Maplesoft MAPLE user guide

User Guide

No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means — electronic, mechanical, photocopying, recording, or otherwise. Information in this document is subject to change without notice and does not represent a commitment on the part of the vendor. The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the agreement. It is against the law to copy the software on any medium except as specifically allowed in the agreement.

Copyrights

Trademarks

Maple, Maple T.A., Maplesoft, and Waterloo Maple are all trademarks of Waterloo Maple Inc.

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Java, all Java-based marks, Sun, and Solaris are trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and other countries. Waterloo Maple Inc. is independent of Sun Microsystems, Inc.

All other brand names or product names are trademarks or registered trademarks of their respective companies.

ISBN 978-1-897310-83-0

Contents

Getting Started.................................................................................... 1

System Overview ....................................................................................... 1

Assignments .......................................................................................... 2

Gradebook ............................................................................................. 2

Logging On ................................................................................................. 2

The Class Homepage ................................................................................. 3

Creating a Class .........................................................................................4

Adding Users to the System ...................................................................... 5

User Rosters .......................................................................................... 5

Adding Individual Users ...................................................................... 8

Registering Users in a Class ..................................................................... 8

The User Manager ................................................................................ 8

Student Self-Registration ..................................................................... 9

Class Rosters .........................................................................................9

Sharing Content................................................................................ 11

Sharing Questions ................................................................................... 11

Course Modules ........................................................................................ 13

Child Classes ............................................................................................ 15

Featured Classes ...................................................................................... 16

Propagation of Material from Featured to Child Classes .................16

Question Repository......................................................................... 19

Overview ................................................................................................... 19

Question Editor ........................................................................................ 19

Example Questions .................................................................................. 21

The Question Designer ....................................................................... 22

Multiple-choice Question using the Question Designer ................... 23

Multiple-choice Question with Randomly Determined Parameters 25

Multiple Choice Question Incorporating 2-D Math .......................... 27

Maple-Graded Question ..................................................................... 29

Plotting the Student's Response ........................................................ 31

Inserting a Maple Plot in the Question Feedback ............................ 31

Apply Partial Grading to Maple-graded Questions .......................... 32

List Question using the Question Designer ...................................... 32

Numeric Question using the Question Designer .............................. 34

Equation Editor .................................................................................. 35

Downloading Questions ........................................................................... 35

Assignments ..................................................................................... 37

Overview ................................................................................................... 37

Assignment Editor Main Menu .......................................................... 37

Warnings and Locking Mechanism ...................................................38

Creating Assignments .............................................................................39

Naming Assignments ............................................................................... 39

Selecting Questions ................................................................................. 39

Individual Versus Grouped Questions .............................................. 40

Setting Policies ......................................................................................... 40

Assignment Types ............................................................................... 42

Feedback ............................................................................................. 45

Assignment Properties ....................................................................... 46

Advanced Policies ...............................................................................49

Reviewing and Saving Assignments .......................................................50

Special Cases ............................................................................................ 51

Deleting Assignments ......................................................................... 51

Shared Assignments: Saving Your Changes ..................................... 52

Gradebook......................................................................................... 53

Overview ................................................................................................... 53

Gradebook Views ..................................................................................... 53

Generating Reports ............................................................................ 54

Student Statistics .................................................................................... 55

Assignment Weighting ....................................................................... 56

Assignment Statistics .............................................................................. 58

Item Statistics .......................................................................................... 59

Add External Assignment ....................................................................... 59

Content Creation in the Question Editor ........................................ 61

Question Types ......................................................................................... 61

Enhancing questions ............................................................................... 63

Feedback ............................................................................................. 63

Information Fields .............................................................................. 64

Hints .................................................................................................... 64

Solution ............................................................................................... 65

Including Formatted Math Expressions in Questions ........................... 65

Using the mathml Function ............................................................... 65

Using the Math Editor ....................................................................... 66

Using Maple's MathML[ExportPresentation] Function ................... 67

Including Images in Questions ............................................................... 67

Static Images ...................................................................................... 67

Maple Plots ......................................................................................... 68

Algorithmic Variables....................................................................... 71

Creating Algorithmic Variables in Maple T.A. ......................................71

Algorithm Design Tool ........................................................................ 72

Maple T.A.’s Built-in Functions and Constants ..................................... 72

Examples of Randomization Functions in Maple T.A. .......................... 77

Basic Arithmetic ................................................................................. 78

Calculating Area ................................................................................. 79

Color Combinations ............................................................................ 80

Randomization Routines in Maple .......................................................... 81

Random Integers ................................................................................. 82

Random Polynomials .......................................................................... 82

LinearAlgebra Functions ................................................................... 83

RandomTools Functions ..................................................................... 83

Examples of Randomization Functions in Maple .................................. 85

Degree of polynomial .......................................................................... 85

Intersection of Sets ............................................................................. 85

Matrix Determinant ...........................................................................86

Maple-graded Questions.................................................................. 89

A Basic Maple-graded Question ..............................................................89

Testing Your Question ........................................................................ 92

A Randomized Question .......................................................................... 92

A Question with Infinitely Many Correct Answers ............................... 96

Testing your question ......................................................................... 98

Another Question with Infinitely Many Correct Answers .................... 99

Accepting Approximations of Exact Symbolic Answers ......................... 99

Questions with Vectors and Matrices ................................................... 100

Allowing for Partial Grading ................................................................. 101

Performing a String Match ................................................................... 102

Performing a Pattern Match ................................................................. 103

Troubleshooting Maple-graded questions ............................................ 104

Flash and Applet Questions .......................................................... 105

Flash Movies in Maple T.A. Questions ................................................. 105

Java Applets in Maple T.A. Questions ................................................. 106

Dynamic Labels on an Image ...........................................................106

Interactive Plots ................................................................................ 108

Flash Question Type .............................................................................. 110

Applet Question Type ............................................................................ 111

Step 1: Create and Deploy a Java Applet ........................................ 112

Step 2: Create and Deploy a Java Class for Grading ..................... 113

Step 3: Author the Maple T.A Question .......................................... 113

Question Authoring in LaTeX ........................................................ 115

Writing Questions in LaTeX ................................................................. 115

Requirements .................................................................................... 115

Authoring Process ............................................................................. 116

LaTeX Document Structure ............................................................. 116

Question Structure ........................................................................... 117

Sample Question File ....................................................................... 117

Converting into a Maple T.A. Script ................................................ 118

Sample .qu File ................................................................................. 119

Working with Algorithmic Variables .................................................... 120

Defining the Algorithm .................................................................... 120

Referencing Algorithmic Variables .................................................. 121

Placing Images in Questions ................................................................. 122

Setting the Image Base ....................................................................122

Inserting an Image ........................................................................... 122

Graph Sketching Questions .................................................................. 123

Overview ........................................................................................... 123

Plain-text Question Files................................................................ 127

Question Tags ........................................................................................ 128

Question Type Modes ............................................................................ 129

Question Fields ...................................................................................... 130

Notes: ................................................................................................. 132

Plain-text File Question Enhancements ............................................... 132

Response-specific Feedback ............................................................. 132

Key Word Questions ......................................................................... 133

Preface

Audience

The information in this guide is intended for instructors using the Maple T.A. system for the first time.

Goals

This guide serves as an introduction to the Maple T.A. system and is grouped into three parts. Chapters One through Five provide information related to each component of the system. Chapters Six through Eight provide instruction on basic question creation using the Question Editor. Chapters Nine through Eleven provide instruction on advanced question creation, including the use of Flash movies and Applets, LaTeX, and Plain-text question creation.

Initially, the chapters should be read in sequence. This provides a linear introduction to the process of using the components in the Maple T.A. system. However, this guide can be used as a quick reference or as a launching point for the Help system.

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1 Getting Started

1.1 System Overview

Maple T.A. uses questions found in the Question Repository as the basis for constructing assignments. The Question Repository is the location of all questions for class homework, test items, or other class problem material.

Four types of users interact with Maple T.A.:

• System administrators manage classes and users.

• Instructors create questions and assignments.

• Proctors validate student identity and grant assignment access.

• Students complete assignments created by instructors.

System administrators can create, modify, and delete classes. They can also create, modify, and delete users individually or by uploading a roster.

Instructors control the rules and policies for assignments, which can range from self-study and homework sessions to proctored exams. Once satisfied with the questions and rules in the assignment, it can be published for use by students. Instructors control availability and due dates, and set grading parameters. Grades are automatically recorded in the system Gradebook and, if necessary, these grades can be changed.

Proctors can log in to validate a student's identity prior to administering a proctored exam.

Students logged in to the system are allowed to register in your class, take assignments as you make them available, and review the results of assignments they have completed.

Once you log in to the Maple T.A. system, you can access your Maple T.A. class or classes. This is where all system interactions occur for instructors,

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proctors, and students. A class contains questions, assignments, resource files, and the class gradebook.

Assignments

Maple T.A. has a variety of assignment types, including:

• Self-study practice

•Mastery

• Homework and quizzes

• Proctored exams requiring student validation

When an assignment is created, you specify the questions to be used, as well as assignment access and feedback parameters. After determining the content (questions), rules, and policies, you publish an assignment to the class web site for use by students. Students can review the results of any previously completed assignments.

Gradebook

After students complete an assignment, you can view the results in a Gradebook or create downloadable performance reports.

With Maple T.A., you can generate comprehensive performance reports for individual students and assignments, classes, or multiple assignments. You can also perform statistical item analysis of questions.

1.2 Logging On

Log in to the system using the username and password your system administrator has provided. The main system page is called the System Homepage. The System Homepage provides access to the classes you are teaching, and those in which you are a student or proctor.

If the system administrator has created a class for you, your class will be listed under the Classes I Am Instructing section on your system homepage. You can click on the class name to navigate to the Class Homepage.

If your system administrator has not created a class for you, you can create a class.

1.3 The Class Homepage • 3

1.3 The Class Homepage

Instructors access the Class Homepage to:

• Create and edit questions

• Create, publish, and manage assignments

• Access a gradebook that records student work and assignment results

Figure 1-A Class Homepage

From the System Homepage, click the link to your class to open the Class Homepage. The Class Homepage displays the class and instructor name, and

the list of assignments, quizzes, and tests that you have posted.

The assignment list displays the name and type of assignment, associated points, availability (that is, scheduled dates and times), and specific policies in the assignment (for example, time limit). Click the listed assignment name to launch the assignment.

The following menu items are available from the Class Homepage.

• Actions -> Class Info, Add Child Class, User Manager, and Proctor Tools

• Content Manager -> Assignments, Question Repository, Course Modules, and Web Site Editor

• Gradebook -> Open, Add External Assign.

• Help -> Instructor, Other Help -> Proctor, Other Help -> Student, Getting Started, and About

• Logout

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1.4 Creating a Class

Both instructors and administrators have sufficient privileges to create unique (new and empty) classes or ones based on shared material.

Creating a new class

1. Start at the System Homepage.

2. From the Actions menu, select Administer Classes (System Administrators only).

3. From the Actions menu, select Add Class.

4. Complete the class registration form. Detailed information on available fields is provided here:

Course ID

Select a unique string of letters and/or numbers as the Course ID.

Class Name

Select a unique name for your class. This name is displayed as the link to your Class Homepage. The class name should be between 5 and 50 characters long. It cannot contain the characters <, >, or &.

Instructor

Your name will be automatically entered in this field.

School

Enter the name of your school.

Description URL

Optional. If you have created a web page with additional information for your class, you can link to the page by providing the URL.

Registration Locked

Open registration allows students in the system to enroll themselves in your class. The default setting is locked, and students will not be able to enroll themselves into your class unless you unlock registration by clearing the check box.

Featured Class

Marking the class as a Featured Class allows the creation of child classes based on this class. This allows you to share assignments, quizzes, tests, and other resources. with other classes by adding an entry to the Inherited Content From drop down menu.

Inherit Content From

You can inherit content from a parent class. This gives you access to already created assignments, quizzes, tests, and other resources.

1.5 Adding Users to the System • 5

5. Click Submit. A summary of the class details is displayed.

Creating a copy of a class

1. From the Class Homepage of the class you want to share, select the Actions menu, and then select Add Child Class.

2. By default, you are listed as the instructor for the new class. Click the Change Instructor link to select a different instructor.

3. Enter details of the instructor you are searching for and click Search. Alternatively, you can search for the instructor in the list of registered users.

4. Select the instructor and click Update. The name of the instructor should be displayed.

5. Complete the Class Registration form and click Submit.

1.5 Adding Users to the System

System administrators and instructors that have create privileges can add users to the system. Users can be created from a roster (to add a large number of users at once) or individually. The system administrator can set up the system to allow students to create user accounts for themselves, but you have more control and the data will be more consistent if user accounts are created by a few chosen individuals.

User Rosters

User rosters are a convenient method to add a large number of users at once. Rosters are easily created and updated. Large numbers of users can also be removed using batch removal.

Creating a Roster

The user roster must be a comma-separated file (for example, *.csv) or tabseparated file (for example, *.tsv) that has one line for each user. The first line must be a header row that specifies the data contained in each column. The headers can be in any order, to make it easy to match your existing format.

The acceptable fields in the roster are as follows:

The corresponding header row values for these are as follows:

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• The fields that are underlined are required.

• Login must be at least one alphanumeric character.

• First Name must be at least one alphabetical character.

• Middle Initial must be no more than one alphabetical character.

• Last Name must be at least one alphabetical character.

• Email addresses must be unique.

• Student IDs must be unique.

• Student ID must be at least five alphanumeric characters.

• Password must be at least five alphanumeric characters.

• If no password is provided, the system generates one which is displayed on the next page. You can print or save this page. If it is not printed or saved, the automatically generated login and passwords will be lost.

