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Learning Mathematical Rules With Reasoning

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Author(s): Baig, S. and Halai, A.,

Journal: Eurasia Journal of Mathematics, Science & Technology Education
ISSN 1305-8223

Volume: 2;
Issue: 2;
Start page: 15;
Date: 2006;
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Keywords: Reasoning | Mathematical Rules | Understanding | Process of Learning Mathematics

ABSTRACT
This research focused on students learning of mathematical rules with reasoning. A small group ofstudents (age 11-12 yrs) was observed closely by the first author as she taught them fraction rules. The area of focuswas fractions and activities were designed pertaining to the four rules of fractions: addition, subtraction,multiplication, and division. The study was undertaken from a constructivist perspective of learning according towhich students’ learn through active participation in the construction of knowledge (Glasersfeld, 1995). This wassignificant in the context of mathematics classrooms in Pakistan which usually subscribe to the objectivistepistemology i.e. knowledge of the ultimate reality is possible. An implication of adhering to this epistemology is theknowledge transmission view of teaching and learning (Halai, 2000). Key findings of the study were that there weretwo significant factors that enabled students to learn rules with reasoning were: Teachers questions and opportunitiesfor students to explain thinking; and opportunity for students to engage with concrete and semi concrete materials. Thestudy also provides some useful insights into the sequence of teaching the fraction rules and raises implications formathematics teaching and teacher education.
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