the number you provide since it will become your initial password and the definitive identifier of your work on the system. You should find your school in the School menu. If you do not find your school in this menu select any school (e.g. University of Kentucky ) temporarily and go ahead and create your account. Then use the Help (see sec 1.1.6) button to email a request for assistance in getting your school listed. Once it is listed you can use the Modify Account menu on the main page to change to your own school.
Importance of the Email Address
The email address is required for two reasons : 1. With it the email address the system can provide communication among the teacher, student, and the system itself. Any type of email account (e.g. AOL, hotmail, school system account, etc.) is fine. 2. The email address becomes the students login id.
If You Dont Have An Email Address
You can, and a short-term measure use a fake email address. For instance if Mary M. Mullins is a student at Wolfgang Beethoven High School she might use [e-mail] The idea is that the full name should keep the address unique amongst the school and the rest of the address will keep it unique in the world. If you use a fake email be sure to use one you can remember. Do not use someone elses email address!! Students should get and use an e- mail address. If the school is not providing this service, there are a number of free internet mail services, e.g. many students at the University of Kentucky prefer to use hotmail.com because it is browser based . Remember that the email address becomes the users login id. If the users email address is subsequently changed (this can be done at Account Modification on the main WHS screen as we will see momentarily) then the login is automatically changed to 7
the new email address. This completes registration. To activate your new account press the Submit Information bar
Things that Might Go Wrong
If there is a problem your registration screen will probably be returned with the following message:
Your E-mail address or social security number has already been registered with another account. If you have already registered, then please login with your already registered account and password. Otherwise, it is likely that there is a typo in the submitted e-mail address or social security number.
Barring a spelling error the most likely thing to have happened is that you already have an account either because it was created for you automatically or because you created it earlier and have forgotten. Because people can use either a student number or a social security number it can happen (through very rarely) that an account has already been created with your social security number (which, perhaps, happened to be someone elses student number). If this has happened then choose a random number and see if you can create you account. If this was the problem you can then use the Help (see sec 1.1.6) button to send email to the system people asking them to change the id number of your account to the correct one.
Persistence of Student Accounts
Student accounts generally vanish when all of the courses in which they are registered are complete. Students are notified by email that accounts are about to expire. Students whose accounts expire can subsequently create new accounts for participation in future courses.
Once you have an account and successfully log into WHS you will be at the WHS main screen. The left side of the screen has a column of eight rollover bars. Touching one of them with the mouse, each corresponding to a different page in the display to the right.
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Selecting the Announcements bar produces a screen with a pull-down menu at which we can select from among the classes in which we are registered (with WHS). If yours is a new account not automatically created by your schools registration system then you menu is probably empty. You need to add at least one class.
Exercises:
1. If you do not already have a WHS account connect to www.mathclass.org and following the above text, create for yourself a WHS account. If you intend to participate in the MA502 class you must use your correct social security number. 2. Once you have a WHS account log in and verify that your account works. Once you have verified that your login and password are valid, write them down somewhere you can remember to look if you forget. 3. Once you have a WHS account attempt to create another using the same email address or the same social security number and observe the system response.
1.1.2 Adding or Dropping a Class Adding a WHS Class
If you are registered (in the WHS system) for a class then it will appear as an option in 9
your Assignment Selection screen. At the University of Kentucky most students who pre-register for mathematics classes (which use WHS) will already have WHS accounts and be registered for their classes. If you have not pre-registered for a class or for some reason you are not registered in the class you expect then it is a simple matter for you to register yourself. Select the Add/Drop Classes link on the WHS main page
Since we are using an account which lists University of Kentucky as the school, UK courses are listed in the pull-down menu . To access classes at other schools select the Other Schools bar at the bottom of the page. Use the resulting screen to change the school. For instance if we wanted to add Dr. Kuhns Calculus I course at the University of Tennessee at Chattanooga we would press the Other Schools bar, select University of Tennessee at Chattanooga and press the Submit bar. Then when we return to the Drop/Add screen the classes listed will be those at UTC. Note: If you change the school from UK and subsequently want to select another UK class in the same session you will need to use the same page to change the school back to UK.
