Abstract
According to psychological and cognitive development theories, the preferences of pupils in elementary school toward inductive versus deductive and general types of reasoning when asked to prove or review mathematical claims, changes along the school years. This study examines this hypothesis through a survey in which 267 pupils from the Arabic sector in three different elementary schools in Israel, in grades 4 to 6 participated. The survey, based on the math reasoning tasks by Healy and Hoyles (1998), is comprised of Algebra and Geometry reasoning tasks. Additionally, 12 of these pupils’ teachers were interviewed in order to explore their attitudes toward mathematical reasoning and math proving tasks. Findings show that: 1) There is a difference in students’ preferences towards types of reasoning, between grades 4 and 6; 2) Sixth graders will be less likely to accept tautologic and inductive reasoning than fourth graders; 3) Elementary school pupils tend to prefer empirical arguments (such as inductive and example-based) as their approach in contrast to the arguments that they believe will receive the highest scores from their teachers. However, findings do not support the hypothesis that there will be a difference in teachers’ preferences towards different types of thinking. The research findings and their practical implications are discussed.
Highlights
While studying mathematics at school, pupils are often required to formulate and test assumptions, to explain and justify conclusions and to prove general theorem or claims
The survey was administrated to 244 pupils in algebra and to 267 pupils in geometry
A survey in which 267 pupils in three different schools in the Arabic sector in Israel participated, has been held in order to learn about the preferences of elementary school pupils toward types of reasoning, in geometry and algebra reasoning tasks
Summary
While studying mathematics at school, pupils are often required to formulate and test assumptions, to explain and justify conclusions and to prove general theorem or claims. The proof is the mathematical tool through which, by argumentation, the correctness of a mathematical claim is established and given universal vali-. An argumentation consists of a claim, a statement that the addresser asks the recipient to accept as a truth or a modus operandi, and a conclusion requiring proof (Toulmin, 1969). The methodology of math and science relies on the discursive nature of claims and include their expression and justification, observation of contrary indications, and the social negotiation of data and theories (Sadler & Fowler, 2006). A high level of argument expresses a high level of literacy (Glassner & Schwartz, 2001), as elementary school students already apply external justification methods, empiric and analytic justification techniques (Flores, 2002)
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