An Analysis of Prospective Teachers’ Mathematical Reasoning on Number Concepts

  • Angel Mukuka The University of Rwanda, College of Education
  • Overson Shumba Copperbelt University, Kitwe, Zambia
  • Sudi Balimuttajjo Mbarara University of Science & Technology, Uganda
  • Vedaste Mutarutinya University of Rwanda – College of Education (UR-CE), School of Education
Keywords: inductive and deductive arguments, mathematical reasoning, number concepts, prospective teachers

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.

Author Biographies

Angel Mukuka, The University of Rwanda, College of Education
African Centre of Excellence for Innovative Teaching and Learning Mathematics & Science
Overson Shumba, Copperbelt University, Kitwe, Zambia
Centre for Academic Development, & School of Mathematics and Natural Sciences
Sudi Balimuttajjo, Mbarara University of Science & Technology, Uganda
Department of Educational Foundations and Psychology
Vedaste Mutarutinya, University of Rwanda – College of Education (UR-CE), School of Education

Department of Mathematics, Science and Physical Education

 

Published
2020-12-30
Section
Articles

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print ISSN: 2508-1128