The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

There are both educational and cultural benefits to first language (L1) instruction, particularly in the early years of school, but in Australia, few Indigenous language-speaking students are taught in their own languages. Teaching mathematics in Indigenous languages requires both linguistically capable Indigenous educators and the identification…

Dominant cultural beliefs contend that mathematics is exclusive; only some have access to "the gift." Within classrooms and amidst everyday vernacular, scripts about mathematics and who can "do" mathematics reify such traditional beliefs. Mathematics teacher educators work with preservice teachers (PSTs) to challenge such…

Supporting students' problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student…

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students' strategies in these two situations, we find that difficulties in…

The present study examines the structure and mathematical content of children's mathematical arguments as part of communication in play-based activities. It shows how Nordin and Boistrup's (The Journal of Mathematical Behavior 51:15-27, 2018) framework for identifying and reconstructing mathematical arguments, which includes Toulmin's model of…

Construct maps and related item type frameworks, which respectively describe and identify common patterns in student reasoning, provide teachers with tools to support instruction built upon students' intuitive thinking. We present a methodological approach--embedded within common assessment development processes--for developing such construct maps…

Describing and analyzing teaching practice has been a focus of researchers interested in the interaction and connections between teachers' content knowledge and their pedagogical knowledge. This study described the role of a teacher's mathematical content and pedagogical content knowledge in involving students in learning and solving Science,…

The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

This study analyzed the variation in teachers' mathematical educational values between distance and traditional face-to-face teaching. Enabled by the unique circumstances of the COVID-19 pandemic, the research explored the impact of remote teaching on primary and secondary mathematics education in Hong Kong. An online survey, completed by 109…

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for…

The interplay between mathematics teachers' beliefs and practices has been widely investigated and research has examined how teachers' beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers' self-reported beliefs and practice changes as they…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

Multiple representations can enhance students' understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students' "learning" with multiple representations, little is known about supportive "teaching"…

An important topic of study in secondary mathematics is non-linear functions, including quadratic equations. In this study, findings from 25 Year 11 students indicated that difficulties with critical prerequisite concepts such as algebraic conventions impeded students' success in understanding and working with quadratics. Analysis of student…