# Evaluation Modes for Math Questions

For many question types in WebAssign, such as Multiple-Choice or pencilPad, the question mode you select has immediately visible effects on the question you are creating. When you create questions that evaluate mathematical expressions, however, the question mode you select affects what kind of responses your students can enter and how your students' responses are evaluated, but has no corresponding visual effect.

Before creating a question that asks your students to enter a mathematical expression or equation, determine how that expression should be evaluated.

## Symbolic Mode

Symbolic questions evaluate your students' responses symbolically by substituting a series of values for the variables in the response and in the key. If the response and the key are equal for all tested values, then the response is accepted as correct.

This evaluation behavior provides reliable scoring of responses and can accept any form of a mathematical expression that is equivalent to the key. However, it cannot evaluate responses that are equations, and it cannot evaluate whether responses are in a particular form, such as a completely factored expression.

## Algebraic Mode using Mathematica^{®}

Algebraic questions evaluate your students' responses algebraically using Mathematica, in much the same way you would solve an equation.

- You must know how to write Mathematica expressions. For reference information, see Mathematica reference information at reference.wolfram.com/mathematica/.
- Older questions created using Algebraic mode do not necessarily use Mathematica; however, the general principles still apply, and these questions will continue to function.

Algebraic mode is a much more powerful method for evaluating your students' responses, but specifying your key in Algebraic mode can sometimes be more complicated than with Symbolic mode. Additionally, you cannot by default accept any mathematically equivalent response using Algebraic mode; you must therefore make sure that your students understand what form of response is needed.

## Choosing a Mode to use Based on Selected Criteria

Refer to the following table to help you decide which mode to use.

Criterion / Example |
Symbolic Mode |
Algebraic Mode using Mathematica |
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Accept any response that is equivalent to the key |
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Allow your students to type commas in large numbers |
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The answer is a single mathematical expression that is not an equation. Solve for |
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The answer is a finite list of set members. List the first three natural numbers. |
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The answer is any member of a set. List any multiple of both 2 and 3. |
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The answer is a single ordered pair. What are the coordinates of the center of the circle defined by the following equation: |
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The answer is two or more ordered pairs. List the coordinates of the first five data points shown on the graph. |
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The answer is a vector. Find a vector perpendicular to ‹1,2›. |
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The answer is an equation. What is the equation for a circle with center
( |
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Only a particular form of the answer is correct. Factor the expression: |
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Key can specify multiple correct answers. |
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Key can perform complex evaluation functions for you, such as factoring polynomials or computing derivatives. |