Abstract
Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under investigation is diverse—which goes along with a diversity of understandings of the term reasoning. The aim of this article is to provide an overview on kinds of mathematical reasoning that are addressed in mathematics education research. We conducted a systematic review focusing on the question: What kinds of reasoning are addressed in empirical research in mathematics education? We pursued this question by searching for articles in the database Web of Science with the term reason* in the title. Based on this search, we used a systematic approach to inductively find kinds of reasoning addressed in empirical research in mathematics education. We found three domain-general kinds of reasoning (e.g., creative reasoning) as well as six domain-specific kinds of reasoning (e.g., algebraic reasoning). The article gives an overview on these different kinds of reasoning both in a domain-general and domain-specific perspective, which may be of value for both research and practice (e.g., school teaching).
Highlights
Mathematical reasoning is an important topic in mathematics education—both in research and in practice
We present our findings with respect to the kinds of reasoning, including the scholars’ definitions or explanatory statements about reasoning and the theories on reasoning that were referred to
We found that some articles regard reasoning as domain-general and others as domain-specific
Summary
Mathematical reasoning is an important topic in mathematics education—both in research and in practice (e.g., at school). According to the Cambridge English Dictionary, reasoning is “the process of thinking about something in order to make a decision” [1]. Mathematical reasoning has often been connected to mathematical proving and the logical process that comes with it [2]. Other scholars take the concept of reasoning in a broader sense, in which reasoning is not restricted to a logical way of thinking but can be based on what makes sense to the person giving the reasons—logical or not [3]. Researchers point out that—on a methodological level—investigating students’ mathematical reasoning helps both teachers and researchers to understand students’ understanding and learning of mathematics. On the other hand, reasoning is seen as the process of learning itself, where the learner builds on knowledge through reasoning [2]
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