• Role can be Administrator, Instructor, Proctor, or Student. The role specified cannot exceed the level of the user who is creating the roster. The default is Student.

• Validate is a yes/no field and determines whether students have to review their data on first login and validate it. The default setting is ‘yes’.

• If you have a null field (for example, a student did not provide a middle initial), use two consecutive delimiters.

Note: If the header row includes Email and Student ID, you cannot have empty values for those fields in the rows of student data. If there are some students who do not have either an email or a student ID, you should use the value <Null>.

Uploading a Roster

You upload a user roster from the System Homepage. This will register users in the system.

1. From the System Homepage, click Actions and select Administer Users.

2. From the Actions menu, select Roster, and then Import.

3. To locate your class roster, click Browse. Navigate to the file and click Open.

4. From the drop-down menu, select the type of file being submitted as either Comma-separated or Tab-separated.

5. Click Submit. A table is displayed that includes all columns and information in the file.

6. Click Enroll Roster. A roster upload summary is displayed.

1.5 Adding Users to the System • 7

Updating a Roster

User rosters can be updated by importing rows with Login values that are already present in the Maple T.A. database. If an import row specifies a Login that already exists and an LDAP system is being used to maintain the database, then the user profile attributes are refreshed from the LDAP system. In this case, the only column required in the import row is the Login column. In other cases, the behavior is as follows:

• The imported attributes overwrite the corresponding attributes in the Maple T.A. database.

• Empty attributes are ignored and do not overwrite existing information. An attribute is empty if it is delimited by successive commas or tabs with no intervening character.

• An attribute may be overwritten to null by providing the special Maple T.A. string <Null> as its import value.

• An attribute that is specified as one or more spaces will be trimmed and will overwrite the database attribute with an empty string (different from a null value).

• Attribute values not included in the import (that is, with no column in the import) are not modified in the database.

Batch Removal

Large groups of students can be removed from the system at once using a special type of import. In this case, only the Login column of the import file is used or required.

1. From the System Homepage, click Actions and select Administer Users.

2. From the Actions menu, select Roster, and then Delete.

3. Select the radio button to determine if the users will be “permanently deleted (cannot be restored)”, or “marked as deleted (can be restored)”.

4. To locate the roster for batch removal, click Browse. Navigate to the file and click Open.

5. From the drop-down menu, select the type of file being submitted as either Comma-separated or Tab-separated.

6. Click Submit. A table is displayed that includes all information in the database for the users selected.

7. Click Delete Roster. A roster validation summary is displayed.

Users that are “permanently deleted” are removed from the entire system, along with any assignment answers or grades owned by those users. Users that are “marked as deleted” are moved to a separate database within the system and no longer have access to the system, but all of their information is

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stored. They can be restored later by doing a search for deleted users in the Administer Users page, selecting the check boxes beside their names and clicking Restore. Permanently deleted users will not show up on a search for deleted users.

Adding Individual Users

You can also add users to the system individually. This is useful for adding a small number of users.

1. From the System Homepage, click Actions and select Administer Users.

2. From the Actions menu, select Add User.

3. Fill in the form.

4. Click Submit.

1.6 Registering Users in a Class

Before the Gradebook can begin tracking student performance, it must have students registered in the course. You can register students in a class by:

• Using the User Manager

• Allowing students to register themselves for your course

• Creating and uploading a class roster

To register students in your course, they must have an account in the system. Creating user accounts is usually done by the system administrator, although the administrator can give instructors the ability to create user accounts. In addition, the system administrator can set up the system to allow students to create their own user accounts.

The User Manager

You can select students to register in your class from a list of system users. All the students you want to register must already have an account in the system. You can search the list for a user that satisfies particular criteria.

1. From the Class Homepage, click Actions and select User Manager. From the Actions menu, select Register Users.

2. Enter search criteria to narrow the list of users down or to search for a particular student.

3. Select the checkbox beside the students you want to register in your class.

4. Click Register.

1.6 Registering Users in a Class • 9

Student Self-Registration

Students can register for your class using the Find classes open for registration link on the System Homepage. The student selects the class he

or she wants to enroll in, and clicks Register. The student then clicks Confirm and must complete the form on the Student Registration screen.

You can lock access to this form of registration from your class homepage. From the Actions menu, select Class Info, click Edit, and select the

Registration Locked check box.

Class Rosters

Creating a Class Roster

A class roster has the same format as a user roster. See “User Rosters” on page 5.

Uploading a Class Roster

You can upload a class roster from your Class Homepage. This will register users in the system as students in your course. If you have create privileges and the user is not already in the system, a new account will be created.

1. From the Class Homepage, click Actions and select User Manager. From the Actions menu, select Roster, and then Import.

2. To locate your class roster, click Browse. Navigate to the file and click Open.

3. From the drop-down menu, select the type of file being submitted as either Comma-separated or Tab-separated.

4. Click Submit. A table is displayed that includes all columns and information in the file.

5. Click Enroll Roster. A roster upload summary is displayed.

As discussed in the User Rosters section, system administrators and instructors with create privileges can also import users from the System Homepage. This will add students into the Maple T.A. system, but you will still need to register the students into a course.

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2 Sharing Content

Sharing content is an important part of using a system like Maple T.A. effectively. Sharing content makes a wider range of questions and assignments available to all users. You can share questions, assignments, and resources in a variety of ways, from choosing specific content to providing access to all the content in a class.

2.1 Sharing Questions

Questions are owned by a class. The creator of a question becomes the default owner of the question. Questions can only be modified by the owner.

Child classes automatically inherit questions from their ancestors.

Instructors can obtain question material for their groups in one of three ways:

1. Create a question. The instructor becomes the owner of this question.

2. Inherit a public question from an ancestor class. Instructors can use the question in their assignments, but cannot modify the question. Only the original owner (creator) of the question will be able to modify the question, and those changes will be automatically propagated to all subscribers' question groups. This is similar to the Question Bank inheritance rules in Maple T.A. 4.0.

3. Shadow a public question from another class. Instructors can use the question in their assignments, but cannot modify the question. Only the original owner (creator) of the question will be able to modify the question, and those changes will be automatically propagated to all subscribers' question groups.

4. Clone a public question from repository. This operation creates a local copy, or clone, of the public question and sets the owner to the instructor

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who made the clone. Only this subsequent instructor will be able to modify the cloned question. All changes made to the original public question will not be visible in cloned questions.

The Inherit, Shadow, and Clone methods have disadvantages:

• When instructors Inherit or Shadow a public question, they should expect it to be modified by the question owner at any time without notice; however, the question most probably will be a valid question with all resources (images, etc.) in place.

• When instructors Clone a question, they can be sure that it will not be touched by anybody, but there is a danger of losing resources (images, etc.) because the cloning process does not copy the resources to the instructor's web space; therefore, they can be deleted any time by the original author of the question.

To create a question:

1. Click the Question Repository link from the menu bar.

2. Click Questions, then New Question.

3. Create the question and add it to one or more Groups.

To share a question:

1. Find the question that you wish to share.

2. Click the share button or click the checkbox beside the questions you wish to share and then click Make Public.

To shadow a question:

1. Click the Public Questions link.

2. Use the search methods available to find the public questions that you wish to use.

3. Add the question to one or more of your question groups by clicking the modify button

or by clicking the checkbox beside the questions you wish

to use and then clicking Add To Groups.

To clone a question:

1. Use the search methods to find the questions (Public or Private) that you wish to clone.

2. Click the clone button or click the checkbox beside the questions you wish to share and then click Clone.

Inherited questions automatically appear in a class’ repository as they are created.

2.2 Course Modules • 13

2.2 Course Modules

If you want to share not just your questions, but also images and assignments that you have created based on those questions, you should use course modules. Once you create a course module, you can send it to other instructors who can upload it into their classes and use it as is or alter it to better suit their needs. Course modules can be uploaded to other installations of Maple T.A., not just the one at your institution.

Note: Only local content can be included in a course module. If you are inheriting content from another class, you will not be shown the inherited content in the course module creation screen.

Figure 2-A The Course Module main menu screen enables you to create, import, export, or delete course modules and their contents.

To share content using course modules, first create a course module by choosing the items you want to include. Once you have created the course module, you can save the course module file ( send that file to other instructors.

To create a course module:

1. Log in as an instructor and click on the class that contains the content you want to share.

2. Click Content Manager, then Course Modules.

3. Click New.

4. Select the question banks, assignments, and web folders that you want included in the course module. Click OK.

5. Enter a name for the module. Optionally, enter a description for any of the items you have included in the module. Click OK. The course module now appears in the list of course modules for your class.

.zip) to your computer and then

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To export a course module:

1. Log in as an instructor and click on the class name that has the course module you want to export.

2. Click Content Manager, then Course Modules.

3. Select the checkbox beside the course module you want to download and then click Export.

4. The following screen allows you to add URLs that you want changed. In most cases, the default URLs are the only ones that need to be updated. Click OK.

5. Once the course module is created and ready for download, you will see a link click here to start the download. Click that link to open the file download dialog.

6. Click Save, then browse to the location where you want to save the file. Enter a new file name or use the existing name of the course module and click Save.

7. Once the download is complete, click Close. You are returned to the download screen.

8. Click Return to go back to the Course Modules menu.

When you receive a course module, you need to import and install it or pieces of it to the desired class.

To import a course module:

1. Log in as an instructor and click on the class in which you want to import the content.

2. Click Content Manager, then Course Modules.

3. Click Import.

4. Click Browse… to locate the course module file (.zip) on your computer.

5. Click Import. The system will display the question banks, assignments, and web resources from the course module. If there are items that use the same name as those in your class, they will be highlighted in yellow on the upload screen.

6. Select the checkboxes beside the items you want to install and click Install. The selected items are installed in your class.

If you have uploaded a course module and decide that you no longer want to keep it, you can delete it. You can do one of two things: delete just the course module name from the list of course modules; or, delete the course module name from the list and all or part of its content from your class.

2.3 Child Classes • 15

To delete a course module:

1. Log in as an instructor and click on the class name that has the course module.

2. Click Content Manager, then Course Modules.

3. Select the checkbox beside the course module you want to delete and then click Delete. This will remove the course module name from the list of course modules, but it will not delete the content of the course module from your class.

4. You will receive a warning. Click OK to delete the course module name from the list.

To delete course module content from a class:

1. Log in as an instructor and click on the class name that has the course module.

2. Click Content Manager, then Course Modules.

3. Select the checkbox beside the course module you want to delete and then click View Details.

4. Select the checkboxes beside the items that you want to remove from your class and click Delete.

5. You will receive a warning. Click OK to delete the course module name from the list and the selected content from your class.

2.3 Child Classes

If you have a class that contains content that you want to share with other instructors at your institution, you have the ability to share the entire class. The benefit of sharing the class rather than providing a course module is that there is a link between a parent class and any child class. Child classes will automatically get any changes that you make to the parent class content. With a course module, there is no link between your class content and the class in which the course module is uploaded.

Creating a child class can be done by an instructor or an administrator.

To create a Child Class:

1. Log in and click on the class you want to share.

2. Click Actions, and then Add Child Class.

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3. Click Change Instructor and then browse the user list or use the search panel to find the user who will be the instructor for the child class. Select the radio button beside the user and click Update to change the instructor.

4. Enter the information in the registration form and click Submit. You will get a notice that the class was created.

2.4 Featured Classes

If you have a class that will be used by many instructors or from year to year, you may want to create a featured class. A featured class is similar to a shared class as described in the previous section. The main difference is that a featured class will appear in the drop-down list of classes from which you can inherit content when a new class is created.

To create a Featured Class:

1. Log in as a system administrator.

2. Click Actions, and then Administer Classes.

3. If the tree view is showing, click Table View.

4. Click the Open link for the class that you want to make a featured class.

5. Click Edit.

6. On the Class Details page, select the checkbox beside Featured Class. Click Submit.

Propagation of Material from Featured to Child Classes

The relationship between featured and child classes allows for quick and easy propagation of material, while still allowing certain features within the child classes to be customized. Details of this relationship are as follows:

• When an assignment is created in a featured class, all child classes will receive only a copy of all assignment attributes (names, policies, restrictions, etc.). The content of the assignment will not be copied to the child classes; instead, inherited assignments will point to one copy of the assignment content stored in the featured class.

• All changes made to the assignment content in the featured class will be immediately visible in all child classes.

• All changes made to the assignment attributes (names, policies, etc.) in the featured class will not be propagated to child classes, allowing them to have their own customized set of attributes.

2.4 Featured Classes • 17

• Instructors of child classes will be allowed to modify all attributes of the inherited assignments, but will not be able to modify assignment content.

• If instructors of child classes wish to customize the content of an inherited assignment, they will have to make their own copy of the assignment.

18 •

3 Question Repository

3.1 Overview

The Question Repository is used to create, organize, and search for questions. This replaces the use of Question Banks and Topics used in Maple T.A. prior to version 5.0.

There are three methods for authoring question banks in the system:

1. Question Editor

2. Maple T.A. .qu plain-text script files

3. LaTeX files that can produce math-intensive questions formatted to Maple T.A. specifications

This document discusses using the Question Editor. For information on authoring questions banks using the other two methods, refer to the Maple T.A. help system.

3.2 Question Editor

To create a question using the Question Editor:

1. Click the Question Repository link from the menu bar.

2. Click Questions, then New Question.

20 •

Figure 3-A Question Editor - New Question

3. Enter the content of your question. Examples are provided in the Example Questions on page 21.

Figure 3-B Entering a Question

4. Once you have completed the question, click Finish.

5. Choose the groups (if any) that you wish the question to belong to and click Submit.

3.3 Example Questions • 21

6. A preview of the question is displayed. Provide an answer and click Grade to see how the question is graded. Click Edit to continue refining the question as necessary.