Note: There is a small checkbox labeled Include Course List Names which can be 10
selected on the Other Schools screen. This results in a more detailed display of course information. This is primarily for use by teachers who wish to offer the same course material. The additional information tells them how to set up a class offering the same assignments This is covered in more detail in a later chapter. To drop a class simply select it in the Drop Class menu on the Drop/Add screen and press the Drop Class bar. Remember that you cannot drop a class in which you are registered until the teacher changes your status from registered back to registration pending.
The Differences between Browsing and Registration
In the example we are Requesting Registration in the course Ma123-000 by pressing the Request Registration bar. Selection for browsing does not provide for course participation, communication with the instructor, etc. However it does provide full access to the course materials. Having requested registration we have registration pending for the Ma123-000 class at the University of Kentucky. This means that we have the same status as a browser until the teacher actually admits us to registration in the class. At this point we can access, work, and submit any of the course homework sets and receive results and feedback from the system. None of the work will, however, appear on the instructors student screens and the course communication links between us and the instructor will not have been created. The course teacher (in this case Dr. Eakin) will receive notice on his class management screen that we have requested registration in the course. He must approve (at his class management screen) our actual registration. Once we are registered for the Ma123-000 course the teacher will have access to our results on all course assignments. In addition the system will create convenient emailbased lines of communication between Jean and the teacher. However it is important to realize that we can go immediately to work without waiting for registration approval. Once our registration is approved all work done while in browsing status will be available to the teacher exactly as if we had been registered from the beginning. One final remark on browsing and registration is in order. If we are registered in a class the teacher can change our password. That is, any teacher in a class in which we are registered can change our password. This is advantageous since it means that if we forget our password we need only ask the teacher to reset the password for us. It can be disadvantageous if we irritate the teacher since he or she need not tell us the new password. Moreover, once we are enrolled in a class we cannot drop the class unless the teacher changes our status from registered to pending. Problems with frozen accounts resulting from a misunderstanding with a teacher must be resolved through ordinary academic procedures. The first of these is to talk to the teacher
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about it.
WHS Registration is NOT Academic Registration!!!
It is very important to understand that the terminology notwithstanding WHS registration is completely independent of academic registration (i.e. registration for credit) and WHS Drop/Add is not the same as a college or schools Drop/Add. WHS registration constitutes an agreement by the teacher for the student to sit in on the WHS class component of a course. There are no fees paid, transcripts created, or other commitments involved and absent other considerations agreement the can be terminated by either party at any time.
Exercises:
1. Log in to www.mathclass.org and, following the above text, add the University of Kentucky course Ma123-000 for browsing 2. If you are registered in Ma502 add the University of Kentucky course Ma502-001 for registration 3. Add for browsing one of the University of Kentucky SPA101 sections. 4. Add for browsing one of the University of Tennessee at Knoxville M119 courses.
Now that we are in a course we can get to work. The first thing to do is check the announcements
1.1.3 Checking the Class Announcements and Home Pages
WHS provides teachers with multiple means for communicating with their students. Ultimately each is an electronic metaphor for a more traditional mechanism. Generations of teachers have used the class chalkboard to write daily announcements and to attend to minor administrative details. The Announcements are intended to serve this purpose. The teacher of a class can quickly write to the announcements pad for the class from any computer connected to the internet. To view the class announcements highlight the Announcements link on the WHS main page. This causes the announcement menu and screen to appear The menu contains all courses we have added whether we have registration or browser status. Selection of a class causes the announcements for that to be displayed.
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The Announcement screen for class contains links to the class homepage and course homepage. The class homepage is simply a web page which is analogous to the traditional class bulletin board. It is maintained by the teacher and can contain any information he or she wishes. In some situation, particularly in colleges, there may be many teachers offering different classes, or sections, of the same course. For instance at the University of Kentucky there are typically 1000 students taking the same basic calculus course in 40 different sections, each with its own instructor. In these courses all of the students have the same web-based homework assignments and often they all take the same examinations. The course homepage is maintained by the course coordinator who compiles the list of homework problems. It contains more general information of interest to all students taking the course. In the special case in which there is a single teacher of one class the course homepage and class homepage are often the same or one of them is left blank.
