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equivSymbolic

Overview

The equivSymbolic method checks that the value entered by the student is mathematically equivalent to the value that the Author has set in the validation, even if they are in different forms.

Use equivSymbolic when working with equations, or other input with variables, where order or form is not important. For example, if the task is to multiply 3 and 2, any response that is mathematically equal to 6 will be considered as correct, such as 6/1, 12/2, 3+3, 6.0.

equivSymbolic accepts decimals, fractions, variables, and percentage.

Additional Options

  • Significant decimal places
    This option specifies the number of significant decimal places. The maximum value is 10.
  • Allow interval
    This option must be enabled when the students are expected to insert interval notation in the response area, ie  ‘[1, 4)’. Otherwise, the response will not validate correctly.
  • Ignore text
    This refers to LaTeX text only, and when enabled will ignore any LaTeX text the student enters in the response area.
  • Compare sides
    Used when comparing two constant equations, when both sides of an equation have not been fully specified, such as {{response}} + {{response}} = {{response}}. By default, expressions such as this will validate as isTrue. This means that as long as the expression is mathematically correct it will be correct, even if the value(s) entered is different to that specified in the validation area. However, enabling Compare Sides ensures that the response given is symbolically equal to the equation set in the validation area.
  • Treat 'e' as Euler's number
    This option treats the variable 'e' as Euler's number. This overrides the default interpretation of 'e' as scientific notation.
  • Allow decimal marks
    Authors can specify what separators can be used by the student. From the Thousand Separator drop-down menu, you can select dot, comma, and/or space. The Decimal Separator menu contains the option for either a dot or a comma. Note that the specified thousand separators and decimal separator cannot be the same, e.g. both dot.
  • Treat all letters as variables
    When this is enabled, the math engine will treat all letters as variables. This is useful in cases where you want to use letters as variables that the math engine may normally recognize as units of measurement. Here are the units of measurement we support: List of S.I and US Customary Units

 

Examples

Example 1 - Basic equivSymbolic scoring

In this example, any value that is equal to 100 will be considered as correct.

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Example 2 - equivSymbolic fill in the blanks

In this question, the students enter a value in the response box in order to complete the equation. Anything that is equal to 100 must be entered in the response box.

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Example 3 - equivSymbolic fill in the blanks

This is a similar example, only with two blank spaces that have to be filled in. Two values that are equal to 100 must be entered in the response boxes. Order is not important.

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Example 4 - equivSymbolic fill in the blanks

This example has 3 empty boxes. The valid response is set to 2+2=4. As neither side of the equation has a set value, it is scored as isTrue. Any equation inserted in the response boxes will be correct as long as it represents a mathematically correct equation in the form x+y=z.

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Example 5 - equivSymbolic with fractions

equivSymbolic handles responses containing fractions of different types.

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Example 6 - equivSymbolic with variables

equivSymbolic can also be used with variables. 

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Example 7 - equivSymbolic with trigonometry questions

equivSymbolic recognises trigonometric functions.

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Example 8 - equivSymbolic with algebraic expressions

In the example below, an expression in any form that is mathematically equivalent to the one in the stimulus will be correct.

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Example 9 - decimal rounding

The decimal places field is used to specify a number of significant decimal places in the response. In this example, the decimal places value is set to 2. This way, the students will not need to enter all the digits after the decimal point for the response to be deemed correct.

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Example 10 - using text blocks

You can set custom units such as ft, kg, mi, etc. as text blocks in the More options section. This means that the units will not be rendered as LaTeX. 

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Example 11 - using compare sides

Compare sides is used with open ended questions. it ensures the equation values entered by the student give the same mathematical result and are symbolically equivalent to the equation set by the author. 

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Combining methods

equivSymbolic is a very flexible method and is often used in conjunction with other methods.

Example - Excluding possible correct responses

In some cases the students might be asked to give a correct response other than the one already specified in the stimulus. Authors can set such exceptions by combining equivSymbolic and equivLiteral, then enabling the inverse result option underneath equivLiteral. Now, any symbolically equivalent equation will be correct except for the actual valid response specified in question validation.

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