Online Assessment of Mathematics

Dr Paul Bolton

School of Mathematics

July 2008

Mathematical Assessment Software

• Mathletics

• Maple T. A.

• MyMathLab

• STACK

• WeBWorK

Mathletics

• Developed by Martin Greenhow at Brunel

• Randomized elements of questions

• Multiple Choice or Numerical Input Only

• But highly developed feedback

• Sample questions available freely

• Source code also available but requires Question Mark Perception

Maple T. A.

• Uses the computer algebra system ‘Maple’• Commercial package from Maplesoft• Examined versions 2.5 and 3.0. Version 4.0 just

released.• Can be run from central server or installed

locally• Questions can be authored with Question Bank

Editor• Alternatively use online LaTeX converter

MyMathLab

• Mathematical engine MathXL

• Commercial; runs with CourseCompass from Pearson

• Students have to buy textbook or access code

• Wide range of teaching and assessment materials tied to this textbook

http://www.mymathlab.com/

WeBWorK

• University of Rochester• Open source• Can be installed and run on a local Web server• Assessments written in Perl; mathematics can

be written in LaTeX or html.• http://webwork.rochester.edu/

WeBWorK Problem Libraries

• WeBWorK problem libraries include:

• Calculus

• Graph Theory

• Linear Algebra

• Physics

• Statistics

• http://webwork.maa.org/wiki/Problem_Libraries

Rochester Problem Library

STACK

• Uses open source CAS ‘Maxima’• Created by Chris Sangwin at Birmingham• Free to HE maths community• Authoring system part menu based, part html,

LaTEX and Maxima; translates to XML.• Can set up decision tree which analyses

students’ response to identify and point out common misconceptions (malrules)

• http://stack.bham.ac.uk/

Evaluation and Comparison of STACK and WeBWorK

• Installed both programs on local Web server

• Devised standard set of questions

• Recruited group of Foundation Year students to try out software on a PC cluster

• Gathered opinions from focus group and questionnaire

Students’ Opinions

• Students positive about both software programs; in particular one commented preferred them to WebCT.

• Seemed able to enter mathematical syntax without too much trouble. (The students already had some experience with Mathematica.)

Students’ Opinions

• STACK somewhat slow even for single user; nevertheless server coped running both programs for multiple users

• Students found WeBWorK more visually appealing; STACK had some problems representing mathematical notation, especially with Firefox browser

• But realised STACK had considerable underlying mathematical sophistication

• “WeBWorK has looks but STACK has brains.”

Diagnostic Tests

• First Year students in engineering and science sit (paper) diagnostic test in Freshers’ Week to clarify mathematical preparation

• Academic year 2007/2008 could choose to use Maple T.A., STACK or WeBWorK for practice (formative assessment)

• Followup summative assessments were still in WebCT

Diagnostic Tests 2008/2009

• STACK to be integrated with Blackboard Vista

• STACK used in place of WebCT for both formative and summative assessment

• More details in Paul Bolton, Computer assisted assessment of mathematics, MSOR Connections Vol. 8 No. 3 August – October 2008