Exercises:
1. If you have not already done so, add MA502-001. If you are taking the course for credit then you need to add it For Registration, otherwise add it For Browsing. Read the class announcements and look at the course and class home pages.
1.1.4 Doing an Assignment
Now its time to get to work which means doing an assignment. When we select the Assignment link on the WHS main screen we get the assignment screen which contains two menus. The upper menu allows us to select a course in which we are registered at which time a menu gives us a choice of all assignments on the current list for the class. Our Ma123-000 assignments have expiration date included. These are the dates by which the assignment must be completed. We choose the first which is an Algebra Review. 13
There remain three buttons in the table: Common Version, Personal Version, and Specific Version. The common version returns the same version of the homework each time it is pressed, regardless of who presses it. If a number is entered in the box above specific version and that button is pressed, a version of the assignment correspond ing to that number is returned (if no number is entered and the button is pressed a random version of the assignment is returned). Finally, if the personal version bar is pressed the assignment corresponding to the users account number is returned. It is therefore specific to the user. The system records only the results of attempts at personal versions.
This particular assignment is a preliminary version of the Kentucky Early Mathematics Testing Program (KEMPT) diagnostic exam for sophomore and junior high school students. The KEMTP, an excellent indicator of whether a students basic algebra skills are adequate for college- level mathematics, is accessed by the KEMTP link on www.mathclass.org main screen.
Version Numbers
Note the version number 0.3595087, in the upper left corner. If we enter this number on the specific version line before pressing Specific Version then this test will be repeated. This is important since we may want to do is print the assignment out, work it out on paper, and then re-select the assignment at a later time and enter the answers. Obviously this is possible only if there is a way to relate the answers to that particular exam. The version number ma y be in scientific notation (e.g. .0900120 E 1). In this case just
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enter it as presented. Although WHS supports numerous answer formats this particular assignment is all multiple choice. Five alternatives are presented as possible answers to each question. The student solves the problem and selects the correct answer from among them. When the answers are entered the Submit and Record Results bar at the bottom of the assignment is pressed and the system promptly returns web page which contains the complete statement of each problem attempted and whether the response was correct or incorrect.. Depending on how the teacher has the homework set up it may or may not return the correct answer.
Individual Homework, Version Number, and Expiration Dates
Homework Versions
As noted above the Personal Version of an assignment uses the students WHS account number as the version number. The WHS system expects the teacher (actually the list coordinator) to specify expiration dates for homework. If no date is specified the system assumes a date several thousand years hence which for practical purposes says such homeworks never expire. The system keeps track of all problems in his/her personal set for which the student submits a correct answer before the expiration data. There is no limit on the number of attempts permitted. At any time the student and the teacher can quickly check the students status relative to an assignment. (See Checking Results, below)
Printing Out WHS Assignments vs Working at the Computer
WHS homework sets generally take an hour or more for a prepared student or even a group of students to do completely. While it is possible to bring a set up on the computer screen and work the problems one at a time the expectation is that students will print the assignments out, work them, and check the answers later. Problem sets are usually developed with generous amounts of white space. This, together with the space on the backs of the pages is almost always sufficient to record student solutions. If when checking with the machine we subsequently find that our answer is inconsistent with the official one we can check the work for obvious errors and then if necessary consult with the instructor or a tutor. Experience has shown that such consultations are much, much more efficient and productive when the student and instructor or tutor work directly with the printed problems and student solutions. Fully half of student difficulties with homework involve understanding of exactly what is being asked. When this is the heart of the difficulty , having the printed problem with the diagram in a form on which notes can be made has proven very useful.
