Development of abstract mathematical reasoning: the case of algebra

Sušac, Ana and Bubić, Andreja and Vrbanc, Andrija and Planinić, Maja (2014) Development of abstract mathematical reasoning: the case of algebra. Frontiers in Human Neuroscience, 8. p. 679. ISSN 1662-5161

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Abstract

Algebra typically represents the students’ first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students’ ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16–17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15–16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students’ transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

Item Type: Article
Keywords: mathematics; education; algebra; problem solving; cognitive development; abstract reasoning; concrete reasoning; strategy
Date: 2014
Subjects: NATURAL SCIENCES > Physics
Additional Information: © 2014 Susac, Bubic, Vrbanc and Planinic. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Received: 19 April 2014; Accepted: 14 August 2014; Published online: 02 September 2014.
Divisions: Faculty of Science > Department of Physics
Project code: 198002
Publisher: Frontiers Media
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 13 Dec 2017 17:05
Last Modified: 13 Dec 2017 17:05
URI: http://digre.pmf.unizg.hr/id/eprint/5751

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