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by Tim Fahlberg, Adjunct Professor of Mathematics,
Northwest College, Kirkland, WA 98033 (Tim.Fahlberg@CoolSchoolTools.com) 

Using ExamView to Create Dynamic Questions
I have a confession to make—I love to create dynamic questions using ExamView.  Why, you ask?  Well I know that the time spent creating a good dynamic question is like the time planting a seed from which a lush tree with many branches can grow. That is, you can spend between 5 and 45 minutes to create a simple or complex dynamic question (the seed). Then, just by adding a few conditions, changing a variable definition, or simply changing the value of a constant (watering the seed), you can quickly create additional dynamic questions (the tree branches).  From just a few dynamic questions, it’s easy to generate many, many copyright-free questions (leaves of the tree).

Once you create your own dynamic questions, you can use them on tests, quizzes, and study guides.  It’s as if you have an unlimited number of questions. That way, you’ll have plenty of questions for students who need extra practice, or you can use the questions with other programs such as the following products that I have used in my classroom.

• MindPoint Quiz Show (see www.mindpoint.com) – Students can learn and have fun practicing in class, in the lab, and at home.

• Classroom Performance System (see www.einstruction.com) – With remote control response pads from eInstruction, I can display an ExamView question and instantly know whether all of my students understand the particular topic.

• Virtual Whiteboard Math Movies – You can create tutorials and/or solutions including audio on a virtual whiteboard that can be delivered over the Internet, LAN, or CD.

Getting Started
If you haven’t created a dynamic question or you are not sure what a dynamic question is, let me suggest that you read and follow the steps in my previous article to learn the basics of dynamic question creation.  Work through the tutorial using ExamView 4.0 and review the online help topics to better understand how to create a dynamic question.

In the following article, you will find three dynamic question examples: Rule of Exponents, Solving a System of Equations Using  Substitution or Elimination, and Pythagorean Theorem.  Before you begin, click here to download the following question bank (Dynamic Corner-Part I.bnk) Windows or (Dynamic Corner-Part I) Macintosh.  The bank includes the sample questions. (Remember that you will need ExamView 4.0 or a more recent version.)

To help you better understand how to create dynamic questions, use the Question Bank Editor to open the question bank and review the algorithms that make up each question.  For each example, I have provided a detailed explanation of the algorithms.  In addition, I have included several variations of each question.

Example 1: Rule of Exponents
This first example is a bimodal question.  That is, you can change its state from a Multiple Choice question to a Short Answer question with a single mouse click.  This feature is great for creating problems that work for advanced placement classes.

As you can see, this question includes the question stem, choices, and a rationale.  The rationale is an explanation of how to determine the correct answer.  You can ask the program to display this information if you create an online test or a study guide.  It provides students with the help they need at that “teachable moment."  You can provide a little help or step-by-step instructions.  It’s up to you.

Rule of Exponents (Question #1)

Rule of Exponets-Variables

Rule of Exponents—Algorithm Definitions

Note: To enter or edit an algorithm, double-click a question and choose Algorithm Definitions from the Edit menu.      

A Closer Look at the Algorithm Definitions
Below is an explanation of the algorithms used in this question.  The names you use for the algorithm definitions (or variables) are not critical as long as you do not use function names.  As for the functions (e.g., list, range, choose, etc.), you can get a detailed description by reviewing the online help information in the program.

• letter, whichletter, and var1 are variables used to generate a random variable from a list of 18 “good” variables.  Notice that letters e, i, l, o, t, u, v, and z are not included for various reasons (e.g., e is the base of natural logarithms; i is often used to represent the square root of -1; the letters l, o, and z look like the digits 1, 0, and 2; t looks like a +; and u and v are easily confused with each other).
• maxExponent is a constant that determines the highest exponent allowed in this question.  Change it to a larger value if desired.
• exp1 and exp2 are variables used to represent the two exponents that are to be added together. range(1, maxExponent) generates a random integer between 1 and maxExponent
• Result1 to Result4 are the exponents for the correct answer and the three distractors (for the multiple-choice version of this bimodal question).
• isunique(Result1, … Result4) is a condition that makes sure that none of the four multiple-choice answers are the same. In general you should add this condition to every multiple-choice question you create to prevent duplicate answers unless the distractors are built in such a way that this would never be the case.
• scramble=TRUE  (not illustrated) causes the program to randomly scramble the answer choices each time you calculate a question

Changing the Algorithm Definitions to Create Variations of the Question
Once you create a dynamic question, you can use it to create one or more variations on the same topic.  For example, the first variation shows how you can edit the algorithm to allow for negative exponents.

You can find this variation in the sample question bank that you downloaded.  Click the Edit menu and choose Algorithm Definitions to see the list of variables.  Click the Calculate Values button to see this question in action, or duplicate the question to create new questions of the same form.

Variation A—Allow for negative exponents  (See Question #2 in the question bank.)

• Change the definition of exp1 and exp2.A third parameter may be used to indicate the increment used. If the increment is not included, it is assumed to be 1. If a 1 is included in the increment position, the range will be from the first parameter to the second with an increment of 1 skipping the value of zero. For example:
  range(1,17,2) would generate random odd integers between 1 and 17.
  range (1,18,3) would include every third number between 1 and 18.
  range (-3,5,1) would generate a random integer between –3 and 5 excluding zero.
  range (-3,5) would generate a random integer between –3 and 5 including zero.
• Add two variables exp1Display and exp2Display (used in the dynamic solution).
• Add a new condition: exp1+exp2<>0 (this prevents the sum of the exponents from equaling zero).
  

Variation B—Answer is always 1 since the sum of the exponents is zero.  (See Question #3.)
You can vary the problem so that the answer is always 1 by changing the condition exp1+exp2<>0 to exp1+exp2=0. Then change the correct choice to _.

