Automatically marked question. The question answered by entering numeric values or algebraic equations.

The Symbolic Math question type in Inspera Assessment is a programmatic, automatically-marked question where candidates can answer using numeric values or algebraic equations. It utilizes a Program Model to randomize values and validate responses. 

This article explains the core elements of Symbolic Math questions, details how to author them, covers configuring response outcomes, outlines testing and previewing procedures, and lists known limitations.

Understanding the Symbolic Math question type

Symbolic Math shares core concepts with Numerical Simulation, where variables and logic are defined within a Program Model. However, unlike Numerical Simulation, Symbolic Math specifically supports candidate responses in the form of algebraic equations, which are automatically validated and evaluated. Program variables are randomly generated when the test starts, providing unique values for each candidate attempt.

• In the question below, a candidate must enter a numeric value in the first input field and an equation in the second. The highlighted values within the question text are randomly generated each time the question is presented. 

  

How to author a Symbolic Math question

There are three core elements when authoring a Symbolic Math question: the Question Text, the Program Model, and the Response Outcome.

• The Question Text: These are the fixed elements of your question. Only the values of the program variables you insert within it will change.
• The Program Model: Define all variables, their parameters, and calculations here.
• The Response Outcome: Decide here how the system will evaluate the candidate’s response.

Instructions

1.  

   1. First start by selecting the Author module > Questions.
   2. Click Create new.

   3. Under Automatically marked, click Symbolic Math.

      

2. The Question Text contains the fixed elements of your question. The only parts that change are the values of the program variables you insert within the question text.
   1. Author the question text in the main authoring area.
   2. To insert a program variable, click + Insert followed by Program Variable wherever you'd like the randomized value to appear. This will insert a variable placeholder.

   3. To add a candidate input field, click + Insert followed by Candidate Response. This will insert a response placeholder. 

      

3. To set all the variables and their parameters, you must edit the Program Model. The Program Model uses MAXIMA for its operations. In MAXIMA, variables are declared by first writing the variable name, followed by a colon. After the colon, you specify the value or parameters for the variable. Remember, each line of code must end with a semicolon to be correctly interpreted.

   1. From the general options in right-hand panel, click Program Model > Edit Program Model.
   2. Write your Program Model.
   3. When finished, click Compile to verify your syntax and ensure the example values are being generated as expected. 

   4. Click Save. 

      

   For a step-by-step example of a question being authored, see Symbolic Math Step by Step Example.

   For further detail on the Program Model syntax, see The Program Model.

4. Once the program model is complete, return to the question text. Click on each Program Variable placeholder you inserted, and from the Program Variables dropdown, select which variable you would like to display at that specific location. 

   

5. For each Candidate Response field, you must set its type of input you expect from the candidate and define how you'd like to validate it. 

   

   1. Click on each Candidate Response field and select Edit response outcome.
   2. Select the required Input Type. Each type has their own set of options for evaluation.
      • Symbolic Math: This input type allows candidates to enter both numeric values or an algebraic formula as their response. Here you can choose between two Symbolic Math options:
        • String Match
        • Algebraic

      • Basic Numbers: Selecting this input type will only allow candidates to input a numeric value (including decimal places). Here you can choose between several Basic Numbers options: 

        • Equal
        • Abs. Tolerance
        • Rel. Tolerance
        • Unequal
        • Greater than
        • Less than

        Read more about the different input types below.

   3. Select the variable to be evaluated against.
   4. Select the outcome: Correct, Partially Correct, or Incorrect

   5. Set the Response-Spesific Feedback.

      You can provide response-specific feedback within the Response Outcome. This allows you to tailor automatic feedback based on whether a candidate's answer was correct, incorrect, or perhaps a common error you factored into your Program Model. 

      This feedback can also include the variable values themselves from the Program Model, so candidates see the exact numbers they were presented with when they attempted the question, rather than just variable names.

      See the article Response Feedback for further information.

6. Once you've finished setting the Question Text, Program Model, and the Response Outcomes, simply click Save.

   If you'd like to preview the question, click the Preview eye icon in the top right. We recommend you do this to ensure it works as intended

   As an Author, each time you refresh your browser the variables will be recalculated. This is not functionality available to candidates. For candidates, once variables have been calculated, they remain fixed for that attempt. 

   

Input types for response outcome

• 

  Selecting the Symbolic Math Input type will allow candidates to enter both values or a formula as their response. How this input is then evaluated is dependent on the option selected from the  next dropdown.

  • String match

    This requires the candidate's input to be an exact match (character for character, in exact order) to the variable selected from the program model.

    Important: Switch off simplification by adding simp: false; to the programme model otherwise the equations within the variable will be automatically simplified (eg. '1+2+3' will become '6' and '6' will be the string validated against. Adding simp: false; will keep the string as '1+2+3').

    Example: If evaluating against the variable answer: x+y+z; to get the correct response the candidate must enter x+y+z exactly. z+y+x or any other combination will not be correct because a match must be identical.

  • Algebraic

    This will mathematically evaluate the candidate’s input. Provided their response is mathematically correct, it will be evaluated accordingly, regardless of the order of terms or how the expression is structured.

    • Example: If evaluating against the variable answer: x+y+z;, the order z+y+x would not matter.

    Even if the required input is entirely numeric, provided the input is mathematically the same, it will be treated the same. 

    • Example: If the question required the answer to (5 + 5) x 10², the following would all be correct answers using the Symbolic Math: Algebraic input type:
      • 10^3
      • 10 * 100
      • 1000
      • 500 * 2

    Important: For Algebraic responses, the multiplication operator must be included in the candidate response.

    eg. \( 2 \times x + 21 \) rather than \(2x + 21\).

    Candidate responses can be reviewed in the Grade module and marks overwritten if they forget this.

• 

  Selecting the Basic Number Input type will only allow candidates to input a numeric value (including decimal places). The functionality with the Basic Numbers Input Type is the same as Numerical Simulation. Where the options are:

  • Equal: The candidate input is exactly the value of the variable from the programme model.
  • Abs Tolerance: The candidate input can be within a set numerical range (lower and higher) relative to the variable. See the article Absolute and Relative Tolerance for more information.
  • Rel Tolerance: The candidate's input can be within a percentage-based range (higher and lower) relative to the variable. See the article Absolute and Relative Tolerance for more information.
  • Unequal: The candidate input is any value other than the variable's value from the program model.
  • Greater Than: The candidate input is greater than the variable's value from the program model.
  • Less Than: The candidate input is less than the variable's value from the program model.

Error Carry Forward

Symbolic Math has Error Carry Forward functionality, which means that an error in an earlier part of a candidate's calculation might not penalize them in subsequent steps if those subsequent steps are logically correct based on their earlier incorrect answer.  See Error Carry Forward for further information.

Known limitations

Symbolic math question type does not support the use of greater/less than symbols as part of the answer.
It means that you can not create a question where the correct answer is, for example, 'x > 5'.
That same rule applies for the equal symbol. It is not possible to answer 'a = 5' or 'x + y = 4'.