## Evaluation through stages

You specify how the student’s input is evaluated through a list of **evaluation stages**. AlgebraKiT will evaluate these stages in the order that they are specified and stop at the first stage that matches the student input.

Consider the following example, which defines three stages to evaluate the student’s input.

The first stage matches the expression y=x^2+x and its commutative variations, which are y=x+x^2, x^2+x=y and x+x^2=y. If the student inputs any of these expressions, then this input will be evaluated as a correct final answer.

If the student enters the expression y=x\cdot x+x\cdot 1, then the first stage is not satisfied and AlgebraKiT will proceed to the next stage. This stage matches because the input can be rewritten to y=x^2+x. The stage specifies that the input should be evaluated as an intermediate step. Therefore, the student will see that his input is correct but not yet finished.

If the student enters the incorrect expression y=x\cdot x + 1, then also the second stage does not match, but the third one does. This stage specifies that error feedback should be given. The feedback is specified by the author as we will see later.

If none of the stages match the student input, then AlgebraKiT will assume that the input is incorrect. There is an exception: If no evaluation stages are specified, then AlgebraKiT will accept every input as the final answer.

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## Specifying an evaluation stage

You can inspect and change an evaluation stage by clicking on it. The single-line summary expands into a form.

The first part of the form specifies the criteria to match this stage. The second part defines the result in case the criterium does or does not match.

There are two types of evaluation criteria: **equality **or **condition**.

## Equality criterium

You can specify that the input must be compared to one or more predefined answers. Use the evaluation mode to specify what kind of equivalence should be applied.

Evaluation mode | Description |
---|---|

Mathematically equal | Two expressions are mathematically equal if their difference is equal to zero.Example\left|x\right| \sqrt{1+x} is mathematically equal to \sqrt{x^2+x^3} |

Mathematically equal, solve for variable | Applies to relations. Two relations are equal if their solutions for the given variable are mathematically equal.Examplex+y=1 is equivalent to y=1-x |

Same expression, commutative | The expressions must have the same form, except for the order of commutative operations, such as +, -, and =.Example1+x\cdot y^2+x^2 and x^2+y^2\cdot x+1 are equal up to commutativity. |

Same expression, literal | The expressions must be exactly the same. This is in fact a textual comparison, where only extra spaces are neglected. Note: The expression does not have to be valid mathematics. ExampleThe expected answer could be something like “y=“, which is not a valid mathematical expression. |

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## Conditional criterium

A more general criterium than equality checking is the criterium based on a condition. Such a condition could be: “the input must be a positive number”. This can be written mathematically as var>0, where var represents the student input.

The following example shows a stage that matches if the student input is an integer and even number.

You can define multiple conditions. The evaluation criterium matches when all conditions are valid.

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Next, you define the result of the stage, based on the output of the criterium. The following options are available:

Final answer | The student input is accepted as the final answer for this question. |

Intermediate step | The student input is evaluated as correct, but not finished. |

Error | The student input is incorrect. You must specify a feedback message which will be shown to the student. |

No action | Proceed to the next stage. |

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