Moodle Math Expression Question Type

A Moodle question type that allows course instructors to create questions that require the student to submit a mathematical equation as an answer.

REQUIRES:

• Math Editor
• MathJax Filter

Usage

Creating a Question

(Important fields and their descriptions)

Question Text: This is the question, this is the part that is shown to the student.

Button Groups and Button List: This is the list of buttons that will appear within the student's editor when answering the question. These are the buttons that are in addition to the variables that are used in the question.

Compare Type: How the student's response is evaluated. Currently there are two methods:

• Simple: Performs a simple symbolic comparison between two expressions. No expansion or factorization is performed hence expressions like "(x+1)^2" and "(1+x)^2" will evaluate as the same but expressions like "(x+1)^2" and "x^2+2*x+1" will not.
• Full: Performs a full symbolic comparison between two expressions. This will involve fully simplifying each and then comparing to see if the result is the same.

Answers: Each possible answer and their corresponding scores and feedback values. There must be at least one answer with 100% score.

Variables: The algebraic variables that are part of the question. These appear within the student's editor when answering the question.

Excluded Expressions: (If full compare type is used) These are expressions that would normally be considered valid but are actually incorrect. See the tutorial below for an example usage.

Tutorials

• Polynomial Simplification
• Gravitational Potential Energy

Question Type

Installation

1. Get the zip file mathexpression.zip (DOWNLOAD)
2. To install this plugin, visit the Moodle plugin installation page and upload this zip as a Question Type the url is typically http://moodle_root/admin/tool/installaddon/index.php
3. Go to the Math Expression settings page and update the URL to the Python Sage server, if you don't have one see the Server installation instructions below.

If this fails, simply extract the zip into the moodle_root/question/type folder and visit the administration notifications page to complete the installation.

References

• http://docs.moodle.org/dev/Question_types

Python Sage Server

This question type uses Sage Math to evaluate the correctness of a student's response. In order to achieve this, we created a simple Python HTTP server with a REST API. The question type's settings contain the parameters used to hook up to this service. See the server source code in the server directory for more information. Installation and running instructions are bellow.

Server Installation

1. Install Sage Math on the server machine, once this is is done running sage from the command line should work.
2. Download Web.py and untar it
3. Navigate to the extracted folder and run the following command ( NOTE: it is important to run this using the Python that is bundled with Sage) sudo sage -python setup.py install
4. Navigate to this project's server folder
5. Start the server sage -python server.py (a port can be specified by using the -p flag)

This will create a server on your machine on port 8080 or the one you specified. Typically the url will be something like http://your_machine:8080/sage.

Server API

Simple Compare
http://your_server/sage/simple?expr1=...&expr2=...

Performs a simple comparison of the two given expressions. To perform the comparison, it parses both equations into the Sage Math symbolic representation and subtracts them. If the result is 0, then the equations can be deemed equivalent.

• Parameter: expr1 - a string representation of an expression, eg. a+b+c/2, can also be in LaTeX format
• Parameter: expr2 - same as above, eg. \frac{a+b+c}{2}
• Returns: a JSON object containing three fields:

{
  'answer': 'algebraic notation for expression 1'
  'response': 'algebraic notation for expression 2'
  'result': true or false
}

The equations are echoed back into their algebraic equivalents, this is mostly for your own debugging purposes.

Full Compare
http://your_server/sage/full?expr1=...&expr2=...&exclude=[]...

Performs a full comparison of the two given expressions. To perform the comparison, it parses both equations into the Sage Math symbolic representation, simplifies them and then subtracts them. If the result is 0, then the equations can be deemed equivalent. An optional list of excluded expressions can also be specified as equations that evaluate to true, would represent an invalid answer. This is used to prevent the student from simply echoing the initial equation in the case a simplification is requested.

• Parameter: expr1 - a string representation of an expression, eg. a+b+c/2, can also be in LaTeX format
• Parameter: expr2 - same as above, eg. \frac{a+b+c}{2}
• Parameter: exclude - an array of excluded expressions, these expressions can be in algebraic or LaTeX format
• Returns: a JSON object containing three fields:

{
  'answer': 'algebraic notation for expression 1'
  'response': 'algebraic notation for expression 2'
  'result': true or false
}

The equations are echoed back into their algebraic equivalents, this is mostly for your own debugging purposes.

Examples:

• sage/full?expr1=(x+1)(x+2)&expr2=(x+1)(x+2)&exclude=[(x+1)(x+2)] returns false
• sage/full?expr1=(x+1)(x+2)&expr2=x^2+3x+2&exclude=[(x+1)(x+2)] returns true

Server Development

This server uses the Web.py library to provide the web server interface. Ensure this package is installed as part of your Sage Python environment. See the server installation instructions for details on how to do this.

All server related code is located in the server folder.

Breakdown of file functions:

• algebra.py - Functionality that converts LaTeX equations into algebraic equivalents that can be understood by Sage
• algebra_test.py - Unit tests for the LaTeX to algebra conversion
• sageserver.py - Interface functions between Python and Sage
• server.py - Main server file, contains the GET and POST web handlers

Server References

• http://webapp-improved.appspot.com/tutorials/quickstart.nogae.html

References

• http://docs.moodle.org/dev/Creating_a_web_service_client
• http://docs.moodle.org/20/en/How_to_create_and_enable_a_web_service
• https://github.com/moodlehq/sample-ws-clients/tree/master/PHP-REST