In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

In Singapore, where primary and secondary students routinely top standardized worldwide mathematics examinations, a paradox emerges: when reaching university, many struggle to apply their skills critically in real-world contexts. This commentary examines the challenges and strategies involved in teaching quantitative reasoning (QR) to…

Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

Visual displays, such as icon arrays and risk ladders, are often used to communicate numerical health information. Number lines improve reasoning with rational numbers but are seldom used in health contexts. College students solved ratio problems related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly-assigned…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

The proposed revisions to the "Australian Curriculum: Mathematics" highlight the importance of learning to mathematise, problem-solve and reason in real world contexts, including financial contexts. Through the Economics + Maths = Financial Capability research project, the authors have been imagining fresh ideas for connecting the…

This paper reports the factors that three Year 11 mathematics students identified as influencing their choice to use a Computer Algebra System (CAS) for solving selected problems, some of which were expected to be outside their pen-and-paper (p&p) range. In individual interviews, the students were presented with eleven algebra problems and…

Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today's sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers' application of…

Learning, development, and response to instruction often involve changes in the strategies that learners use to solve problems. In this chapter, our focus is on mathematical problem solving in both children and adults. We offer a selective review of research on three classes of factors that may influence processes of strategy change in…

This quantitative longitudinal study sought to highlight the difference between the proportion of men and women who planned to pursue a STEM major in the fields of mathematics, natural sciences, engineering, and computer and information sciences as freshmen, as well as to determine the proportion of men and women who changed their major choice by…

Multidisciplinary teams are responsible for identifying reasonable accommodations that mediate the impact of a disability and level the playing field between those with and without disabilities on high-stakes mathematics assessments. However, minimal guidance is provided to teams selecting accommodations. This article provides a decision framework…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…

Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students' mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can…

Diagnostic information is a centrepiece of educational decision making. Far-reaching decisions like placements within multi-tiered school systems may have a huge long-term impact on the achieved level of education. Therefore, such decisions should be substantiated or complemented by objective and prognostically valid information. To this end, we…