Maple T.A. provides the following question types:

• Mathematical & Scientific Free Response Question Types (14 varieties including formula, numeric, and questions that use the Maplesoft™ Maple™ mathematical software to grade and plot student responses)

• Multiple-choice (permuting and non-permuting)

• Multiple-selection (permuting and non-permuting)

•True-or-False

• Ungraded Essay

• Fill-in-the-blank including text region or drop down menu

• Question Designer

•Key Word or Phrase

•List

• Clickable Image

• Short Phrase

•Matching

• Multipart Questions (consisting of parts that are of any question type; can be nested)

• Palette Questions (using a programmable palette of symbols for the entry of student responses)

• Questions with applet interaction

• Questions using web references / objects (including plots)

3.3 Example Questions

This document discusses three question types: Question Designer, Maplegraded, and List. You are guided through the process of designing a simple multiple-choice question using the Question Designer, followed by editing the previous question to incorporate randomly determined parameters. You will also learn how to insert 2-D math into your question. Creating a Maplegraded question, inserting plots into the Maple-graded question, and a creating List question will also be discussed.

22 •

The Question Designer

The Question Designer provides a flexible format for creating free response questions that can include multiple response cells. These questions are similar to multipart questions in that they provide a shell structure in which to embed other questions.

The Question Designer is an authoring environment as familiar as your word processor. Using the Question Designer, you enter question text and the correct answers wherever they should appear. Many formatting options such as bold, italics, and fonts are available through the text editor icons. You can also insert images, tables, or links to other file resources.

When you are satisfied with the appearance of the question, you define answer regions, or Response Areas, and then apply grading and other behaviors. Like all questions in Maple T.A., you can insert algorithmic variables and inline math expressions as required.

Figure 3-C Question Designer

From the Question Designer, you can launch the Response Area window, which allows you to define the question type, weighting, grading behaviors, display behaviors, and correct answers. You can define additional behaviors according to the individual question mode you select. Additionally, you can add feedback, algorithms, hints, and solutions.

At the top of the Question Designer is the toolbar which includes the unique

Insert/Edit Response Area button that you use to activate the Response Areas defined in your question.

3.3 Example Questions • 23

Figure 3-D Insert/Edit Response Area

The Question Designer supports the following question types:

• Formula Question Types: Formula, Formula Mod C, Restricted Formula, Equation, Vector of Formulas, and Chemical Equation

• Maple-graded Question Types: Formula and Maple Syntax

• Multiple-choice, Non-permuting Multiple-choice (displayed horizontally or vertically)

• Numeric Question Types: With and without required unit dimensions

• List Questions, including text or menu input styles, exact or relaxed graders, multiple correct or incorrect responses can be specified, partial credit can be defined for each response

• Essay Question

The following provides instruction for creating a simple multiple choice question using the Question Designer. In addition, navigating, previewing, and enhancing the appearance of a question are discussed.

Multiple-choice Question using the Question Designer

To use the Question Designer:

1. Select Questions, then New Question.

2. Select the Question Designer question type from the Question Type menu.

3. Enter "Multiple-choice" in the Question Description field.

4. Click Next. The Question Editor opens the Question Designer.

5. In the Text of the question field, enter the following:

Question: What is 17 + 9?

24 •

6. Click the Insert/Edit Response Area button to launch the Edit Response Area window.

Figure 3-E Edit Response Area

7. Select Multiple-choice in the left pane.

8. Select Permuting in the Permute Choices row.

9. Highlight and delete choice 1 and enter 26.

10.Highlight and delete choice 2 and enter 27.

11.Press Enter to display a third multiple choice option.

12.Enter 23. Now that you are finished entering choices, click OK.

13.Click the radio button beside the correct answer to mark this answer as correct and click OK.

14.Click Finish. The Question Editor>Preview Question window opens, displaying the question as it appears to the student.

3.3 Example Questions • 25

Figure 3-F Multiple-choice Question Preview Window

To test and review your question:

1. In the Question Editor>Preview Question window, select the correct answer (26) and click Grade. The Preview Grade window opens. A Correct icon is displayed along with your answer matching the correct answer. Click OK to close this window and return to the Preview Question window.

2. Again in the Preview Question window, select an incorrect answer (23) and click Grade. The Preview Grade window opens. An Incorrect icon is displayed along with your answer and the correct answer. Click OK to close this window and return to the Preview Question window.

In the next example, the Multiple-choice question created in the previous example is extended by specifying algorithmic variables, hints, solutions, and feedback.

Multiple-choice Question with Randomly Determined Parameters

Specifying algorithmic variables allows you to generate a question that changes each time you view it. Because values in the question are randomly

26 •

determined for each instantiation, students answer variations of the same question.

Figure 3-G Question Editor with Algorithmic Example

To specify algorithmic variables:

1. In the Preview Question window, click Edit. The New Question window opens.

Note: This procedure will overwrite the first question and not create a new one.

2. In the Question Description field, change the description to "Multiple- choice Enhanced".

3. Click Next. The Question Designer window displays.

4. Select the Algorithm tab and click Edit.

5. Enter the following code in the text box:

$a=range(10); $b=range(10); condition:ne($a, $b); $sum = $a + $b; $product = $a*$b;

• The range(n) function generates a random integer in the range 1,..., n (inclusive). There are n numbers in that range. Hence, it is a selection of one number from a choice of n.

• The condition:ne function ensures the two variables are not equal.

• $ is required to indicate a variable.

• The question variables are set to $a and $b. These will range from 1 to 10. The answer is set to $sum, which is the integer value of $a+$b.

• As this question is multiple-choice, you must generate wrong answers to be displayed alongside the correct answer. For variation, the wrong answer variable $product is set to the randomly generated variable $a*$b.

3.3 Example Questions • 27

• All lines end with a semicolon.

6. Click Save. The Question Designer window is displayed.

7. Select the Feedback tab and click Edit. The Edit Feedback window opens.

8. Enter the following text in the feedback text field:

The sum of $a and $b is $sum.

Note: As the instructor, you can choose to have this information shown to students when they view their graded assignments.

9. Click Save. The Question Designer window is displayed.

10.You must now edit the text of the question and the answer choices to use the variables. In the Text of the question field, replace:

What is 17+9?

with

What is $a + $b?

11.Double-click Edit below the multiple choice options and replace the previous answers with the variables $sum and $product.

12.Delete the third option by clicking the Back Space key.

13.Click OK.

14.Ensure that the $sum variable is selected to be the correct answer.

15.Click OK to return to the Question Designer window.

16.Click Finish. The Preview Question window opens. Test the question by selecting an answer and clicking Grade.

Note: Using the Question Designer, you can add feedback, algorithms, hints, solutions, and information fields in the same interface as the question text as illustrated in this example. You can also add these fields in the New Question screen by selecting Edit beside each field. For all other question types, the New Question window is the only place to add these fields.

The following example provides instruction for creating a multiple choice question using the question designer to determine a square root.

Multiple Choice Question Incorporating 2-D Math

1. Select Questions, then New Question.

2. Select the Question Designer question type from the Question Type menu.

3. Enter "Multiple-choice with 2-D Math" as a description in the Question

Description field.

28 •

4. Click Next. The Question Designer window displays.

5. In the Text of the question field, enter the following:

What is

6. Click the Sigma button to insert 2-D math. The Equation Editor opens.

7. Right-click in the Equation Editor field. From the displayed palettes, select a square root symbol. The symbol is displayed in the Equation Editor.

Figure 3-H Equation Editor

8. Replace the "a" in the square root with 144 and click OK. The square root of 144 is now displayed in the text region in the Question Designer.

9. After adding a question mark to complete the question, click the Insert/Edit Response Area icon.

10.Select Multiple-choice in the left pane.

11.Select Permuting in the Permute Choices row.

12.Enter 12, 14, 72, 13, and 15 as possible answers, one for each field.

13.Click OK.

14.Click the radio button beside the 12 to mark this as the correct answer and click OK.

3.3 Example Questions • 29

15.Click Finish. The Question Editor>Preview Question window opens, displaying the question as it appears to the student.

Figure 3-I Multiple choice question incorporating 2-D math preview

Maple-Graded Question

The Maple-graded question type uses Maple to evaluate a student response and to render a plot of the student's response. The Maple-graded question type gives you access to the computational power of Maple. It includes facilities for algebra, calculus, differential equations, discrete mathematics, graphics, numerical computation, and many other areas of mathematics. You can also use Maple to create questions whose responses require sets, differential equations, unevaluated integrals, and many other types of mathematical data. You can find common errors and reward partial marks.

With the Maple-graded question type, you also have access to the plotting capabilities of Maple. You can use Maple to plot a student response (or a function derived from a student response, such as the definite integral of the student response) for a Maple-graded question type. You can also use Maple to display a plot for any question type.

You must adhere to the following guidelines when using Maple code for Maple-graded questions:

• A Maple-graded question must use valid Maple code to evaluate the answer. Complete each line of code with a semicolon. For information on Maple code, refer to your Maple system documentation.

• The grading code must evaluate to a Boolean value or a floating-point number between 0 and 1.

• Use the long form name for all package commands, for example, VectorCalculus[ArcLength].

• Maplet applications are not presently accessible in Maple T.A.

30 •

Figure 3-J Question Editor - Maple-Graded Question

To create a Maple-graded question:

1. Select Questions, then New Question.

2. From the Question Type menu, select Maple-graded.

3. In the Question Description field, enter "Differentiation".

4. Click Next.

5. Enter the text of the question field:

Differentiate sin(x) * x with respect to x.

6. Enter Maple code that evaluates to the correct answer:

diff(sin(x)*x, x);

7. The following Maple code to grade the student response is provided automatically:

evalb(($RESPONSE)-($ANSWER)=0);

3.3 Example Questions • 31

$RESPONSE is a system variable that corresponds to the response the student entered when completing the question and $ANSWER refers to the correct answer you entered in step 6.

8. By default, the Maple-graded question type accepts Formula expressions. In Maple-graded Formula question types, students can enter a math formula, that is, an expression constructed of numbers, variable names, and the standard arithmetic expressions and functions. The student must not use Maple commands in the response. The instructor must write code such that the student does not have to use a trailing semicolon in the response. For details, refer to the Maple T.A. Help system.

9. Scroll to the top of the page and click Finish.

10.Enter the correct answer, cos(x)*x+sin(x), and click Grade.

Plotting the Student's Response

Using the Maple-graded question type, you can generate a plot of the student's response. This allows students to visually check their response before proceeding.

To plot the student's response:

1. Click Edit, and then Next. The Question Editor>Edit Question>Maple Graded window opens.

2. Scroll to the bottom of the question. Using a standard plot command in Maple, enter the student's response as well as the derivative of the question. If the student is correct, the plot region will display a plot with a single curve. In the Plotting field, enter:

plot([$RESPONSE, diff(sin(x)*x, x)], x=-10..10);

$RESPONSE is a system variable that corresponds to the student's response.

3. Scroll to the top of the screen and click Finish.

4. Test the question by entering a response and selecting the Plot link. The plot is displayed in a separate window.

Inserting a Maple Plot in the Question Feedback

You can also insert a Maple generated plot in the question text, hints, or feedback of any type of question.

To insert a Maple plot as an algorithmic variable:

1. Click Edit to edit the current question.

32 •

2. Click the Add button in the Algorithm section.

3. Enter the following:

$plot1=plotmaple("plot(sin(x)*x, x=-10..10)");

4. Click Save. You can use the algorithmic variable $plot1 to display the Maple plot in all question types anywhere algorithmic variables can be used (that is, in the question text, hints, and feedback).

5. Click the Add button in the Feedback section.

6. Enter the following:

A plot of the expression is $plot1.

7. Click Save.

Apply Partial Grading to Maple-graded Questions

You can modify Maple-graded questions to allow grading between 0.0 and 1.0 for part marks. The following is a simple application of partial marks. In solving they made this error, but divided by 3 properly, they would get a result of 6. In this case, the instructor can give them half marks by using the grading code shown below:

3x 6+12= x

for , students may add 6 to 12 instead of subtracting it. If

Text for the question

Maple code that evaluates to the correct answer

Maple code to grade the student response

See Chapter 8 for more in-depth coverage of the Maple-graded question type.

Solve for x in the following equation: 3x+6=12

solve(3*x+6=12,x);

if ($RESPONSE=6) then 0.5 else evalb($RESPONSE($ANSWER)=0 end if;

List Question using the Question Designer

To create a List question:

1. Select Questions, then New Question.

3.3 Example Questions • 33

2. Select the Question Designer from the Question Type menu.

3. Enter "List" as a description in the Question Description field.

4. Click Next. The Question Designer window opens.

5. In the Text in the question field, enter the following question:

Who introduced the Arabic number system to Europe?

6. Click the Insert/Edit Response Area button to launch the Edit Response

Area.

Figure 3-K Insert/Edit Response Area Button

7. In the Choose Question Type area, click List.

Figure 3-L List question type using the Question Designer

8. The default Matching Type is set to Exact text match which applies strict grading, case-sensitive, literal string-matching as your grading mode. To invoke a less stringent grader that ignores case sensitivity and

34 •

punctuation, select Ignore case text match. The List mode also provides a regular expression-matching grader, useful for customization of the grading routine. These fields are applicable when the Display mode is set to Text Field, which presents students with a blank response area. For this example, select Drop-down Menu. Ensure the Permute list check box is selected.

9. Enter answer choices in the Item fields. To add additional items, click the Add Item button.

10.As you add possible answers, the system assigns them a credit value of "0.0" in the right column. Additional answers are graded as fully correct ("1") or partially correct answers (with any value between 0 and 1 assigned). Edit the weight for Leonardo Fibonnaci and enter 1.0.

