Generation of abundant multi-choice or STACK type questions using CAS


The Boiler House

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In the past four years, the author has developed more than 120 video lectures for a linear algebra course, each of which is of about 10 minutes duration, and has tried to conduct flipped class. The author set tasks for the students using Moodle questions, which are mainly of STACK type, in order to check if they have really studied the video materials and how deeply they understand them.

According to the questionnaire result, in the case that the questions have too many input fields (e.g. such as 4 by 4 or 5 matrix entries) or require some CAS-formatted texts, the students may have some difficulty to answer the questions, especially on a smartphone. Multiple choice type or true-false type questions are very simple to answer on such devices.

In the latter half of the last academic year, the author developed CAS (Mathematica) programs to automatically generate multiples of 100 mutually different matrices for some problems. For example, one of the programs generates the question data to select all diagonalizable matrices, the number of which is ranging from 3 to 7, from 10 matrices of degree 3. In order to prove that the students actually solved the questions by themselves, they were instructed to submit papers describing the process of the solution. To utilize a large amount of “smartphone-friendly” suggestive questions, we are planning to develop more generating programs to cover the entire course, including non-computational tasks, by using Mathematica/webMathematica or other systems/languages, such as Maxima, Maple, Python, Ruby, PHP, etc.