Assessment of e-Mathematics with Maple

Abstract

In our mathematics courses, computer laboratory sessions with Maple are being used to fundamentally change the way we teach. Sophisticated computer algebra systems (CAS) such as Maple (and Mathematica) can do it all: numerical computation, symbolic manipulation, graphics (visualization and animations), word processing, programming and communication (via internet). This can be exploited not only in the teaching and learning of mathematics, but also in the assessment. We discuss our assessment experience with several first year courses (where Maple supports a traditional approach) and third year courses (run in Maple ?mmersion? mode where everything is done with Maple). Our students have done some calculus at high school, so we have, since 1998, a first year course, Nonlinear Mathematics, that is taken concurrently with a fairly standard type of calculus subject. The nonlinear mathematics subject introduces some modern ideas, namely Phase Plane Methods and Iteration, and the use of Maple is integrated throughout this subject. Animation is introduced in this subject and students must, in small groups, choose an animation project and present their animation (in the lab) for assessment.

The assessment is demanding of staff time but is almost a tutorial. We would like to do more in this style although it is difficult to do so ?fficiently? With the first year ?alculus +?courses, Maple is used in separate lab sessions to support traditional first year courses. We use Blackboard to post the teaching and assessment materials (Maple files) on the web. We discuss in detail two assignments that have been individualized for each small group. Students submit their solutions, as Maple files, to proxy email accounts. They are marked with the overall marks distribution and detailed comments interspersed throughout the Maple file ?all in a new paragraph style, coloured dark green. The marked Maple files are emailed back to each student. One of these assignments focuses on numerical integration using trapezoidal and Simpson? rules. After careful analysis of student work, we will now re-design this to be submitted and marked by AIM ?a computer based assessment system that uses Maple to interrogate the answers and provide feed back for particular errors (in how Simpson? rule has been incorrectly programmed). Another individualized assignment is where students use our version of the Polya type of problem solving approach using Maple to maximise the area in the Norman window problem. A labelled diagram is required ?something that computer based assessment (CBA) programs don? help with! We emphasize that Maple files should include graphics and a ?rite-up?and propose that CBA tools should provide a semi-automatic marking mode where some text and graphics can be marked by the lecturer with the computations (symbolic and numeric) marked automatically. We conduct third year courses in Vector Calculus, Geometry of Surfaces and Finite Element Methods in Maple immersion mode and discuss our experience with CAS assessment: Maple assignments and examinations, some of which have been individualized. We find that grading e-examinations takes similar staff resources as the usual marking of hardcopy scripts.