'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

Teachers have long struggled with the tension between ensuring a rigorous education for all their students and the reality that students arrive at the start of a school year with vastly different skills and conceptual understandings. The tension can be even more acute in math, which relies heavily on students mastering foundational concepts in…

Big Ideas in school mathematics can be seen as overarching concepts that occur in various mathematical topics in a syllabus. Although there has been much interest recently in the understanding of Big Ideas, there is little research done in the assessment of Big Ideas thinking. In this paper, we discuss our research on Big Ideas in School…

Argumentation is an important mathematical practice, highlighted by research and policy documents that describe ways to structure reform-oriented classrooms (Nardi and Knuth 2017; NCTM 2000; NGA Center and CCSSI 2010). Participating in argumentation can enhance students' mathematics learning as they make sense of mathematical ideas, provide…

Histories of mathematical practice account for mathematical knowledge and action by interpreting presently-available evidence as traces of the events, contexts, and relations that make up the past. Interpretations depend on the assumptions one makes about how mathematical knowledge works, insofar as it is knowledge and insofar as it is…

The article describes a science activity designed to increase students' knowledge and awareness of the spread of COVID-19. It helps students achieve scientific literacy through improving their views about the nature of science and their argumentation skills. It also promotes students' engagement in scientific practices such as modelling,…

This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the…

In this brief article, Peter, Larissa and Doug present a single-page scaffold that challenges us to think of the mathematical proficiencies in a whole new way. By thinking of the proficiencies as verbs, they can be seen as purposeful learner actions and offer clues as to what it might mean to be a mathematician.

In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

In this paper, we focus on the design of assessments of mathematics teachers' knowledge by emphasizing the importance of identifying the purpose for the assessment, defining the specific construct to be measured, and considering the affordances of particular psychometric models on the development of assessments as well as how they are able to…

This article aims to discuss processes of transformation and mobilization of knowledge related to the history of Mathematics as a teaching approach for mathematics at the Basic Education level. The core of the discussion is to highlight ways to explore this theme and point out guidelines to integrate information related the historical development…

Despite its central place in the mathematics curriculum the notion of mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for inculcating mathematical thinking, studies have revealed that students experience serious difficulties with proving that include…