11.Click OK to exit the Edit Response Area window.

12.Click Finish to exit the Edit Response Area window.

13.Click the Finish button at the top of the Question Designer. The Question Bank Editor displays the question as it is viewed by students.

Numeric Question using the Question Designer

1. Select Questions, then New Question.

2. Select the Question Designer from the Question Type menu.

3. Enter "Question Designer Numeric" as a description in the Question Description field.

4. Click Next. The Question Designer opens.

5. In the blank text area, enter the following question:

Round 2.76789 m to three significant digits.

6. Click the Insert/Edit Response Area button (check mark symbol) to launch the Edit Response Area window.

7. In the Choose Question Type area, select Numeric.

8. Enter the correct answer "2.77" in the Numeric Part field.

9. Click the blank field next to the Units Part field and enter a required unit dimension for the correct answer (in this case, m for meters.) If you do not enter a required unit dimension, the system displays only a single response cell that accepts only numbers for student answers. If you do enter a required unit dimension, students are presented with two cells: one for the number part and one for the unit dimension. The student must enter correct values in both cells to receive full marks for the question.

10.To set the margin of error, click the Required with menu, which is set to Absolute Accuracy by default. You can specify absolute precision (student

3.4 Downloading Questions • 35

answers must match the defined answer exactly), or a significant figure precision for an exact answer match.

11.Modify the tolerance by choosing one or more of the numeric formatting options. The available options are:

• Absolute Accuracy

• Set # figures

• Margin of error

• Margin in n'th digit

• Percentage margin.

12.Click OK and then Finish to save and preview the question.

Equation Editor

You can enter symbolic math in any question type. In the Add Question Text window, (this window usually displays after the Question Editor>New Question window for each question type), click the Sigma toolbar. The Equation Editor dialog opens. Right-click to access the palettes.

Figure 3-M Enter symbolic math

button in the

3.4 Downloading Questions

To back up questions by downloading to your hard drive:

1. From the Question Repository, find the questions you wish to save.

2. Select the checkboxes next to the questions.

36 •

3. Click Export. The files are saved as testbank.qu.

4. A message is displayed indicating the download is complete. Click Close.

You can import the saved question bank file (plain-text script file), and then continue editing or install it in your class.

To open a question bank file that was downloaded to your hard drive:

1. From the Question Repository, click Questions, then Import Question Bank

2. To locate your file, click Browse.

3. Navigate to the source file on your hard drive and click Open. The path and filename are displayed in the Question Bank field.

4. Select how the questions will be organized when importing.

5. Click Import. The topics are displayed in the left panel of the Question Bank Editor.

6. Save your imported question bank. From the Actions menu, select Save Question Bank.

When you upload a question bank file into the system, it performs a set of validation routines to ensure that the questions function. Occasionally, you may encounter an error with a variable name or definition upon uploading. The following is a summary of the system's analysis of variables upon initial loading of a question bank file.

• For variables displayed within HTML text, for example, in a question statement or feedback area, a problematic variable does not produce a data value generated from its definition. Instead its variable name is displayed, highlighted in red.

• For variables appearing in non-displayed field parameters, for example, the answer to a question, the variables $ANSWER and $RESPONSE default to 0. All others have the variable name passed.

4 Assignments

4.1 Overview

Assignments are created by selecting questions from the Question Repository. The assignments you create can be organized such that Maple T.A. reorders questions, generates questions, or displays a subset of questions. Each student viewing your assignment can potentially complete a unique set of questions.

The Assignment Editor allows you to create new assignments, edit the content, properties, and appearance of existing assignments, delete assignments, and change the order of existing assignments.

Assignment Editor Main Menu

From the Class Homepage, click Content Manager and select Assignments. From the Assignment Editor main window, you can:

•Click New to create a new assignment.

• Reorganize the order of displayed assignments using the numbered list beside each assignment.

• Open assignments for editing by clicking the assignment name link.

To activate other options, hover your mouse over the assignment name. Six option buttons are displayed.

• Edit assignments by clicking edit.

• Copy assignments by clicking copy.

• Delete assignments by clicking delete.

• Hide/show assignments from student view in the Class Homepage by clicking hide/show.

38 •

• Print assignments. Clicking the print link displays the print preview of the assignment. You then have the option to print the assignment or click Back to return to the Assignment Editor.

• View a summary of the assignment by clicking summary.

Figure 4-A Assignment Editor

The Assignment Editor main menu lists assignments created for your class. These assignments may be populated with a series of assignments based on testing materials or other shared questions. If not, you initially see a blank list here. For more information on shared classes, see

Chapter 2.

Warnings and Locking Mechanism

When an assignment is opened for edit, the system checks and warns the instructor whether the assignment has associated student records in the Gradebook or is currently in use by a student.

Note: The number of students currently using the assignment is displayed in the Active field of the Assignment Editor main menu.

• If the assignment is currently in use, the questions in the assignment are locked so that an instructor cannot edit them. You can edit some of the policies of the assignment like the time limit for example.

• If the assignment is not currently active, the assignment is locked for editing so that new active tests cannot be started during the editing process. Students who try to start the assignment while it is locked are notified with a warning message.

4.2 Creating Assignments • 39

4.2 Creating Assignments

The Assignment Editor organizes assignment creation into a four step process.

1. Naming your assignment

2. Selecting questions

3. Establishing rules and policies

4. Reviewing, finishing, and publishing assignments to your class

To start a new assignment:

1. From the Assignment Editor screen, click New to begin a new assignment. The Assignment Editor displays four tabs: Choose Name, Select Questions, Set Policies, and Review & Finish.

2. Proceed to the instructions in Naming Assignments.

4.3 Naming Assignments

The assignment name is displayed to students on the Class Homepage.

To name your assignment:

1. In the Choose Name tab, enter a name for your assignment in the Choose A Name For Your Assignment field.

2. Optional. Click the Advanced button. Add assignment-level page headers and text for the results page in the appropriate fields.

3. Proceed to the instructions in Selecting Questions.

4.4 Selecting Questions

The Select Questions tab of the Assignment Editor allows you to select questions (individually or as a group) from the question repository, assign question weighting, scramble the sequence of delivery, and merge individual questions to form specific question groups.

To select questions from the repository:

1. In the Assignment Editor, click the Select Questions tab.

40 •

2. From the Question Group list, select a source question bank.

3. If required, expand the topic lists and select the questions you want from the list on the left using the check boxes. Click the Add button after selecting a question or complete the selection process and click the Add As Items button. In either case, individual questions are added to your assignment.

4. Optional. To add a selection of items as a group, select questions using the check boxes. Click Add As Group to include them as a pool of questions within your assignment.

5. Optional.

• Change the default question weighting (one point per question) to match your requirements.

• Select Scramble questions to randomly order the questions when assignments are created.

• Reorder questions within your assignment by using the drop-down lists.

• Merge individual selected questions to form new question groups in your assignment.

6. Proceed to the instructions in Setting Policies.

Individual Versus Grouped Questions

Individual Questions If you add selected questions to your assignment as

individual questions, each one is included in every version of the assignment served to a student, and you control question weighting individually.

Question Groups Adding questions in question groups provides you with the added option of selecting a group of questions and having the system select from the questions at random, according to criteria you specify (for example, choosing three of seven questions from the group each time a new assignment is created for a student). You set a single point value that is applied to every question in the group.

4.5 Setting Policies

In the Set Policies tab of the Assignment Editor window, you can:

• Select the type of assignment

• Set feedback options for the assignment

4.5 Setting Policies • 41

• Decide when to make it available to your class

• Establish other grading policies

You can configure the number of questions on a page, create test instruction sheets and headers, and set policies for restricted access, repeated attempts, and other options.

Students answer questions one page at a time, and the system records their responses between pages. Jumping from question to question within an assignment is allowed until students complete all questions (or choose to ignore the warnings to do so) and submit their responses for automatic grading.

42 •

Figure 4-B Assignment Editor, Set Policies Tab

Assignment Types

You can create graded assessments (Homework or Quiz and Proctored Exam), ungraded practice tests (Anonymous Practice), or assignments

with set criteria (Mastery and Study Session). To take any assignment, the student must be logged in and registered in the class.

4.5 Setting Policies • 43

To set the assignment type:

1. Select one of the options in the Type of Assignment group box in the Set Policies tab of the Assignment Editor. Homework or Quiz is the system default assignment type.

2. For any assignment type, you can click the Advanced button to set prerequisite conditions.

Homework or Quiz assignments have the following format.

• Students are presented with an assignment consisting of any number of instructor-selected questions.

• Questions are delivered either in an instructor-specified or random sequence.

• Student responses during sessions are recorded after every question, so assignment sessions can be interrupted and continued upon next login.

• By default, Homework or Quiz assignments can be attempted multiple times for credit. To limit the number of attempts a student can make on a particular assignment, use Assignment Properties of the Set Policies tab in the Assignment Editor.

• Results for every attempt at a Homework or Quiz assignment are recorded in the Gradebook for the class.

Proctored Exams are similar to Homework or Quiz assignments, but with an additional security measure to confirm the identity of the student taking the test. All Proctored Exams require a proctor to authorize students submitting their test for grading. You can require proctor authorization to validate student identity and grant assignment access at the start of a proctored exam. Students must be registered in your class. They are required to provide their student login and password to access assignments in addition to proctor authorization.

There are two types of proctors: Global and Local.

• Global proctors are defined by the System Administrator and can give authorization for any class.

• Local proctors are defined by the Instructor and can only give authorization for a particular class. To set up a local proctor, navigate to the Class Homepage. From the Actions menu, select User Manager. From Actions menu, select Register Users. In the User Role row, select the Proctor radio button. Select, or search for, a user from the list of registered users and click Register.

Proctors can give authorization directly, at the student's computer, or remotely through the Proctor Tools menu. In both cases, the proctor must sign in by giving a login name and password. To give authorization remotely,

44 •

the proctor must login, select the class and from the Actions menu, select Proctor Tools.

Anonymous Practice assignments are similar to Homework or Quiz assignments; however, the students results are not recorded. Any number of questions can be included, and the assignment is delivered in an instructorspecified sequence (or scrambled). Graded assignment reports are produced upon conclusion of the assignment, but results are not recorded in the Gradebook. Students can view their results at the end of the session; no permanent record is maintained. Results can be printed, but are only available for as long as a student displays them.

Study Session assignments usually draw from a large pool of assignment material (often algorithmically generated to produce limitless question permutations). The instructor chooses the questions to include, but these assignments are delivered one-question-at-a-time, and the student submits each question for grading individually and immediately, instead of having the entire test graded at the end.

For Study Sessions, students control the study process by practicing question after question. You can provide hints and full solutions for questions to students while they work. Results are displayed one question at a time and are not recorded in the Gradebook.

Mastery assignments are similar to study session assignments, except the results are recorded in the Gradebook. These assignments usually draw from a large pool of assignment material (often algorithmically generated to produce limitless question permutations). The instructor chooses the questions to include and sets criteria for mastery. These assignments are delivered one-question-at-a-time, and the student submits each question for grading individually and immediately, instead of having the entire test graded at the end.

For Mastery assignments, instructors create carefully structured collections of questions grouped by learning objectives. The default delivery is in sequential order. You can specify additional criteria for your assignment, by clicking the Edit mastery policies link.

For a summary of assignment attributes, see the following table.

Table 1: Assignment Attributes

Assignment Typ e

Anonymous Practice

Graded

yes no yes no

Recorded in Gradebook

Hints Available

Solutions Available

4.5 Setting Policies • 45

Table 1: Assignment Attributes

Assignment Typ e

Homework/ Quiz

Mastery yes yes yes no

Proctored Exams

Study Session yes no yes yes

Graded

yes yes yes no

Recorded in Gradebook

Hints Available

Solutions Available

Feedback

You can specify which feedback elements are displayed to students when they grade an assignment. The default system behavior is to show the final assignment grade as well as question feedback, but you can switch either of these elements on or off, control access to hints during assignment sessions (before grading), or allow students to check grades while taking an assignment.

Figure 4-C Feedback

Hints

You can allow access to question hints (if they exist) in any assignment type. Hints will appear as hyperlinks below the question answer region and the student can click on the link to display the hint, if they want.

• To display hints during an assignment, select the Show hints check box.

Feedback

You can show feedback during the assignment or after it is graded, for example, displaying the grade, correct answer, or comment for each question. In the drop-down lists of the Feedback group box, select from Always, If

correct, If incorrect, or Never condition options for displaying the correct

46 •

answer and question comment. You can also restrict feedback until a certain date.

• To allow students to display a grade for each question while they are taking the assignment, select the Allow students to check grades and feedback check box.

• To display the final grade after the assignment is graded, select the Show the final grade check box. You can customize the message students receive by clicking the Edit grading message link and modifying the default messages.

• To restrict the feedback to a certain date, select the Restrict feedback until check box and enter in the date. This is very useful if you give students a certain amount of time to do a homework assignment and you don't want to the students who finish early from giving answers to other students.

Hints and Question Feedback (contained in the Comment field of a question) are not always present in the source question bank content. You can add hints or comments by using the Question Editor and editing these fields for individual questions. If you choose to display hints and comments and your source questions lack them, the system simply ignores the display settings.

Sending Email

Maple T.A. can send you an email whenever a student completes an assignment in Homework and Proctored mode. The email will contain the name of the class, assignment, student and their grade. To receive email notification, select the Send email reports to check box and enter your email address.

Note: To use this feature, your system administrator must have an SMTP server configured.

Assignment Properties

In the Assignment Properties section, you can set the following information.