Variation C—Answer always has negative exponent. (See Question #4.)
To create a problem so that the answer always has a negative exponent, change the condition exp1+exp2>0 to exp1+exp2<0.

Notice how we’ve taken a single algorithm and tweaked it just a little to create questions that are similar but different.  We could have created a more complex algorithm to start with that did all of these things but I think you’ll see the advantages of creating questions that each do one thing well.

Example 2:  Solving System of Equations Using Substitution or Elimination
This problem illustrates a dynamic question with a set of conditions that can be easily changed to generate a variety of types of systems of equations best solved by different methods.

Solving a System of Equations (Question PR #1)

Solving a System of Equations—Variables and Algorithm Definitions

A Closer Look at the Algorithm Definitions
• maxValue is a constant which determines the range of values for x and y.
• x, y, a, b, d, and e are all random integers.
• c and f are calculated using the values of  a, x, b and y (for c) and d, x, e, and y (for f).
• condition a*e-b*d<>0 is included to make the system of equations solvable.  This value
    is the determinant of the system.

Changing the Algorithm Definitions to Create Variations of the Question
Check the information below to see how you can easily create multiple versions of this problem.

Variation A—(See Question PR #2.) Make it so exactly one of the coefficients of x or y equals 1. This makes for a system most easily solved by substitution. Include the condition a=1 xor b=1 xor d=1 xor e=1  xor means exclusive or –one or the other but not both or in this case only one).

Variation B—(See Question PR #3.)  Make it so exactly one of the coefficients of x (a or d) equals 1 and so that neither of the coefficients of y (b or e) equals 1.  Include the condition (a=1 xor d=1) and not(b=1 or e=1).

Variation C—(See Question PR #4.) Make it so that a = -d or b = -e so that the system is most easily solved by just adding the two equations together using the method of elimination.  Include the condition a+d=0 xor b+e=0.

Variation D—(See Question PR #5.) Make it so that the system of equations is most easily solved by elimination but so that each equation will need to be multiplied by a constant in order for elimination to occur.   Include the condition a+d<>0 and b+e<>0

Example 3:  Pythagorean Theorem
While this problem shows you how to create a question to test your students’ knowledge of the Pythagorean Theorem, it also shows how to create a dynamic question using a picture.

Pythagorean Theorem (Question PR #6)

Pythagorean Theorem-Variables

The algorithm below shows one constant (maxLength), and nine variables. Most of these are used "behind the scenes" to label a Cartesian Graph that includes a picture of a right triangle (see below). The variables a and b are defined (using the range function) as random integers between 1 and 100 (the value of maxLength). The variables aSquared, bSquared, and aSquaredPlusbSquared are longer variable names but self-explanatory. The variables are not used in the algorithm itself but in the display of the complete dynamic solution. The variable c is calculated using the Pythagorean Theorem. To make this problem more interesting, three variables were added to put English units next to the lengths of the sides.

Pythagorean Theorem—Variables and Algorithm Definitions

It turns out that creating the algorithm for this dynamic question is only half the work since we still need to use variables defined in the algorithm to label a right triangle.  Try clicking and then double-clicking on the picture of the right triangle in the sample question bank (Question #6) to see the format (pieces of) the Cartesian Graph shown below:

In order to include a picture of a right triangle (or another picture), do the following:

• Click Insert-Graph-Cartesian.
• In the Format Graph – Cartesian window, click the drop-down box next to f(x) and choose Picture.
• Click New.  The New Picture window should appear.
• Type RightTriangle2 next to Picture name: and the following image should appear.

• Click OK to see the following window.

• Try changing the Left x, Top y, Width, and Height values of the picture to make it a reasonable size in a good location.
• Now add text boxes used to display the attributes of the triangle. See the question, figures, and instructions below for details about these.

To add a text box like the one shown below, click on the drop-down arrow next to f(x), choose Text Box, and then click New. Then change the options to match the following window.

Repeat this procedure two more times to add three additional text boxes for the other leg, hypotenuse, and “Drawing not to scale” legend:

• Hide the x and y axes by clicking the Axes tab and then clicking the Clear button and then OK.

Changing the Algorithm Definitions to Create Variations of the Question
Variation A—(See Question PR #7.)  Make it so that the values of a and b (the two legs) are never equal.  Include the condition:   a <> b  (Spaces before and after the not equal sign are optional.)

Variation B—(See Question PR #8.)  Make a, b smaller (or larger) values by changing the constant MaxLength to values less than (or greater than) 100.

Variation C—(See Question PR #9.)  Make a, b non-integer values by changing a and b to range(1,maxLength,0.1).

Variation D—(See Question #10.)Make it so x (the hypotenuse) comes out even (is an integer) by including the condition   c=int(c)

Variation E—(See Question #11.) include metric units by changing WhichUnit to range(1,8), including MetricLengthUnits = list("mm","cm","m","km"), and including LengthUnits =list(EnglishLengthUnits,MetricLengthUnits). Change the definition of the variable Unit to choose(whichUnit,LengthUnits).

Variation F—(See Question #12.)  Include a complete dynamic solution.  Use the variables a, b, c, unit, aSquared, bSquared, and aSquaredPlusbSquared to add a solution which changes to match each newly generated dynamic question.  Such a solution is particularly useful for a test key that you print or study guide that you make available online or in printed form.

Dynamic Solution to Pythagorean Theorem (Showing Variables in Gray)

Dynamic Solution (with Variables Replaced by Values)

Now plant your own dynamic question “seeds” and enjoy the “fruits” of the trees that grow from them!

Tim Fahlberg (Tim.Fahlberg@CoolSchoolTools.com)
Adjunct Professor of Mathematics
Northwest College
Kirkland, WA 98033