10.22. Math Expression Input Problems

Note

EdX offers full support for this problem type.

The math expression input problem type is a core problem type that can be added to any course. At a minimum, math expression problems include a question or prompt and a response field for a numeric answer.

For more information about the core problem types, see Working with Problem Components.

10.22.1. Overview

In math expression input problems, learners enter text that represents a mathematical expression. The text is converted to a symbolic expression that appears below the response field. Unlike numerical input problems, which only allow integers and a few select constants, math expression input problems can include unknown variables and more complicated symbolic expressions.

For more information about how learners enter expressions, see Entering Mathematical and Scientific Expressions in the EdX Learner’s Guide or Entering Mathematical and Scientific Expressions in the Open edX Learner’s Guide.

Note

You can make a calculator tool available to your learners on every unit page. For more information, see Calculator Tool.

For math expression input problems, the grader uses numerical sampling to determine whether a learner’s response matches the math expression that you provide, to a specified numerical tolerance. You specify the allowed variables in the expression as well as the range of values for each variable.

When you create a math expression input problem in Studio, you use MathJax to format text strings into “beautiful math.” For more information about how to use MathJax in Studio, see Using MathJax for Mathematics.

Note

Math expression input problems currently cannot include negative numbers raised to fractional powers, such as (-1)^(1/2). Math expression input problems can include complex numbers raised to fractional powers, or positive non-complex numbers raised to fractional powers.

10.22.1.1. Example Math Expression Input Problem

In the LMS, learners enter a value into a response field to complete a math expression input problem. The following example shows a completed math expression input problem that contains two questions.

A problem shown in the LMS that requests the symbolic expressions for displacement and for elongation of a blade. Both questions were answered correctly. The solutions are not shown.

The open learning XML (OLX) markup for this example math expression input problem follows.

<problem>
  <formularesponse inline="1" type="cs" samples="R,omega,E,rho,L@0.1,0.1,0.1,0.1,0.1:10,10,10,10,10#10" answer="(rho*omega^2*L^2)/E*((11*L)/48 +(3*R)/8)">
    <label>Find a symbolic expression for the displacement of the blade mid-section, \( u_{x}(L/2) \), in terms of \(R\), \(L\), \(\rho\), \(\omega\), and \(E\).</label>
    <description>\(u_x(L/2) = \)</description>
    <responseparam type="tolerance" default="1%"/>
    <textline inline="1" math="1"/>
    <solution>
      <div class="worked-solution">
        <p><b>Obtaining the displacement at the mid-section \( u_{x}(x = L / 2)\):</b></p><p>According to the definition of strain,</p>
        \[ \frac {du_{x}(x)} {dx} = \epsilon_a(x).\]
        <p>Therefore, we can obtain the displacement field as</p>
        \[ u_x(x) = u_x(0) + \int_0^x \epsilon_a (x') dx' = u_x(0) + \left[ \frac{\rho \omega^2}{E} \left(\frac{L^2x'}{2} - \frac{(x')^3}{6} + RLx' - \frac{R(x')^2}{2} \right) \right]_0^x\]
        <p>Since the bar is fixed at x=0, therefore \(u_x(0)=0\). Hence we obtain</p>
        \[\Rightarrow u_x(x) = \frac{\rho\omega^2}{E} \left( \frac{L^2x}{2} - \frac{x^3}{6} + RLx - \frac{Rx^2}{2} \right).\]
        <p>The displacement of the bar at \(x=L/2\) is </p>
        \[u_{x}(L/2) = \frac {\rho\omega^2L^2}{E} \left( \frac {11L}{48} + \frac {3R}{8} \right).\]
      </div>
    </solution>
  </formularesponse>