• Passing score

•Time limit

• Number of questions on a page

• Maximum number of times an assignment may be taken

• Scheduling

• Visibility

4.5 Setting Policies • 47

Figure 4-D Assignment Properties

Setting a Passing Score

You can set a passing score for the assignment. If you set a score, the system assesses each attempt as either Pass or Fail, and records this information in the Gradebook automatically. The field shows the total available score for the assignment (for example, out of 10), which varies according to the composition of your assignment.

You can customize the message students receive by clicking the Edit feedback messages link and modifying the default messages. You can use the dropdown menu to specify when to display the feedback: Always, Never, or If the

final grade is shown.

Setting a Time Limit

You can set a time limit for Homework or Proctored assignment types. If you set a limit, the program shows the student the time remaining during the course of the test. If the time limit expires during the test, the system informs the student, and does not allow the student to enter responses to any more questions.

Note: The timer does not stop until the student runs out of time or clicks Grade. The timer will continue to run even if the student clicks Quit and Save.

Setting the Number of Questions per Page

By default, the program displays one question per page when presenting an assignment to students. You can use this option to deliver more than one question per page. If you have used question annotations and set the annotations to display at the top or the bottom of the page in which the

48 •

question is loaded, your annotations appear as a page-level header or footer (rather than immediately before or after the question).

Note: Mastery and Study Session assignments automatically serve one question at a time. This is part of their instructional design and this setting cannot be changed for these assignment types.

Tip: If you are concerned about a student's ability to assess complicated questions over a slower online connection, it is recommended that you accept the default setting of one question per page. Loading one question at a time usually allows a student to move through the assignment effectively, but also saves each question response as it is completed.

Setting the Maximum Number of Attempts

You can set the maximum number of times a student can take an assignment. If the student attempts more than the maximum amount, a message is displayed indicating the restriction. In this case, the student can click the Exception button displayed in the restriction message screen. A proctor or the instructor can then provide authorization.

Scheduling

Using the calendar function under Scheduling, you can set Start and End times for each assignment. These times govern the availability of the assignment to students in your class. Scheduled times refer to your server clock and system's time zone set by your system administrator.

Figure 4-E Scheduling

Before and after the indicated availability window, the assignment is still displayed in the list viewable by students on your Class Home Page, but it cannot be selected. Note that unavailable assignments will continue to be listed on the Assignment Editor Main Menu page. Additionally, unavailable assignments will appear in the student's past results page, if the student completed them.

Visibility

Check the Visible check box to include the assignment in the list of assignments displayed to students on your Class Home Page.

Alternatively, you can select the assignments to display to students by doing the following.

4.5 Setting Policies • 49

In the Assignment Editor main menu, click the show option available on mouse rollover of the assignment name. Note that if the assignment is already visible for students, the rollover menu will include hide instead of show.

Figure 4-F Setting Visibility of Assignments

Advanced Policies

Setting Assignment Requirements: Limiting Student Access to Assignments

You can restrict access to an assignment so that only students meeting certain criteria can take the assignment. You can also create assignment requirements that refer to the current assignment, even if you are working with a new assignment that has not yet been saved. The assignment on which you are working is now listed along with all other available assignments in the Criterion specification box. This is useful when you want to ensure minimum competencies in prerequisite topics. For example, you can limit access to students who have already passed an earlier assignment.

To restrict assignment access:

1. From the Assignment Editor screen in the Set Policies tab, click Advanced. The Set Policies - Advanced screen with a Requirements field

is displayed.

2. To set criteria, click Design. A Criterion 1 rule based field opens. The program adds input fields for the first criterion, as shown:

Figure 4-G Restricting Student Access

50 •

The program automatically propagates the settings in the Criterion panel to the Requirements panel, and updates the criteria in this field as soon as you select a different option from the list. You do not need to take any action to add the criterion to the text area.

Note: You can also enter the criterion directly in the Requirements field, but using the Designer is recommended.

Criterion Options

• The first drop-down list gives a choice between has and has not.

• The drop-down list in the middle lists a range of states and actions, as shown.

• The drop-down list on the right lists all of the assignments for the class, including the assignments whose restrictions you are defining.

• Adding an OR Criterion: Click the Add alternative criterion button immediately below the list of assignments. The program adds the list fields for another criterion.

• Adding an AND Criterion: Click the Add additional criterion button at the bottom right of the form, below the frame that encloses the criterion fields. The program adds another criterion group, in a separate frame.

• Deleting a Criterion: To delete an OR criterion, click the Remove criterion button inside the frame for that criterion group. The program deletes the last criterion from the group. You may have to change the settings for the remaining criteria in the group to set the requirements that you want. To delete an AND criterion group, click the Remove criterion button at the bottom of the form, below the last criterion group. The program deletes the last group. You may have to change the settings for the remaining groups to set the requirements that you want.

• Save Changes to Criterion: To close the Set Polices - Advanced page and save changes made to the criteria, click the Set Policies tab.

4.6 Reviewing and Saving Assignments

In the Review & Finish tab of the Assignment Editor, you can review assignment summary information, including:

• "Assignment Type

• "Questions Selected

• "Scheduled Availability

• "Rules and policies you established

4.7 Special Cases • 51

To change settings in your assignment:

1. In the Review & Finish tab, click the highlighted link in the category to be changed.

2. A prompt appears asking whether to return to the tab where the option is set. Click OK. The appropriate Assignment Editor tab opens.

3. Make changes and return to the Review & Finish tab.

Finishing an Assignment

To accept and publish the assignment you have created or modified:

•Click Finish in the Review & Finish tab. You are returned to the Assignment Editor list of assignments for your class, where your new

assignment is displayed in the list of all class assignments.

Assignment Status

Consider the following information regarding your assignment status.

• If you have scheduled the assignment for immediate availability, your new assignment is available for students in the Class Homepage.

• The system does not save partially completed assignments until you click Finish in the Review & Finish tab of the Assignment Editor. If you begin to create an assignment and then abandon it without clicking Finish, your additions and changes are lost. If you need to leave the Assignment Editor without finishing the assignment, it is recommended that you mark the assignment as hidden so that students cannot access it. Hide assignments from student view in the Class Homepage by hovering the mouse over the assignment name in the class assignment list, and then clicking hide.

• If the server shuts down before you click the Finish button, your editing changes will be lost. When the server restarts, it uses the last saved version of your assignment data. To reduce the risk of this during long assignment editing sessions, it is recommended that you periodically click the Finish button, then select your assignment from the main

Assignment Editor list of assignments to start a new editing session.

4.7 Special Cases

Deleting Assignments

You can select and delete assignments in the main Assignment Editor window. If there are grades associated with an assignment, and you rename

52 •

or delete the assignment, a copy is made. Also, results continue to be available through individual student records.

Shared Assignments: Saving Your Changes

Inheritance has changed slightly so that now you only inherit the content (groupings of questions and their weightings). When you edit an inherited assignment, only the options in the policy tab can be changed. Assignments can still be copied to make a local assignment that can then be fully edited.

5 Gradebook

5.1 Overview

Maple T.A. automatically stores assignment session scores in the Gradebook. The Gradebook stores information for each student, such as the assignment start time, the time spent on the assignment, and the individual assignment question performance.

The Gradebook allows you to:

• View, analyze, and report scores and statistics for students, assignments, and question items

• Review and edit student results

• Create reports organized by student, assignment, or by question

• Export grades to comma-delimited, Microsoft® Excel, or XML files

To access the Gradebook:

•From the Class Homepage, click Gradebook and select Open.

5.2 Gradebook Views

The Gradebook provides three views of assignment data: by student, by assignment, and by assignment item or question.

• To view the grades for an assignment, select an assignment in the search panel and select Submit. The results are displayed below the Search and View panels.

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• To view summary statistics for each assignment, click the link to a particular assignment in the student results table. From this view, you can see summary statistics for each question on an assignment.

Figure 5-A Gradebook

Generating Reports

You can change assignment weighting, grades, or add comments from within a generated report of an assignment or test.

To generate a report in the Gradebook:

1. In the Search Panel, select the assignment(s) to include in the report.

• To include more than one assignment, press the CTRL key and click the assignments.

• To include all assignments, select All.

2. Specify the search criteria from the following options:

• Assignment Type - To specify a single type of assignment from Proctored, Homework/Quiz, Mastery, and External.

• Show Results - To display results, for example, best or most recent.

• Completed/In Progress - To display only Completed, In Progress, or To Be Reviewed assignments.

• Date Range - To specify date range. Assignments completed within that date range will be included in the report.

3. In the View Panel, select the data to include in the report from the following options:

5.3 Student Statistics • 55

• Assignment - To display the date and time the assignment was started and finished, the time required to complete, and the number of attempts.

• Student - To display student information, such as first and last name, middle initial, login and password, email address, and student ID.

• Grade Style - To indicate presentation style for the grade.

• View Results for - To display statistics for student, proctors, or instructors (multiple items can be selected simultaneously).

• List - To display all users, or only users with grades.

• Summary Data - To display the weightings information, number of attempts and average number of attempts, total number of points, and average score.

4. Click Submit to generate the report.

5.3 Student Statistics

Figure 5-B Student Statistics

From the generated report, you can view a student record report, change the weighting for assignments, and change grades.

To view a student record report, click on the first or last name of a student in your generated report. The student record report contains the following details about the student: login, email, student ID, number of completed assignments, and number of active assignments. The student’s best and average scores are displayed for each assignment, as well as the number of attempts. The overall class best score, average score, and number of attempts

56 •

are displayed for comparison purposes, as well as the total points for the assignment.

Additional information about each assignment session is displayed: start and end time and date, and duration.

Assignment Weighting

To set weightings for each assignment, generate a report with the Weightings option selected, and then click the Weighting link in the report. You can set weighting for each assignment with respect to the cumulative grade for the class. Enter the weighting for each assignment, with the total for all assignments equal to 100%. You can Lock individual assignments to prevent their weighting from being adjusted.

Additionally, you can change the total points of the assignment. If, for example, one question was clearly too difficult in comparison to the rest of the assignment, you can override the total points, making the assignment out of 9 instead of 10 points.

The Zero button sets all weightings to 0% and the Reset button resets the weightings to the original settings.

Changing Grades

From a generated report, you can change a student’s grade. You may change a student’s grade for several reasons:

• The system does not automatically grade essay questions, so you must enter a grade for any essay questions included in your assignment.

• You might choose to raise a student’s grade based on effort, improvement, or other subjective measures.

• You might choose to apply a curve, based on the performance of the entire class.

5.3 Student Statistics • 57

Figure 5-C Student Record

To change a student grade:

1. In the resulting report, click the student name. The student record opens as shown in

Figure 5-C.

2. Beside each assignment is a link called Details. Click this link to display the assignment results.

3. Edit the grade in the New Grade field.

4. Optional. Add comments in the Comment on Grade box. These comments are strictly for your records; they are not visible to the student.

5. Optional. Add comments in the Instructors Comment box. Students see these comments when they review their performance on the test. You can add personalized comments to help individual students understand their scores and master the material.

6. Click Update at the top of the page.

7. Click Submit to regenerate the statistical information.

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5.4 Assignment Statistics

From the generated report, you can view details about the assignments.

To view assignment details, click on one of the assignment links at the top of the student report table.

Figure 5-D Assignment Link

The following details are displayed: original and current total points, date last modified, class average, number of attempts, average number of attempts, and number of active assignments. Details about the assignment setup are displayed as well. A histogram of the assignment statistics is provided.

The student report table now displays the students’ performance on each question in the assignment. Click on a question table to display the details of the question.

in the

Figure 5-E Assignment Statistics

5.5 Item Statistics • 59

5.5 Item Statistics

The system collects statistical data on the questions used in your assignments. It can automatically produce various statistical analyses based on item usage and student performance.

View item statistics by clicking on the Item Statistics link below the View Panel. Statistical information for each question includes the success rate, pValue, d-Value, number of times the question was answered, the number of times the question was answered correctly and incorrectly, and if any partial marks were given.

Additionally, for non-permuting, non-algorithmic multiple choice questions a chart is automatically displayed with the frequency each choice was selected.

Figure 5-F Item Statistics

5.6 Add External Assignment

The Gradebook gives you the ability to add the marks of an assignment that is not in the system. To add the marks of an external assignment:

•From the Class Homepage, click Gradebook and select Add External Assign.

• Enter the assignment name, total points, and a passing score in the appropriate fields.

60 •

• Enter a score for each student and, optionally, a comment.

•Click Save to finish, or Save & Add Another, to add another external assignment.

External assignments are displayed in the gradebook with other assignments.

6 Content Creation in the Question Editor

6.1 Question Types

There are many different question types that you can choose. The following table lists the most used question types and gives a brief description.

Blanks – Blank questions are a type of free-response question. They present the student with a question and response object in which to enter their response. The response object can either be a text region or a drop-down menu of choices. The blank question does not provide as many features as the list question.

Clickable imagemap - A clickable image question presents an image with a number of hot spots. Students are required to identify the correct image element by clicking the appropriate hot spot.

Essay – An essay question provides a text region for the student to enter their response. It is not automatically graded by the system. Student responses are sent to you, the instructor, who scores them traditionally, and assigns a grade in the system Gradebook.

Formula – The formula question allows instructors to compare student results to a specified answer. It has several variants that can be accessed as a dropdown menu in the formula question creation screen.

Formula mod C – accept answers within an additive constant Formula with physical units – requires units as well as a numeric value List (ordered or unordered) – accept answers as lists of values Restricted – the correct answer only uses basic operations Equation – the correct answer contains an equal sign Chemistry – the correct answer must match the given formula

No answer or feedback is available to the student.

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Question Designer – The Question Designer is a powerful and flexible

question container that can hold multiple response areas, i.e., answer regions supporting various question types including formula, Maple-graded, numeric, multiple-choice, multiple-selection, essay, and list types – all in a single question. Note: The Question Designer supersedes the Inline question type.

