International Portal of Teacher Education

The online resource of academic content on teacher training and teacher education

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In this article, the authors elaborate a conceptualisation of mathematics for teaching as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics). Furthermore, the authors examine implications of this conceptualisation for the mathematical preparation of teachers.

Published: 2010

Updated: May. 09, 2010

The article describes research in mathematical knowledge that useful in mathematical teaching. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity.

Published: 2008

Updated: Nov. 17, 2008

The concept of truth has been central in all students' mathematical experiences across all grades, and the success of instilling the concept highly depends on the mathematics teachers' knowledge of proof. The study in this article examines knowledge of proof by mathematical induction among elementary and secondary mathematics teachers and is based on interviews of 95 participating teachers. Finding reveal that teachers from both groups had difficulties around the essence of the basic step of the induction method, the meaning associated with the induction step, and the possibility that the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse.

Published: 2007

Updated: Jan. 28, 2008