  <formularesponse inline="1" type="cs" samples="R,omega,E,rho,L@0.1,0.1,0.1,0.1,0.1:10,10,10,10,10#10" answer="(rho*omega^2)/E*(L^3/3 + (R*L^2)/2)">
    <label>Find a symbolic expression for the blade elongation \( \delta \) in terms of \(R\), \(L\), \(\rho\), \(\omega\), and \(E\).</label>
    <description>\(\delta = \)</description>
    <responseparam type="tolerance" default="1%"/>
    <textline inline="1" math="1"/>
    <solution>
      <div class="worked-solution">
        \[  \delta = \frac {\rho \omega^2}{E} \left( \frac {L^3} {3} + \frac { RL^2} {2} \right) \]
        <p><b>Obtaining the total elongation of the blade  \( \delta \):</b></p>
        <p>The strain field in the bar is</p>
        \[  \epsilon_a(x) = \frac {\mathcal{N}(x)}{EA} = \frac {\rho \omega^2 \left( \frac {L^2 - x^2}{2} + R\left(L-x\right)\right)}{E}. \]
        <p>We can now calculate the elongation of the bar as the following.</p>
        \[ \delta = \int_0^L \epsilon_{a}(x)dx = \int_0^L \frac {\rho \omega^2}{E} \left( \frac {L^2 - x^2}{2} + R\left(L-x\right)\right)dx. \]
        \[ \Rightarrow \delta= \left[ \frac { \rho \omega^2}{E} \left( \frac {L^2x}{2}  - \frac {x^3}{6} + RLx - \frac {Rx^2}{2} \right)\right]_0^L.\]
        \[ \Rightarrow \delta = \frac {\rho \omega^2}{E} \left( \frac {L^3}{2} - \frac{L^3}{6} + RL^2 - \frac {RL^2}{2} \right).\]
        \[\Rightarrow \delta= \frac {\rho \omega^2}{E} \left( \frac {L^3}{3} + \frac {RL^2}{2} \right). \]
      </div>
    </solution>
  </formularesponse>
</problem>

10.22.1.2. Analyzing Performance on Math Expression Input Problems

For the math expression input problems in your course, you can use edX Insights to review aggregated learner performance data and examine submitted answers. For more information, see Using edX Insights.

10.22.2. Adding a Math Expression Input Problem

You add math expression input problems in Studio by selecting the Problem component type and then using the advanced editor to specify the prompt and the acceptable answer or answers.

To create a math expression input problem, follow these steps.

  1. In the unit where you want to create the problem, under Add New Component select Problem.
  2. Select Advanced.
  3. From the list of Advanced problem types, select Math Expression Input. Studio adds a template for the problem to the unit.
  4. Select Edit. The advanced editor opens the template and shows the OLX markup that you can use for this problem type.
  5. Replace the guidance provided by the template to add your own text. For example, replace the question or prompt, answer options, and solution.
  6. Update the OLX to use any additional elements and attributes in your problem.
  7. Select Settings to provide an identifying Display Name and define settings for the problem. For more information, see Defining Settings for Problem Components.
  8. Select Save.

10.22.3. Math Expression Input Problem OLX Reference

10.22.3.1. Template

Note

The following template includes a Python script. When you add a script to a problem component, do not add to or change its internal indentation. A “jailed code” error message appears when you save the problem in Studio if the <script> element is indented.

<problem>
  <formularesponse type="ci" samples="R_1,R_2,R_3@1,2,3:3,4,5#10"  answer="$computed_response">
    <label>Problem text</label>
    <responseparam type="tolerance" default="0.00001"/>
    <formulaequationinput size="20" />

<script type="loncapa/python">
computed_response = PYTHON SCRIPT
</script>

    <solution>
      <div class="detailed-solution">
        <p>Explanation or solution header</p>
        <p>Explanation or solution text</p>
      </div>
    </solution>
  </formularesponse>
</problem>

This template includes a placeholder value for the samples attribute of samples="R_1,R_2,R_3@1,2,3:3,4,5#10". You enter values for this attribute in the following format: samples="VARIABLES@LOWER_BOUNDS:UPPER_BOUNDS#NUMBER_OF_SAMPLES". Additional detail follows in the description of the <formularesponse> element.