Key words – Key word or key phrase questions search the student's response for specified key words or phrases but ignore other text. This question type is not supported by the Question Editor.

List – List questions are a type of free-response question. They present the student with a question and response object in which to enter their response. The response object can either be a text region or a drop-down menu of choices. With list questions, you have the ability to give partial credit to certain answers.

Maple-graded – The Maple-graded question type uses the Maple™ computer algebra system to generate algorithmic variables in questions, generate plots, and evaluate student responses. The Maple-graded question type gives you access to the computational power of Maple. You have access to many different kinds of mathematical objects, not just simple expressions. The Maple-graded question type allows for questions with complicated answers, questions with different possible answers, and questions requiring a powerful answer-equivalence checker. You can even find common errors and assign partial grades.

Matching – Matching questions display two lists. A student must match each element of the first list with an element in the second list. Matching question types allow only 1 to 1 matches in the correct answer. Matches of 1 element to many are not available in the system.

Multipart – A multipart question can contain a variety of related question materials, data, even case scenarios for different types of assessment and learning. Although the multipart mode is a question type, its component question parts can be of any question type, including multipart. This allows nested multipart questions. You must create the question parts in a separate topic and then create the multipart question that combines all the parts.

Multiple-choice – Multiple-choice questions in the system can have any number of choices, but there is only one correct answer. You can add incorrect choices after questions are initially created. You can deliver the question with the choices permuting or remaining static.

Multiple-selection – Multiple-selection questions are similar to multiplechoice questions. The key difference is that they can contain more than one correct answer. You can deliver the question with the choices permuting or

6.2 Enhancing questions • 63

remaining static. The grading for a multiple-selection question is as follows, with the exception that if the numerator is less than 0, it is set to 0.

# selected correct answers – # selected incorrect answers

Total # of correct answers

Numeric – The numeric question type compares a student’s response to a given number, with or without units. You have the ability to set a tolerance in the answer that you will accept, from a certain number of significant digits to a percentage.

Palette – Palette questions enable you to use an Equation Editor to create your own customized palette for student response entries.

True or false – True-or-false questions are treated as a class of multiple-choice question featuring only two choices.

In Example Questions on page 21 we explored the Question Designer as a container for authoring multiple-choice, Maple-graded, list, and numeric type questions. Examples of formula questions, essay questions, and other question types can be found in Maple T.A.’s built-in help system. In a closer look at the Maple-graded question type.

Chapter 8 we take

6.2 Enhancing questions

You can enhance your questions by including feedback (or comments that a student will see when they finish their assignment), information fields, hints, and even a fully-worked solution.

Feedback

To return custom feedback when a student enters an incorrect response, each question type supports a feedback field. The comment in this field is displayed after grading. In the comment field, you can include additional explanations about solution method or final answer. When editing a question in the Question Editor, you can add or edit the comment.

To add or edit a comment:

1. On the New Question window, click the Add or Edit button in the Feedback area.

2. Enter or edit the comment in the text box. Comments can include HTMLformatted text, JavaScript™, and variables.

64 •

3. Click OK.

4. To add your changes to the cached question bank, proceed to the Question

Display screen, and then click Finish.

Information Fields

The info field allows you to add information subfields to a question to indicate subtopic, learning objective, level of difficulty, authorship, ownership, or other information. The information fields are defined as name/value pairs and can be used for sorting and filtering during assignment creation. When editing a question in the Question Editor, you can add or edit information fields.

To add or edit information fields:

1. On the New Question window, click the Add or Edit button in the Information Fields area.

2. Enter or edit field names and corresponding values in the Field and Value text boxes.

3. Each question can contain any number of information fields. To add rows, click the More button.

4. Click OK.

5. To add your changes to the cached question bank, proceed to the Question

Display screen, and then click Finish.

Hints

You can enter hints that can be displayed when taking an assignment. To use hints, you must enable them in the Set Policies tab of the Assignment Editor. When editing a question in the Question Editor, you can add or edit hints.

To add or edit a hint:

1. On the New Question window, click the Add or Edit button in the Hints area.

2. Enter or edit the hint in a text box. Hints can include text, HTMLformatted text, JavaScript™ code, and variables.

3. Each question can contain any number of hints. To add hint boxes, click the More button.

4. Click OK.

5. To add your changes to the cached question bank, proceed to the Question Display screen, and then click Finish.

6.3 Including Formatted Math Expressions in Questions • 65

Solution

In the solution field, you can enter a worked solution that is displayed in Study Session assignments. In these sessions, the student can view the solution before entering an answer or after submitting the question to be graded. When editing a question in the Question Editor, you can add or edit the solution.

To add or edit a solution:

1. On the New Question window, click the Add or Edit button in the Solution area.

2. Enter or edit the solution in the text box.

3. Click OK.

4. To add your changes to the cached question file, proceed to the Question Display screen, and then click Finish.

Note: The solution field is only shown in study session assignments. To include a solution that can be used in other assignment types, you should use the feedback field.

6.3 Including Formatted Math Expressions in Questions

Maple T.A. renders the question text as HTML/MathML if the Use HTML: check box has been selected. This allows you to include formatted math expressions in questions.

There are three ways to create nicely formatted expressions in Maple T.A.:

1. The built-in mathml function

2. The built-in Equation Editor

3. Maple's MathML[ExportPresentation] function

Using the mathml Function

Maple T.A. contains a built-in mathml function. This is an algorithmic function that accepts a string and, treating it as calculator-style syntax, transforms it into MathML.

For example, suppose we define an algorithmic variable $y as follows:

$y = mathml(“x^n”)

66 •

Then $y will be rendered as wherever it is referenced in the question

statement, comment, and hints.

This function is designed for small expressions and is limited in scope. For full MathML functionality, it is recommended that you use either the Equation Editor or Maple's MathML[ExportPresentation] function.

Using the Math Editor

Maple T.A. provides a graphical equation editor for use with all question types except fill in the blank. This editor is the same editor that is included with Maple and is used to translate the graphical form of your expression to MathML code.

To use the equation editor:

1. Add a question.

2. Click Next.

3. Enter the text of your question. When you get to the place where you

would like to add a formatted expression, click the Sigma brings you to the Equation Editor screen.

Figure 6-A The Equation Editor applet is used to create a nicely formatted expression.

button. This

4. Create your expression. Use keyboard shortcuts or right-click in the region to get a palette from which you can choose.

5. When you are finished creating your expression, click OK. The expression appears in the question text window.

6. Finish creating your question as you would normally.

Note: You can include algorithmic variables in your math expressions. If the variable name is alphabetic only, you can enter $var in the Math Editor and it will maintain the variable name as one unit. If the variable name is alphanumeric, you

6.4 Including Images in Questions • 67

will have to use an alphabetic name in the editor and then replace it with the correct variable name in the question text area.

Using Maple's MathML[ExportPresentation] Function

Maple's MathML[ExportPresentation] function can take any expression in Maple and convert it to presentation MathML for display purposes.

To use Maple’s MathML[ExportPresentation] command:

1. Create an algorithmic variable for the expression that you want to use.

2. Create a second algorithmic variable for the MathML version of that expression using Maple's MathML[ExportPresentation]. This variable will be used for presentation purposes only.

For example, suppose we define an algorithmic variable $z as follows:

$z = maple("MathML[ExportPresentation](x^2-3*x+2)")

Then $z will be rendered as wherever it is referenced in the question statement, comment, and hints.

x23x 2+–

6.4 Including Images in Questions

You can include a number of different types of images in your questions: static images, Maple plots or animations, and images with algorithmic variables overlaid.

Static Images

You can include static images in all question types. They can be included in the question text itself, the comments, the hints, or the solution.

To include a static image in a Maple T.A. question, there are two steps.

Step 1: Upload the image to the class web site.

1. Log in as an instructor and click on the class in which you want to use the image.

2. Click on Content Manager, then Web Site Editor.

3. Create a subfolder where you can place the image. It is possible to upload your image at this point, but for maintainability, it is recommended that you create a subfolder and place your images in it.

68 •

a) Click "new subfolder …".

b) Enter a name for your subfolder in the text region and click OK. You

are returned to the Web Site Editor page with your subfolder expanded.

4. Click "upload file(s) to this point …".

5. Click Browse… to locate the file on your computer.

6. Select the radio button beside Single File – Save As: to use the same name that the image has on your computer or enter a name for the file in the text region. The name must be alphanumeric and can contain "_", "-", or a single period. It cannot start or end with a period and it cannot contain a space.

7. Click OK.

If you click on the image in the class Web Site Editor, you will be shown the URL for that image. You can click on that link to see the image.

Step 2: Include an html reference to the image in your question or solution.

1. Create or edit a question in the Question Editor.

2. In the field where you want to include the image (question text, feedback, hints, or solution), click the Insert/Edit Image

button.

3. Under the Image Info tab, click Browse Server and select the image you uploaded in Step 1. You will be shown a preview of the image.

4. Click OK and the image will be added.

Note: The Browse Server screen (#3 above) also allows you to upload an image to the server, in case you had not previously uploaded the image through the Web Site Editor.

Maple Plots

There are two ways to include a Maple-generated plot in Maple T.A.: the drawMaplePlot script and the plotmaple command. The plotmaple command was added in Maple T.A. 2.5 and is now the recommended way to include Maple plots in questions. The drawMaplePlot script is still available, but does not provide the same functionality as the plotmaple command.

plotmaple command

The plotmaple command was introduced in Maple T.A. 2.5. With it, you create algorithmic variables that contain your plots. You can then reference these algorithmic variables in your questions, feedback, hints, or solutions.

Some of the benefits of using the plotmaple command are as follows:

1. You can specify in the command whether you want the image to be saved as a GIF or JPEG. This is important if you want to display most of your

6.4 Including Images in Questions • 69

images as JPEGs, so you set the default image type to be JPEG, but occasionally want to add an animation to a question and, thus, require a GIF image for one question. Maple animations can only be displayed as animated GIFs.

2. You can define the height and width of the image without losing any quality in the image.

3. You can see the plot immediately in the algorithm editor. There is no need to finish the question before being able to tell if you used the correct plot command or if you need to change it slightly to improve the presentation.

The format of the plotmaple command in the algorithm editor is as follows:

$myplot=plotmaple("plot(sin(x), x=-Pi..Pi), plotdevice='gif', plotoptions='height=250, width=250'");

$myanimation=plotmaple("plots[animate](sin(a*x),x=-Pi..Pi,a=1..4), plotdevice='gif',plotoptions='height=200, width=200'");

Figure 6-B Using the plotmaple command, you can include algorithmic variables in your plot statement. You will see a preview of the image in the algorithm editor. Here, the algorithm editor text region and the corresponding image are shown.

70 •

7 Algorithmic Variables

You can use algorithmic variables to randomize your questions in Maple T.A. These algorithmic variables can use the built-in algorithmic generator or can use any of Maple’s randomization routines.

7.1 Creating Algorithmic Variables in Maple T.A .

To create an algorithmic variable in Maple T.A., use the algorithm designer in the Question Editor. Algorithmic variables can be used in any question type and can be used in the question text, the answer region, as well as in the hints and feedback sections. Algorithmic variables are denoted by a dollar sign, for example, $var.

To create an algorithmic variable:

1. Upload an existing question or create a new one.

2. Click Questions, then New Question.

3. Choose the question type from the drop-down menu.

4. In the Algorithm field, click Add.

5. If you know the format of the command, you can type it in the text box and proceed to designer tool.

6. Type the required information in the algorithm designer template. Note that you do not need to use the $ to denote variables in the template. Click OK to add the command to the algorithm text box and display a possible value for the variable.

Step 7. Otherwise, click Show Designer to load the algorithm

72 •

7. Click Refresh to have Maple T.A. generate another possible value for the variables.

8. Click Save to return to the main page for the question.

You can now continue creating your question and can use the variables that you created.

Algorithm Design Tool

Figure 7-A You can use the algorithm designer to create simple random integers,

set conditions on the variables, or enter a Maple command that will generate a random object.

7.2 Maple T.A.’s Built-in Functions and Constants

Maple T.A. contains several functions for creating algorithmic variables. You can create random integers or real numbers, perform operations on lists of items, or set conditions on variables.

It is important to note that the algorithm generator in Maple T.A. works linearly. This means you must be careful to define variables before referencing them in other variable definitions.

Table 2: Numbers and Constants

e 2.71818...

7.2 Maple T.A.’s Built-in Functions and Constants • 73

Table 2: Numbers and Constants

pi ( )

2.9E8 Scientific Notation:

3.14159...

290,000,000

Table 3: Arithmetic Operators

Operation Description

+ Addition

– Subtraction

* Multiplication

/ Division

^ Exponential

Table 4: Assorted Math Functions

Function Return Value Example Output

abs(x) Absolute value of x abs (-2) 2

sqrt(x) Square root of x sqrt(9) 3

ln(x) Natural (base e) logarithm of x ln(1) 0

log(x) Common (base 10) logarithm of x log(10) 1

exp(x) Base e exponential function of x exp(1) 2.71818...

fact(n) Factorial n fact(4) 24

gcd(a, b) Greatest common divisor of a and b gcd(4, 6) 2

frac(a, b) A string that expresses the fraction a / b in its lowest terms.

