Abstract
This paper presents and discusses the results of a case study that was carried out to understand the mathematical reasoning of 73 second-year student teachers at a university in Zambia. The paper also demonstrates why it is important to develop the reasoning abilities of mathematics student teachers during their initial training programs. The questionnaire items presented to student teachers required them to justify the validity of selected algebraic statements and arguments on odd and even numbers. Factors that influenced participants’ modes of argumentation were also identified, clearly highlighting their implications for mathematics teacher education. Findings of the study revealed that 70% of the participants gave explanations that were aligned to an empirical or inductive mode of argumentation while 7% used the analytical or deductive argumentation mode. The rest of the participants gave explanations that did not reflect valid mathematical justification of the given algebraic statements and arguments. These results clearly indicate that only the minority of participants exhibited an adequate understanding of representing odd and even numbers in general form. Analysing and developing prospective teachers’ mathematical reasoning abilities are necessary to anticipate how they would practice when they are professionally qualified.
Highlights
Mathematics education research has persistently affirmed that the further development of mathematics depends on reasoning (Aricha-Metzer & Zaslavsky, 2017; Ball & Bass, 2003; Brodie, 2010; Ellis, Özgür, & Reiten, 2018; Ross, 1998). Henriques (2013) regards the ability to reason mathematically as the gathering and mastery of specific knowledge of mathematical content
Another inductive argument B received high ratings (M = 3.31, standard deviation (SD) = .87), an indication that student teachers were mostly convinced that argument B reflected a valid mathematical justification of a given statement
The content and pedagogy taught in courses taken by prospective teachers at their colleges and universities should be aligned with the demands of school mathematics curriculum
Summary
Mathematics education research has persistently affirmed that the further development of mathematics depends on reasoning (Aricha-Metzer & Zaslavsky, 2017; Ball & Bass, 2003; Brodie, 2010; Ellis, Özgür, & Reiten, 2018; Ross, 1998). Henriques (2013) regards the ability to reason mathematically as the gathering and mastery of specific knowledge of mathematical content. Mathematics education research has persistently affirmed that the further development of mathematics depends on reasoning (Aricha-Metzer & Zaslavsky, 2017; Ball & Bass, 2003; Brodie, 2010; Ellis, Özgür, & Reiten, 2018; Ross, 1998). Henriques (2013) regards the ability to reason mathematically as the gathering and mastery of specific knowledge of mathematical content. The National Council of Teachers of Mathematics [NCTM] (2000) highlights that mathematical reasoning occurs only when students are able to state and test conjectures as well as building arguments to justify those conjectures. The above argument demonstrates that reasoning is an indispensable component of mathematics and it is one of the features that distinguishes mathematics from other disciplines. According to Mata-pereira and Ponte (2017, p.170), “students engaged in mathematical reasoning gain familiarity with the mathematical language and increase their conceptual understanding”.
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