Whilst educational goals in recent years for mathematics education are foregrounded the development of mathematical competencies, little is known about mathematics teachers' competencies. In this study, a group of practising teachers were asked to solve an algebra problem, and their solutions were analysed to determine the competencies apparent…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

We articulate a framework for delineating student thinking in active, STEM-rich learning environments. Researchers have identified ways of reasoning that relate to specific content areas and practices within each of the STEM disciplines. However, attempts at characterizing student thinking in transdisciplinary STEM environments remains in its…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

The development of computational thinking is as important as writing, reading and arithmetic, and, it should start as early as kindergarten (Wing, 2008). However, little has been done in terms of investigating the factors influencing the development of computational thinking in preschool education (Bers et al., 2014; Ching et al., 2018; Kazakoff…

The positive correlation between spatial ability and mathematical ability has been well-documented, but not well-understood. Examining student work in spatial situations that require numerical operations provides us with insight into this elusive connection. Drawing on student work with angle, length, volume, and area, we examine the ways in which…

This reflection paper argues that the design and development of digital games teach essential 21st century skills. Intrinsic to application and game development is design thinking. Design thinking requires iterative development, which demands creativity, critical thinking and problem solving. Students are engaged through learning by doing in both…

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

Reasoning is considered to be an important proficiency in national mathematics curricula both in Australia (ACARA, 2014) and Malaysia (MOE, 2013). However, the nature of reasoning that supports learning and problem solving in mathematics is an area that requires further study (Schoenfeld, 2013). In this study we explored the link between…

Although students' difficulties in developing and understanding proofs in mathematics is well documented, less is known about how students' example use may support their proof practices, particularly at the middle school level. Research on example use suggests that strategic thinking with examples could play an important role in exploring…

In this paper, the RBC+C framework (Hershkowitz, Schwartz, & Dreyfus, 2001) is used to analyse and describe construction and consolidation of mathematical knowledge by primary pupils in a whole-class setting. I describe a lesson that concerned what is commonly termed the Handshakes problem. One pupil spontaneously established a connection with…

Proportional reasoning is important for informed decisions in proportional problem situations. This paper reports on mathematical content knowledge related to proportional reasoning of second-year, pre-service teachers. Responses to two ratio items provide insights into their correct method of solutions and common misconceptions. Anchor Points…

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…

This research report examines how two groups of bilingual algebra students made connections among representations while solving a non-routine generalization problem. Using a socio-cultural orientation to mathematics learning, together with a semiotic lens on students' joint mathematical activity, this report details the type of connections among…

The routine jobs of yesterday are being replaced by technology and/or shipped off-shore. In their place, job categories that require knowledge management, abstract reasoning, and personal services seem to be growing. The modern workplace requires workers to have broad cognitive and affective skills. Often referred to as "21st century…