Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the…

Novice secondary mathematics teachers attempting teaching consonant with the National Council of Teachers of Mathematics (1991, 2007) "Professional Standards for Teaching Mathematics" experience many stresses related to their attempts at student-centered instruction; prominent among those were novices' challenges when orchestrating…

Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were…

In order to promote mathematical understanding among English Language Learners (ELLs), it is necessary to modify instructional strategies to effectively communicate mathematical content. This paper discusses the instructional strategies used by four pre-service teachers to teach mathematics to secondary students in English-medium schools in…

Students' struggles in learning reasoning and proof (RP) in mathematics are well known. Despite the instantiation of RP opportunities in mathematics textbooks in the USA and the important role that textbooks play in teachers' instructional decisions, little research has been conducted on analyzing student textbook tasks and narrative sections of…

This study presents a content analysis of the new Iranian Grade 9 mathematics textbook and two Australian Year 9 mathematics textbooks, examining the extent to which the problems show characteristics associated in the literature with promoting mathematical literacy. The new Iranian book was produced to meet a range of needs including several well…

This article describes the process of development of assessment instruments for a three-year longitudinal comparative study that focused on evaluating American high school students' mathematics learning from two distinct approaches to content organization: curriculum built around a sequence of three full-year courses (Algebra 1, Geometry, and…

This article adds to current research on enhancing student discourse in mathematics teaching specifically in secondary schools but with equal relevance to elementary schools. Three mathematics teachers in secondary education were confronted with the question of how to encourage students to discuss their work with each other in the daily practice…

In this article, I outline processes that supported or hindered Elin, a mathematics teacher, to engage in pedagogy development. In a setting inspired by critical mathematics education, Elin was encouraged to bring societal themes into her upper secondary teaching so that mathematics was connected to social science subjects. A classroom environment…

We report the results of a classroom study of three secondary mathematics teachers who had no prior experience teaching with technology as they began to use an online mathematics learning system in their lessons. We gave the teachers only basic instruction on how to operate the system and then observed them intensively over four school terms as…

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence…

When questioned, secondary mathematics teachers in rural and regional schools in Australia refer to their limited opportunities to engage and share experiences with peers in other schools as an under-utilised and cost-effective mechanism to support their professional learning and enhance their students' learning. The paper reports on the creation…

Rural schools, students, teachers, administrators, families and community leaders face unique challenges from those of their urban and suburban counterparts. This paper investigates motivation in rural secondary schools, with a particular focus on mathematics, from teacher and student perspectives. It integrates recent research on math learning…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…