Mathematics teacher knowledge: mathematics in the foreground

Abstract

The four research reports published in this issue of JMTE study teacher knowledge focusing mainly on its mathematical dimension. Issues concerning the characteristics of teacher knowledge for mathematics teaching especially at secondary level as well as the interplay between mathematics and pedagogical knowledge emerge. In the first article, Sarah Bleiher, Denisse Thompson and Mile Krajcevski study prospective secondary mathematics teachers’ (PSMT) knowledge of mathematical proof focusing on how they validate students’ arguments and the feedback they provide. In particular, 34 prospective secondary mathematics teachers validated high school students’ arguments before and after implementation of a set of activities in a mathematics methods course. The authors adopt Stylianides’ (2007) position of proof as a mathematical argument that is a connected sequence of assertions for or against a mathematical claim with certain characteristics such as accepted statements, modes of argumentation and modes of argument representation. In their design of the instructional activities, they took into account two difficulties reported in the literature about proof validation: the focus on local specifics of an argument overlooking the global logical structure and the tendency to use an empirical inductive proof scheme. The research questions are related to the effectiveness of the instructional activities on PSMT’s validation skills and to the type of errors they identify. The results indicate that PSMT were successful at judging the validity of an argument in the preand posttest. Concerning the errors to which they attend, it appeared that they did not any longer hold an empirical proof scheme. Although the intervention seemed to have an impact on PSMT’s understanding of proof, using indirect methods seemed to be difficult. Prospective secondary mathematics teachers are also the focus of the second article by Jill Adler, Sarmin Hossain, Mary Stevenson, John Clarke, Rosa Archer and Barry Grantham who study how PSMT experience mathematics in a course (Mathematics Enhancement Course—MEC) addressing mathematics in ‘depth.’ The course is offered in a range of institutions in England and provides an alternative route to mathematics teaching for