Types of reasoning required in university exams in mathematics

Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students’ understanding of the underlying mathematical con...

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Bibliographic Details
Published in:The Journal of mathematical behavior 2007, Vol.26 (4), p.348-370
Main Author: Bergqvist, Ewa
Format: Article
Language:English
Subjects:
Algorithms
Assessment
Calculus
Calculus exams
Creativity
didactics of mathematics
Foreign Countries
Higher Education
Introductory Courses
MATEMATIK
matematikdidaktik
Mathematical Concepts
Mathematical reasoning
MATHEMATICS
Mathematics Instruction
Mathematics Tests
Sweden
Task Analysis
Tests
University level mathematics
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Summary:Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students’ understanding of the underlying mathematical concepts. It is therefore important to study the types of reasoning students have to perform in order to solve exam tasks and pass exams. The purpose of this study is to examine what types of reasoning students taking introductory calculus courses are required to perform. Tasks from 16 exams produced at four different Swedish universities were analyzed and sorted into task classes. The analysis resulted in several examples of tasks demanding different types of mathematical reasoning. The results also show that about 70% of the tasks were solvable by imitative reasoning and that 15 of the exams could be passed using only imitative reasoning.
ISSN:0732-3123
1873-8028
1873-8028
DOI:10.1016/j.jmathb.2007.11.001