SCHOOL OF EDUCATION: Teaching Mathematics for Understanding

This is a position paper in which we argue for Teaching for Mathematising as a pedagogy that supports teaching mathematics for understanding in primary school. Mathematics education in Australia currently emphasises teaching for mathematical understanding, a shift that redirects children's learning from merely memorising computation procedures to helping children construct knowledge of the mathematics that informs mathematical concept and processes.

This study aims to investigate how secondary mathematics teachers understand and intend to use textbooks for their mathematics instruction. For this purpose, we developed a set of survey items in order to unpack what the teachers understand the mathematical tasks suggested in the textbooks in terms of the levels of cognitive demand and how they intended to use the tasks in the textbooks for their teaching. Twenty-five teachers participated in the survey. The data from the survey were analyzed.

In Zimbabwe, school pupils study matrix operations, a topic that is usually covered as part of linear algebra courses taken by most mathematics undergraduate students at university. In this study we focused on Zimbabwean teachers who were studying the topic at university while also teaching the topic to their high school pupils. The purpose of the study was to explore the mental conceptions of matrix operations concepts of a sample of 116 in-service mathematics teachers.

Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn.

When I did my master’s in mathematics education in the 1980s in Copenhagen, Denmark, my professor, Bent Christiansen, used to say that the aim of mathematics education research is “to understand mathematics teaching and learning in their full complexity and contribute to their further development” (personal communication). Except for the somewhat absolutist connotations of the way he phrased it, I think most in our field today would agree with Christiansen’s intention: we are to develop comprehensive understandings of the problems of mathematics teaching and learning, and the ambition is, at least in the long run, to support the development of institutionalised teaching–learning practices.

Recovering Mathematics: An Ontological Turn Toward Coming to Understand the Teaching of Mathematics with Children is an interpretive study into the teaching of mathematics to children. Drawing from Gadamer's (1989) ontological hermeneutics, this research examines lived experience through narrative pedagogic events to explore the idea of recovering mathematics as a living human enterprise for children and teachers in schools.

Heaton (2000), a nine-year veteran of elementary school teaching and the winner of the outstanding teacher award from the University of Vermont, describes the issues she faced when trying to teach with the Comprehensive School Mathematics Program (CSMP) curriculum - a curriculum that, even though developed prior to the current curriculum standards, promoted a similar reform-based view of mathematics learning and teaching.