Saving Paper When Printing
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Printing 4-Up
Most students have good enough eyesight to be able to read WHS problems printed much smaller than that dictated by customary print settings. When printing a WHS problem set from a browser, after selecting Print from the File menu look for a chance to choose Pages Per Sheet. One may also have the choice of 1- up, 2-up, 4- up, etc. It may be on the main page or on the Preferences link. A choice of 4 pages per sheet will almost always be quite adequate and will use a fourth as much paper and ink as the conventional 1 page per sheet. If 4 is too small then 2 pages per sheet will halve the paper and ink consumed. For 4-up it is often the case that the landscape orientation works better than the default portrait but this is a matter of individual preference.
Landscape Orientation and 4 pages per sheet
Video/Audio Hints From Server and Local Machine
Some WHS homework contain links to brief (up to three minutes) audio or video clips
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which are intended to help the student better understand the material. Selection of one of these links might, for instance, bring up a video of someone explaining the solution to a related problem.
The links are of two types. The first is a familiar html link which when selected will cause the WHS server to send the requested file to the local machine
The second is displayed as a bar with a listbox (or pulldown menu) of letters A-Z to its left. If the bar is selected when there is nothing selected in the listbox then the result is exactly the same as in the first case. That is a file is sent from the WHS server and displayed on the local machine. On the other hand if a letter is selected on the listbox and the browser is a recent version of Internet Explorer then WHS instructs the local machine to go to that drive on the local machine and look for the file to be displayed there. The drive is typically a CD. Since the video files are quite large (up to 5 Mb each) they are not practical for dialup connections or even for relatively fast connections when a significant number of people want to use them at the same time. The second type of video link addresses both of these.
Importance of Properly Logging Out and Timeouts
Timeouts
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Students (and teachers) are busy people who frequently walk away from WHS sessions without properly logging out. In the current system this is done by terminating the browser session. This can be done by closing down the browser or directing it to another URL (e.g by clicking on Home on the browser toolbar). The problem with not logging out is that someone else might sit down and start to work in that session either naively or maliciously. In the first case the second person might enter homework answers, thinking he or she was crediting the work to his/her own account. There are safeguards/reminders to guard against this but students have been known to miss them. The second, more dangerous case, is when the second individual impersonates the owner of the account. He/she might, for instance, submit bogus responses to an assignment or use the system to send offens ive queries or comments back to the instructor. Most institutions have rules against such behavior but in such circumstances they are difficult to enforce and the best. Timeouts are a safety mechanism to protect users who forget to properly log out of a session. In a WHS session if the user interacts with the server frequently then the server assumes that the person pressing the keys is the proper owner of the account. If there is a long period of inactivity the server assumes that the owner left the session and the bad guy has taken over. It then asks the user to prove he/she is the owner by asking for his/her identity and password. This is called a timeout ; they occur after ten minutes of inactivity if a person is doing anything but an assignment and after an hour when working on an assignment. They are particularly likely to occur when one is working on an assignment a problem at a time, entering the answers as he/she goes. In this situation the browser is collecting all of the information locally and goes to the server only when the Submit and Record.. bar is pressed. Since under this scenario it might have been some time since the last trip to the server a timeout is likely to occur before the students answers have actually been submitted and the result upon pressing the Submit and Record.. bar will be the following Authentication Screen
If timeout occurs nothing is lost!! The server would simply be saying that it has been sufficiently long since we contacted it directly that it wants to be sure who is at the
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keyboard. The steps to be taken are: 1. 2. Enter login and password in the Authentication screen. Press the BACK button on the Authentication screen. Pressing the BACK button on the browser toolbar will not produce the same result. If you do press that button, press the Forward button on the toolbar and then press the BACK button on the screen.
This takes one back precisely to the point at which the action (e.g. pressing Submit and Record ) was taken which caused the Authentication screen to appear. Remember that in this case we must press the Submit and Record Results bar again. This is because in case of a timeout the original Submit will not have been recorded since the system was unsure who actually pressed the bar.
Upload Submissions
Submitting Uploads
The simplest...