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GET-Forschungsseminar Abstracts

Multiple-Choice Questions for Testing Understanding in Higher Mathematics

Dr. Kerstin Hesse, Institut für Mathematik

07.12.2016, 16:30, P 1.4.17


In an educational project in the lecture course "Höhere Mathematik A für Elektrotechniker" (Higher Mathematics A for Electrical Engineers) understanding and logical reasoning are tested with an innovative kind of multiple-choice questions. The questions offer each five options of which exactly one must be selected, and they test knowledge, problem solving and understanding. The majority of the multiple-choice questions are in the ?Online-Lernerfolgstests? (online tests for learning success), but some questions are presented on the weekly exercise sheets, and solutions to these questions can be submitted for (manual) marking. For the questions on the weekly exercise sheets, a proper mathematical analysis of the selected option must be given to get full marks.

In the first part of my talk, I will explain the motivation and the educational background for the project and present the theoretical background using a taxonomy for learning, teaching and assessing. This taxonomy is not the widely used taxonomy by Anderson & Krathwohl (2001), based on Bloom?s taxonomy, but a mathematical taxonomy developed by Smith et al. (1996) for the purpose of classifying exercises and exam questions. This taxonomy has been slightly modified, and a second dimension for measuring the level of difficulty has been added. The modified taxonomy is used to map the direct learning outcomes of the course and to classify the multiple choice questions developed in the project.

In the second part of my talk, I will present several multiple-choice questions from the project and show some explanations given by students to justify their chosen option among the five possible answers. The students? explanations will illustrate several misconceptions about individual topics among the course material.

More detailed information can be found here.