Atomic Jolt

Math Scoring Methods

What Are The Different Scoring Methods Available?

Math question types can use various scoring methods. These methods fall into two categories; evaluation types and form checking. 

These scoring methods can be used alone or you can also combine methods for more thorough validation.

Evaluation type methods cover the main three methods you will need to know about for authoring math questions in Learnosity. Most of the time, you will be using one of these methods in Question validation.

Form checking covers the rest of the scoring methods; the primary purpose of these methods is to check that the student response matches a particular form specified by the author.

For more information and examples of the methods below click on the method name to go to the Learnosity article. 

Evaluation Types

equivSymbolic (symbolic equivalence)

Checks that the student response and the answer set by the author are symbolically equivalent in meaning 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 percentages.

equivLiteral (literal equivalence)

The equivLiteral method checks if the response from the student is literally equal to the correct value specified by the Author. 

This means that the form, order, elements, and values entered by the student should match the value in validation. Responses that are mathematically equal, but are in a form other than the one specified by Authors, will return false. Use equivLiteral when you want to strictly specify a particular form of the mathematical expression as the correct answer.

Note that equivLiteral ignores parentheses that have no specific meaning by default.

equivValue (value equivalence)

The equivValue method compares numerical values that may be represented in different ways, such as units of measurement, where 1m = 100cm. equivValue will evaluate the expression to a numerical form for comparison. As long as the value given by the student is mathematically equal to the result the author was expecting, the question will validate as correct.

Although similar to equivSymbolic, the equivValue method cannot be used with variables. It does, however, work with decimals, fractions, and percentage. 

equivValue is particularly useful if you are using units of measurement. This method also handles the validation of lists and ranges, using the tolerance symbol.

Form Checking

isSimplified (simplification)

The isSimplified method checks if a value is in its most simplified version. isSimplified does not take any value and is generally used as a supporting method in conjunction with equivSymbolic.

isFactorised (factorization)

The isFactorised method checks that a mathematical expression is in factorised form. It can handle polynomials up to degree 2, with a single variable.

When using isFactorised, Field must be specified. Authors can select between the following depending on the type of expression they are dealing with:

  • integer
  • real numbers
  • complex numbers

isFactorised doesn’t take any value and is generally used as a supporting method in conjunction with equivSymbolic.

isExpanded (expansion)

The isExpanded method checks that an expression is in its most expanded form.

isExpanded doesn’t take any value and is generally used as a supporting method in conjunction with equivSymbolic.

isTrue (boolean evaluation)

The isTrue method checks that an expression has a comparison or equality, that is true. This means that when this method is used alone, any true equation entered by the student will be marked as correct.

Expressions that include a relational (‘<’, ‘<=’, ‘>’ or ‘>=’) or equality (‘=’) operator are evaluated for their truthfulness.

isUnit (unit comparison)

The isUnit method checks if an expression contains the expected units.

isUnit is commonly used in conjunction with equivValue. For worked examples of combining isUnit with equivValue, please see equivValue Combining Methods section.

stringMatch (string comparison)

The stringMatch method is used for literal string comparison. This compares the value set by authors in validation against the student's response and evaluates whether they are the same or not. stringMatch is a simple comparison method: it does not take the syntax and data type set in the validation area into account.

equivSyntax (syntax comparison)

equivSyntax compares a LaTeX string against a syntax pattern specified in the validation settings.

This method is a purely syntactic check and is unaffected by numeric values. Use equivSyntax as a supporting method in combination with equivSymbolic and equivValue to constrain possible response options.

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