This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This research synthesizes studies that used a Digitalized Interactive Component (DIC) to assess K-12 student mathematics performance during Computer-based-Assessments (CBAs) in mathematics. A systematic search identified ten studies that categorized existing DICs according to the tools that provided language assistance to students and tools that…

Research in both the New Zealand and international contexts identifies the need for New Zealand classrooms to foster culturally responsive and mathematical practices that align with Påsifika students' cultural values, backgrounds, interests and experiences. The aim of this study was to investigate how the use of culturally responsive tasks along…

The purpose of this study is to develop design principles for crafting tasks that will encourage conjecturing and proving in the context of elementary number theory at the undergraduate level. From the analyses of the written work of 46 prospective mathematics teachers on a task designed according to these principles, we think that there is…

We present findings from a study of prospective middle school teachers' reasoning as they transitioned from thinking arithmetically to thinking algebraically about even and odd numbers. Teachers were asked to make sense of and use two representations of even and odd numbers to model them and to make connections between the representations.…

To implement current reforms regarding proof and reasoning in secondary school mathematics successfully, pre-service secondary mathematics teachers must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that pre-service secondary mathematics teachers had for…

This study determined if overall mathematics performance of male and female students was: (1) different within each of six content areas; (2) differentially affected by ability grouping within each of the six content areas; and (3) differentially affected by the combination of ability grouping and grade level within each of the six content areas.…

The purpose of this study was to characterize and compare novice and experienced elementary teachers' pedagogical knowledge and pedagogical content knowledge of three major topics in mathematics: whole number operation, fractions, and geometry. The study participants were 26 preservice elementary teachers and 28 experienced kindergarten through…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…