This function can be combined with function mathml to produce nicely typeset fractions.

frac(4, 6) “2/3”

Random numbers can be generated with the following functions:

Table 5: Random Number Generators

Command Output Example Output

rint(n)

rint (m, n) A random integer among

A random integer among 0, 1, ..., n-1

m+1, ..., n-1

rint(3) 0, 1, or 2

rint(3, 6) 3, 4, or 5

74 •

Table 5: Random Number Generators

Command Output Example Output

rint(m, n, k) A random integer among

range(n) A random integer among 1, 2, ..., n range(3) 1, 2, or 3

range(m, n) A random integer among m, m+1, ..., n range(3, 6) 3, 4, 5, or 6

range(m, n, k) A random integer among

rand(m, n) A random real number between m and

rand(m, n, k) A random real number between m and

m+k, ..., m+q·k where q is the

m, largest integer such that m+q·k £ n–k

Note that rint(n) = rint(0,n) = rint(0,n,1)

m+k, ..., m+q·k where q is the

m, largest integer such that m+q*k £ n

Note that range(n) = range(1,n) = range(1,n,1)

n (inclusive)

n (inclusive), expressed to k significant

digits.

Note that in this definition, k represents the number of significant figures, not the step size (as it indicates in defining range and rint).

rint(3, 12, 3) 3, 6, or 9

range(3, 12, 3) 3, 6, 9, or 12

rand(0.5, 9.5) A real number between

rand(0.5, 9.5, 3) A real number between

0.5 and 9.5 (inclusive)

0.5 and 9.5 (inclusive),

expressed to 3 significant digits.

You can place conditions on your variables. For example, you can specify that two variables are not to be equal, or define a value for a specific variable based on the values of other variables.

Table 6: Conditions

Command Effect

condition:x Imposes the condition defined by statement x, which is typically constructed using one

if(a,b,c)

Function Return Value

eq(a,b) 1.0 if a is equal to b; 0.0 otherwise

ne(a,b) 1.0 if a is not equal to b; 0.0 otherwise

gt(a,b) 1.0 if a is greater than b; 0.0 otherwise

lt(a,b) 1.0 if a is less than b; 0.0 otherwise

not(a) 1.0 if a is equal to 0.0; 0.0 otherwise

Example

or more of the functions below.

If statement a is nonzero, returns b. Otherwise, returns c. Typically, a is constructed using one or more of the functions below.

7.2 Maple T.A.’s Built-in Functions and Constants • 75

The following code generates a non-zero integer variable $a between -10 and 10 (inclusive), and a string variable $b that reads either positive or negative, depending on the sign of $a.

$a = range(-10, 10);

condition: ne($a, 0);

$b = if( gt($a, 0), “positive”, “negative” );

Numbers can be manipulated and/or displayed in a specific format with the following functions.

Table 7: Number Formatting Functions

Function Return Value Example Output

int(x) The integer part of x int(20.8571) 20

decimal(n, x) x as a floating-point number, rounded to n

sig(n, x) x expressed as a floating-point number

lsu(n, x) The unit in the nth significant place of x

numfmt(fmt, x) x formatted according to the template fmt numfmt("#.00", 20.9) 20.90

decimal places.

Trailing zeros are truncated and not displayed. However, see numfmt function below.

rounded to n significant digits.

In cases of possible ambiguity, scientific notation is used to display the value.

This operation is designed to be used when setting the tolerance for correct answers. For example, to accept an answer to within a tolerance of one unit in the third significant digit, use:

$ans = <formula>;

$tol = lsu(3, $ans);

and set the answer field to:

$ans ? $tol

decimal(3, 20.8571) 20.857

sig(3, 20.8571) 20.9

lsu(3, 20.8571) 0.1

There are several functions in Maple T.A. that operate on lists. These allow you to choose an item out of a list based on a property or a value. They are very useful if you want to create a question with the same stem or base information, but have answers with different properties.

Table 8: List Operations

Function Return Value Example Output

min(a, b, c, d,…) the smallest element from a list min(2, -1, 3, 5, 4) -1

76 •

Table 8: List Operations

Function Return Value Example Output

max(a, b, c, d,…) the largest element from a list max(2, -1, 3, 5, 4) 5

switch(n, a, b, …) the nth item from a list (where

switch(rint(n), a, b, …) the nth item from a list (where n

indexof(k, a, b, ..)

rank(n, a, b, c, …) the nth smallest item from a list

position numbering in the list starts at 0)

is a random integer from the given list)

the index of item k within a list (where position numbering starts at 0)

If k is not present in the list, the returned value is -1.

(where position numbering starts at 1)

switch(1,"red","green","yellow”) green

switch(rint(5), 2, 3, 5, 7, 11)

indexof(3, 2, 3, 5, 7, 11) 1

rank(1, 9, 6, 11) 6

either 2, 3, 5, 7, or 11

Table 9: Trigonometric and Hyperbolic Functions

sin(x), cos(x), tan(x), arcsin(x), arccos(x), arctan(x), sec(x), csc(x), cot(x)

sinh(x), cosh(x), tanh(x), sech(x), csch(x), coth(x), arcsinh(x), arccosh(x), arctanh(x),arcsech(x), arccsch(x), arccoth(x)

Table 10: Statistical Functions

Function Return Value Example Output

binomial(n, r) the rth binomial coefficient of degree n, that is,

erf(z) the cumulative probability for a standard normal

inverf(p) the inverse function of erf(z) inverf(0.5) 0

studentst(k, x) the cumulative probability distribution at x of the

invstudentst(k, x) the inverse function of invstudentst(k, x) invstudentst(2, 1.55) 1.55

the number of ways of choosing r objects from a set of n, ignoring order

distribution (that is, with mean 0 and variance

Students-t distribution with k degrees of freedom

binomial(6, 2) 15

erf(0) 0.5

studentst(2, 1.55) 0.869362

Table 11: More Functions

Function Return Value

sum(var_name, start, stop, expr) Sums the expression (expr) with respect to the dummy variable (var_name)

between the values start and stop.

7.3 Examples of Randomization Functions in Maple T.A. • 77

Table 11: More Functions

Function Return Value

strcat(a, b, c, d, ...) The concatenation of the strings in the list

mathml(f) A string consisting of the formula f typeset in MathML

Note: The system renders MathML; the MathML tags do not appear on the screen when the value of the string is displayed. See Section x.x[ca5] for more information on this function.

java(cn, a, b, c, d, ...)

maple(text) The text is passed to the Maple™ kernel, which returns the value of the last line

The arguments a, b, c, d, … are passed to a custom Java evaluation engine that returns the result. The first argument (cn) must be a string giving the fullyqualified name of a Java class that implements the interface

gateway.question.random.AlgorithmicFunction.

This interface has a single public method.

public String eval(String[ ] args);

The arguments a, b, c, d,... are passed to eval() in a string array.

processed. See sections 7.4 and 7.5.

Table 12: Examples

Command Output

sum(i, 1, 20, i^2) Evaluates 1^2 + 2^2 + 3^2 + ... + 20^2 and returns 2,870

strcat("$a", " and ", "$b") Returns “cats and dogs”

mathml(“x^n”)

mathml(frac(4, 6))

java("com.mycompany.QuoteFunction", "SUNW")

maple(“diff(x^3,x)”); 3*x^2

when $a=”cats” and $b=”dogs”

--3

A real-time quote for Sun Microsystems, Inc. stock (assuming that the class QuoteFunction had been suitably programmed)

7.3 Examples of Randomization Functions in Maple T.A.

The following examples demonstrate some of the randomization routines that are available in Maple T.A.

78 •

Basic Arithmetic

In this example we use a multiple choice question and ask the student to add two numbers. In the algorithm designer, we define two integer variables, $a and $b, and then define a third variable, $ans, which is the sum of $a and $b. In the choices to be displayed, we create an inline algorithmic variable that is the product of $a and $b by using the format ${expression}.

To create the question:

1. In the New Question window, select the Multiple Choice question type from the Question Type drop-down list.

2. Enter “Addition” as a description in the Question Description field.

3. In the Algorithm section, click Add. The Edit Algorithm window opens.

4. Enter the following code in the text box:

$a=range(2,10);

$b=range(3,15);

condition:not(eq($a,$b));

$ans=$a+$b;

5. Click Save. You return to the New Question window.

6. Click Next. The Question Editor>Add Question window opens.

7. In the Text of the question field, enter the following:

What is $a + $b?

8. In the Choices for the answers section, enter $a, $b, $ans as possible answers, one for each field.

9. We can also define an algorithmic variable on the question screen. To do this, enter ${$a*$b} in the fourth choice box.

10.Select the radio button beside $ans to mark this as the correct answer.

11.Select Yes for Change the order of answers. Select No for Allow more than one selection.

7.3 Examples of Randomization Functions in Maple T.A. • 79

12.Click Finish. The Question Editor>Preview Question window opens, displaying the question as it appears to the student.

Figure 7-B One of the features of Maple T.A. is the ability to define inline algorithmic expressions directly in questions by using the format ${expression}.

Calculating Area

In this example, we use a numeric question and ask the student to calculate the area of a rectangle given two algorithmically-generated values for the width and length. This example shows that you can combine commands, such as decimal(x,n) and rand(m,n). We've also added a condition on the variables $width and $length so that they will not be equal.

To create the question:

1. In the New Question window, select the Numeric question type from the Question Type drop-down list.

2. Enter “Area” as a description in the Question Description field.

3. In the Algorithm section, click Add. The Edit Algorithm window opens.

4. Enter the following code in the text box:

$width=decimal(1,rand(2.5,6.5)); $length=decimal(1,rand(4.5,10.0)); condition:not(eq($width,$length)); $area=$width*$length;

5. Click Save. You return to the New Question window.

6. Click Next. The Question Editor>Add Question window opens.

7. In the Text of the question field, enter the following:

80 •

Given a rectangle with width of $width meters and length of $length meters, calculate its area.

8. In the Number text box of The correct answer: area, enter $area.

9. In the Units text box of The correct answer: area, enter m^2.

10.In the Specify precision area, select the radio button beside Require absolute accuracy.

11.Click Finish. The Question Editor>Preview Question window opens, displaying the question as it appears to the student.

Color Combinations

This fill-in-the-blanks example illustrates the use of the switch command to customize the question. Given two lists of information, one of three pairs of colors and one of the colors when the pairs of colors are mixed, we can define a random index value and then base the question on one of these three pieces of matching information.

To create the question:

1. In the New Question window, select the Question Designer question type from the Question Type drop-down list.

2. Enter “Color” as a description in the Question Description field.

3. In the Algorithm section, click Add. The Edit Algorithm window opens.

4. Enter the following code in the text box:

$index=rint(3); $choice0="red and blue"; $choice1="red and yellow"; $choice2="blue and yellow"; $mix=switch($index,"$choice0","$choice1","$choice2"); $color=switch($index,"purple","orange","green");

5. Click Save. You return to the New Question window.

6. Click Next. The Question Editor>Add Question window opens.

7. In the Text of the question field, enter the following:

When you mix $mix, you get $color?

8. Position the cursor after the word “get” but before the period and click the Insert/Edit Response Area button.

9. Choose List question for the question type.

10.Leave the radio button beside Text field selected. Add $color as the first item and set the Weight to 1.0.

11.Click OK to return to the Question Editor>Add Question window.

7.4 Randomization Routines in Maple • 81

12.Click Finish. The Question Editor>Preview Question window opens, displaying the question as it appears to the student.

Figure 7-C The Algorithmic Editor shows both the algorithmic commands and a sample value for the variables.

7.4 Randomization Routines in Maple

In addition to Maple T.A.’s built-in functions, you can access Maple routines as well from within Maple T.A. In particular, Maple has many randomization routines that can be used in Maple T.A. This section discusses a subset of the available functions. The function rand will generate a random integer, while randpoly will generate a random polynomial with specific properties. The LinearAlgebra package contains the RandomMatrix and RandomVector functions. The RandomTools package contains a variety of functions for creating random Maple objects, from simple random integers or polynomials to lists of values that follow specific probability distributions. In addition, since Maple is a programming language, you could write your own customized program in Maple to generate any type of variable or object that you need.

All random number generators use the same underlying random number sequence, so when using Maple’s randomization routines, you must include randomize( ): as the first part of the call. This uses a number based on the system clock as the initial state instead of the default seed that is used in Maple. If you don’t include randomize( ), each call will return the same

82 •

sequence of values since each call to Maple from within Maple T.A. starts a new Maple kernel and that will reset the default randomization seed.

Notes:

When entering multiple commands, ensure that all (except the last) have a trailing colon. The last command should have a trailing semi-colon.

When referencing negative (or possibly negative) random variables in a maple variable definition, be sure to place the negative variable in parentheses, otherwise you may receive an error message.

Random Integers

The rand( ) function is a simple way to create random integers. You can also use the RandomTools[Generate] command as shown in the RandomTools section below.

Table 13: Random Integers

Function Return Value

rand( ) Generates a 12-digit non-negative integer

rand(n)( ) Generates a random integer between 0 and n-1 (inclusive)

rand(a..b)( ) Generates a random integer between a and b (inclusive)

Random Polynomials

The randpoly( ) function is the most straightforward way to create random polynomials. You can also use the RandomTools[Generate] command as shown in the RandomTools section below.

Table 14: Random Polynomials

Function Return Value

randpoly(variables, options) Generates a random polynomial in terms of variables using the options specified.

These options are specified as follows:

coeffs=rand(a..b) – the default is rand(-99..99) degree=n – the default is 5 expons=n – the default is rand(6) terms=m – the default is 6, but this value is overridden by the degree option if there is a conflict

The most common options are used to specify the type of coefficients and exponents, the degree of the polynomial, and the number of terms in the polynomial.

7.4 Randomization Routines in Maple • 83

LinearAlgebra Functions

The two most common random objects that can be created using the LinearAlgebra package are Matrices and Vectors. You can create both row and column vectors.

Table 15: LinearAlgebra Functions

Function Return Value

LinearAlgebra[RandomMatrix] (m, n, density, generator)

LinearAlgebra[RandomVector][o] (dimension, density, generator)

Some examples:

$M=maple("randomize(): LinearAlgebra[RandomMatrix](3,3)"); returns a random 3x3 matrix

$V=maple("randomize(): LinearAlgebra[RandomVector][row](6, generator=rand(1..5)/10))"); returns a row vector of 6 elements whose entries are rational numbers with a denominator of 10 and a numerator between 1 and 5. The elements are returned in simplified form.