10.22.3.2. Elements

For math expression input problems, the <problem> element can include this hierarchy of child elements.

<problem>
    <formularesponse>
        <label>
        <description>
        <formulaequationinput>
        <responseparam>
        <script>
        <solution>

In addition, standard HTML tags can be used to format text.

10.22.3.2.1. <formularesponse>

Required. Indicates that the problem is a math expression input problem.

The <formularesponse> tag is similar to the <numericalresponse> tag used by numerical input problem types, but <formularesponse> allows unknown variables.

10.22.3.2.1.1. Attributes
Attribute Description
type Can be "cs" for case sensitive, which is the default, or "ci" for case insensitive, so that capitalization does not matter in variable names.
answer

The correct answer to the problem, given as a mathematical expression.

If you precede a variable name in the problem with a dollar sign ($), you can include a script in the problem that computes the expression in terms of that variable.

samples

Specifies important information about the problem in the following lists.

  • variables: A set of variables that learners can enter.
  • lower_bounds: For every defined variable, a lower bound on the numerical tests to use for that variable.
  • upper_bounds: For every defined variable, an upper bound on the numerical tests to use for that variable.
  • num_samples: The number of times to test the expression.

Commas separate items inside each of the four individual lists. The at sign (@), colon (:), and hash tag (#) characters separate the lists. An example of the format follows.

"variables@lower_bounds:upper_bounds#num_samples"

For example, a <formularesponse> element that includes the samples attribute might look like either of the following.

<formularesponse samples="x,n@1,2:3,4#10">

<formularesponse samples="R_1,R_2,R_3@1,2,3:3,4,5#10">

10.22.3.2.1.2. Children
  • <label>
  • <description>
  • <formulaequationinput>
  • <responseparam>
  • <script>
  • <solution>

10.22.3.2.2. <label>

Required. Identifies the question or prompt. You can include HTML tags within this element.

10.22.3.2.2.1. Attributes

None.

10.22.3.2.2.2. Children

None.

10.22.3.2.3. <description>

Optional. Provides clarifying information about how to answer the question. You can include HTML tags within this element.

10.22.3.2.3.1. Attributes

None.

10.22.3.2.3.2. Children

None.

10.22.3.2.4. <formulaequationinput>

Required. Creates a response field in the LMS where learners enter a response.

Learners also see a second field below the response field that displays a typeset version of the entered response. The parser that renders a learner’s plain text into typeset math is the same parser that evaluates the response for grading.

10.22.3.2.4.1. Attributes
Attribute Description
size Optional. Defines the width, in characters, of the response field in the LMS.
10.22.3.2.4.2. Children

None.

10.22.3.2.5. <responseparam>

Used to define an upper bound on the variance of the numerical methods used to approximate a test for equality.

10.22.3.2.5.1. Attributes
Attribute Description
type "tolerance" defines a tolerance for a number.
default Required. A number or a percentage specifying how close the learner and grader expressions must be. If you do not include a tolerance, the expression is vulnerable to rounding errors during sampling. The result of such unavoidable errors is that the grader can mark some learner input as incorrect, even if it is algebraically equivalent.
10.22.3.2.5.2. Children

None.

10.22.3.2.6. <script>

Optional. Specifies a script that the grader uses to evaluate a learner’s response. A problem behaves as if all of the code in all of the script elements were in a single script element. Specifically, any variables that are used in multiple <script> elements share a namespace and can be overridden.

As with all Python code, indentation matters, even though the code is embedded in XML.

10.22.3.2.6.1. Attributes
Attribute Description
type Required. Must be set to loncapa/python.
10.22.3.2.6.2. Children

None.

10.22.3.2.7. <solution>

Optional. Identifies the explanation or solution for the problem, or for one of the questions in a problem that contains more than one question.

This element contains an HTML division <div>. The division contains one or more paragraphs <p> of explanatory text.