If you've arrived at this post, you're likely to have a STEM background. You may have heard of or had experience with Maple T.A. or similar products in the past. For the unfamiliar, Maple T.A. is a powerful learning and assessment system designed for STEM courses, backed by the power of the Maple computer algebra engine.
These posts mirror conversations we’ve had among the development team and with our colleagues at the University of Birmingham, and we hope they’ll be of interest to the wider Maple T.A. community and potential adopters as well. The implementation of Maple T.A. over the last couple of years at UoB has resulted in a strong and enthusiastic knowledge base which spans the STEM subjects and includes academics, postgraduates, and undergraduates as both users and developers, and the essential IT support in embedding it within our virtual learning environment (VLE), Canvas at UoB.
By effectively extending our VLE so that it can “understand” mathematics, we are able to deliver more robust learning and assessment in mathematics-based courses. Take a look at the following example comparing the learning experience between a standard multiple choice question and a question delivered using the Maple T.A. context.
Let’s compare methods for solving a quadratic equation. For background, here’s a typical paper-based example so you can see the steps to solving this sort of problem.
Here’s an example of a quadratic equation.
To find the roots of this quadratic equation means to find what values of x make this equation equal to zero. Of course, we could just guess the values. For example, guessing 0 would give:
So 0 is not a root, but -1 is.
There are a few standard methods that can be used to find the roots. The answer to this sort of question takes the form of a list of numbers; for the above example, the two roots are -1, 5. For the uninitiated, quadratic equations always have two solutions—but in some cases, the two roots could be the same number. Therefore, the correct solution for a quadratic equation could be presented as a pair of different numbers (e.g. 3, -5), the same number repeated (e.g. 2, 2), or a single number (2). The point is: There are several possible ways to correctly format an answer to this type of question.
With these basics covered, let’s see how we might tackle this question in a standard VLE. Most VLEs are not designed to deal with lists of variable length, so we’d have to present this as a multiple-choice question. Fig. 1 includes a slightly different quadratic equation that shows how this might look.
Fig 1: A multiple choice question from a standard VLE
Unfortunately, presenting the question this way gives the student a lot of implicit help with the answer, and students are able to play a process-of-elimination game to solve the problem, rather than use the key concepts to understand the solution.
Now, let's see how we could ask this question in Maple T.A, shown in Fig. 2. In this example, the student is encouraged to answer the question using a simple list of numbers separated by commas. The students are not helped by a list of possible answers and are left to genuinely evaluate the problem. They’re able to provide one or multiple roots, if they can find them— either type of answer is accepted. After a student has attempted to answer the question, they’re able to review their response and the teacher's response, as well as question-specific feedback. See Fig. 3.
Fig. 2: Free response question in Maple T.A.
Fig. 3: Grading response from Maple T.A.
Want to see more? The question can be downloaded here and imported as a course module to your Maple T.A. instance. It can also be found on the Maple T.A. cloud by searching for "Find the roots of a quadratic." Simply click on the “Clone into my class” button to get your own version of the question to explore and modify.
Dr. Nicola Wilkin
Head of Teaching Innovation (Science), College of Engineering and Physical Sciences
University of Birmingham, Maple T.A. user group