Generates a random m x n matrix using the options specified.

Generates a random vector using the options specified. [o] can be used to specify a row vector instead of a column vector (which is the default).

RandomTools Functions

There are many functions in the RandomTools package, including subpackages that implement different pseudo-random number generators. There are several RandomTools[Generate] functions that can be used to create random objects, a selection of which are included in the table below. Each of the functions in the table below should follow RandomTools[Generate], as in RandomTools[Generate](choose({a,b,c,d,e,f}));

Table 16: RandomTools Functions

Function Return Value

choose(collection) Select one of the entries in a non-empty collection with equal probability

complex(flav) A random complex number with real and imaginary parts described by the given

exprseq(flav,n) An expression sequence with n entries where each entry is described by the given

float(opts) A random floating-point number in a particular range. The options can include a

identical(expr) Describes the object expr itself

random flavor flav

range (e.g., range=2.532..7.723) and the number of digits (e.g., digits=4).

84 •

Table 16: RandomTools Functions

Function Return Value

integer(opts) negint(opts) nonnegint(opts) nonposint(opts) nonzeroint(opts) posint(opts)

list(flav, n) A list with n entries where each entry is described by the given random flavor flav

listlist(flav, m, n) A list of m lists, each with n entries, where each entry is described by the given

rational(opts) negative(opts) nonnegative(opts) nonpositive(opts) nonzero(opts) positive(opts)

polynom(coeffs, x, opts) A random polynomial in a given number of variables x with coefficients coeffs of a

set(flav,n) A set containing n entries where the entries of the set are described by the given

truefalse(opt) Describes the values true or false. By default, the values true and false will be

A random integer in a particular range. The options can include a range (e.g., range=0..10) and a statistical distribution from where the integer is chosen (e.g., distribution=poisson[5])

random flavor flav. In the case where only m is given, n is assumed equal to m.

A random rational number in a particular range. The options can include a range, a statistical distribution from where the rational number is chosen, or a denominator.

given random flavor. The default degree of the polynomial is 5, but you can specify the degree of the polynomial by using the degree option (e.g., degree=3).

random flavor flav. The final set can contain fewer than n entries if the same object is generated more than once.

chosen with equal probability, but you can modify this by using the probability option (e.g., probability=p, where p is a numeric value between 0 and 1 that specifies the probability that the object will be true).

Some examples:

$a=maple("randomize(): RandomTools[Generate](integer(range=2..9))"); returns a random integer between 2 and 9 (inclusive)

$b= maple("randomize(): RandomTools[Generate](list(rational(denominator=30), 10))"); returns a list of 10 rational numbers whose denominator is 30. They are returned in simplified form.

$c=maple("randomize(): RandomTools[Generate]([integer(range=3..10),rational(range=3..10, denominator=13)])"); returns a list of two elements where the first element is an integer in the range 3 to 10 and the second element is a rational number between 3 and 10 whose denominator is 13

You can also include other Maple commands in the algorithmic variable definition. $d=maple("randomize(): seq(RandomTools[Generate](integer(distribution=normald[3.5, 1.5])), i=1..10)"); creates a 10-item sequence of integers that follow a normal distribution.

7.5 Examples of Randomization Functions in Maple • 85

7.5 Examples of Randomization Functions in Maple

The following examples include the Maple T.A. source code required to generate the question.

Degree of polynomial

This numeric question uses Maple to generate a random polynomial and Maple's MathML[ExportPresentation] function to generate a nicely formatted version of it. We then ask the student to determine the degree of the polynomial.

To create the question:

1. Click Questions, then New Question to create a new question. The New Question window opens.

2. From the Question Type drop-down menu, select Numeric.

3. In the Question Description field, enter “Degree of polynomial”.

4. In the Algorithm section, click Add. The Edit Algorithm window opens.

5. Enter the following code in the text box:

$a=range(0,2); $b=range(2,5); $poly=maple("randomize(): randpoly(x,degree=$b)"); $displaypoly=maple("printf(MathML[ExportPresentation]($poly))");

6. Click Save.You return to the New Question window.

7. Click Next. The Question Editor>Add Question window opens.

8. In the Text of the question field, enter the following:

What is the degree of $displaypoly?

9. In the Number text box of The correct answer: area, enter $b.

10.Leave the Units text box of The correct answer: area blank.

11.In the Specify precision area, select the radio button beside Require absolute accuracy.

12.Click Finish.

Intersection of Sets

Here we use the RandomTools[Generate](set) function, to generate two unique sets and ask the student to determine the intersection. This question is written as a Maple-graded question because we want the student to enter a set as the answer.

86 •

To create the question:

1. Click Questions, then New Question to create a new question. The New Question window opens.

2. From the Question Type drop-down menu, select Maple-graded.

3. In the Question Description field, enter “Intersection of sets”.

4. In the Algorithm section, click Add. The Edit Algorithm window opens.

5. Enter the following code in the text box:

$set1=maple("randomize():RandomTools[Generate](set(posint(range=8),5))"); $set2=maple("randomize():RandomTools[Generate](set(posint(range=10),4))");

6. Click Save.You return to the New Question window.

7. Click Next. The Question Editor>Add Question window opens.

8. In the Text of the question field, enter the following:

What is the intersection of $set1 and $set2? Enclose your answer in braces.

9. Enter Maple code that evaluates to the correct answer:

$set1 intersect $set2

10.Change the Maple code to grade the student response to:

is($RESPONSE=$ANSWER);

11.In the Select the type of expression you want to accept: drop-down list, choose Maple syntax – e.g., diff(2*f(x),x)

12.Click Finish.

Matrix Determinant

In this example, we use Maple's LinearAlgebra[RandomMatrix] function to create a square matrix with entries between -9 and 10. Again, we use MathML[ExportPresentation] to generate a nicely formatted version for display.

To create the question:

1. Click Questions, then New Question to create a new question. The New Question window opens.

2. From the Question Type drop-down menu, select Maple-graded.

3. In the Question Description field, enter “Determinant”.

4. In the Algorithm section, click Add. The Edit Algorithm window opens.

5. Enter the following code in the text box:

$n= int(rand(2,4));

7.5 Examples of Randomization Functions in Maple • 87

$matrix=maple("randomize():LinearAlgebra[RandomMatrix]($n,$n,generator=rand(-9..10))"); $m=maple("printf(MathML:-ExportPresentation($matrix))");

6. Click Save. You return to the New Question window.

7. Click Next. The Question Editor>Add Question window opens.

8. In the Text of the question field, enter the following:

Calculate the determinant of the following matrix. $m .

9. Enter Maple code that evaluates to the correct answer:

LinearAlgebra[Determinant]($matrix);

10.The following Maple code to grade the student response is provided automatically:

evalb($ANSWER-$RESPONSE=0);

11.In the Select the type of expression you want to accept: drop-down list, choose:

Formula – e.g., x^2 sin(x^2)

12.Click Finish.

Figure 7-D Two Maple commands are being used; one to create the matrix construct, and one to generate a nicely formatted version for display.

88 •

8 Maple-graded Questions

Maple T.A. offers numerous question types to ensure you can present and properly grade your question. The Maple-graded question type connects to the Maple engine when grading students’ responses. This will give credit for any response that is mathematically equivalent to the correct answer. For

example, if your Maple-graded question is

x()tan

x() x()tansec

asked for a set, the system would accept any response that contained the correct elements, regardless of the order in which the student gave them. You can write questions that ask for differential equations, unevaluated integrals, and so on. You can write questions that have more than one answer or infinitely many answers.

, , , or anything equivalent as correct. If your question

----------------

x()cos

x()sin

------------------2 x()cos

------ x()sec dx

, the system would accept

This document will guide you through the creation of some example Maplegraded questions. The examples reflect only a small sampling of the possibilities.

8.1 A Basic Maple-graded Question

In this first example, we build a question that asks for the derivative of and uses Maple to grade the response.

1. Log in as an instructor and go to the Question Editor.

2. Click Questions, then New Question to start a new question.

3. From the Question Type menu, select Maple-graded.

x()sec

90 •

4. In the Question Description text region, enter the description Derivative of Secant as shown in

Figure 8-A.

Figure 8-A Creating a Maple-graded question

5. Click Next to proceed to the Maple-graded Question and Answer screen. This screen displays regions to enter the question text, the Maple code for calculating the correct answer, the Maple code for grading the student response, and more.

6. In the first text region, enter the question text as shown in Figure 8-B.

Compute the derivative of .

x()sec

7. In the second text region, enter the Maple code that will compute the correct answer. The system stores this result in the variable $ANSWER, which can then be used in the grading routine.

diff x()x,sec()

;

8. The third text area includes Maple code to grade the student response. The last line of your Maple code must evaluate to true for a correct response, false for an incorrect response, or a floating-point value between 0 and 1 for partial credit (available as of Maple T.A. 2.5). Maple’s evalb command is frequently the best way to do this, but any Maple command that returns a boolean is allowed. This region already contains the code

evalb( ($ANSWER) – ($RESPONSE) = 0 );

For this example, alter the line of code to,

evalb(simplify( ($ANSWER) – ($RESPONSE) )= 0 );

The system stores the student response in the variable $RESPONSE, which you can use as a Maple variable anywhere inside your Maple code.

8.1 A Basic Maple-graded Question • 91

Caution: We strongly recommend that you test your Maple code in a Maple worksheet. Frequently, you will find that your first version of Maple code is inadequate to give credit for all correct answers. In this example, if we had just used evalb( ($ANSWER) – ($RESPONSE) = 0 ), the system would only give credit for sec(x)tan(x) and reject all other responses, even if they are algebraically equivalent to sec(x)tan(x). The reason is that evalb does not perform any simplification.

Figure 8-B The Maple-grading Question and Answer screen

9. From the drop down menu titled Select the type of expression you want to accept, ensure Formula - e.g. x^2 sin(x^2) is selected.

Note: The Formula option accepts basic algebraic expressions, either by entering them in standard calculator syntax, for example, (2x/y + sin(x y))(4x^2-1), or by using the symbol palette. When the student submits a response with this option selected, the system translates it into Maple syntax so that the Maple engine can apply your Maple code to it. If you want the student to enter equations, differential operators, integral signs, summations, vectors, matrices, DEs, or other advanced mathematical expressions, select the Maple syntax – e.g. diff(2*f(x),x) option. This option allows a much wider range of student response types. However, it requires the student to enter the response using proper Maple syntax because the system runs your Maple code directly on what the student types. Also, this option

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allows the student to enter Maple commands, for example, diff(sec(x),x);, so you need to be careful when you choose it.

10.Click Finish. This will take you to the Preview screen in which you can test your question or start a new one.

Testing Your Question

1. Now pretend you are a student doing the assignment and enter a typical response in the text area as shown in

Figure 8-C A preview and test of the question

Figure 8-C.

2. Click Grade to check that Maple is correctly assessing the response.

3. Click OK and you will return to the Preview screen. Try a variety of student responses to convince yourself that the Maple code for grading the question is adequate.

4. If the question or the Maple code needs revision, click Edit.

8.2 A Randomized Question

To provide multiple problems of the same form or to hinder cheating during exams, you can include random parameters such as random problem data or coefficients into math questions.

In this example, we build a question that asks for the equation of a 3-D plane that passes through the points <1,0,0>, <0,1,0> and a third point picked at random. This example will also show how to use multiple lines of Maple code to grade a more complicated question.

Maplesoft MAPLE user guide

Specifications and Main Features

Frequently Asked Questions

User Manual

1 Getting Started

1.1 System Overview

Assignments

Gradebook

1.2 Logging On

1.3 The Class Homepage

1.4 Creating a Class

1.5 Adding Users to the System

User Rosters

Adding Individual Users

1.6 Registering Users in a Class

The User Manager

Student Self-Registration

Class Rosters

2 Sharing Content

2.1 Sharing Questions

2.2 Course Modules

2.3 Child Classes

2.4 Featured Classes

Propagation of Material from Featured to Child Classes

3 Question Repository

3.1 Overview

3.2 Question Editor

3.3 Example Questions

The Question Designer

Multiple-choice Question using the Question Designer

Multiple-choice Question with Randomly Determined Parameters

Multiple Choice Question Incorporating 2-D Math

Maple-Graded Question

Plotting the Student's Response

Inserting a Maple Plot in the Question Feedback

Apply Partial Grading to Maple-graded Questions

List Question using the Question Designer

Numeric Question using the Question Designer

Equation Editor

3.4 Downloading Questions

4 Assignments

4.1 Overview

Assignment Editor Main Menu

Warnings and Locking Mechanism

4.2 Creating Assignments

4.3 Naming Assignments

4.4 Selecting Questions

Individual Versus Grouped Questions

4.5 Setting Policies

Assignment Types

Feedback

Assignment Properties

Advanced Policies

4.6 Reviewing and Saving Assignments

4.7 Special Cases

Deleting Assignments

Shared Assignments: Saving Your Changes

5 Gradebook

5.1 Overview

5.2 Gradebook Views

Generating Reports

5.3 Student Statistics

Assignment Weighting

5.4 Assignment Statistics

5.5 Item Statistics

5.6 Add External Assignment

6 Content Creation in the Question Editor

6.1 Question Types

6.2 Enhancing questions

Feedback

Information Fields

Hints

Solution

6.3 Including Formatted Math Expressions in Questions

Using the mathml Function

Using the Math Editor

Using Maple's MathML[ExportPresentation] Function

6.4 Including Images in Questions

Static Images

Maple Plots