This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students' conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many…

The COVID-19 pandemic provided students a rare opportunity to use their mathematical knowledge to make sense of a top-of-mind crisis. Based on a report in a major regional newspaper, we designed tasks that require an understanding of infection rates and an interpretation of a misleading claim made in the newspaper. Our analysis of 91 undergraduate…

We investigated the cognitive demand of the exercise problems that middle school students from Nepal are expected to complete. The middle school (grades 6, 7, and 8) mathematics textbooks examined in this study were published and distributed by the government of Nepal. Our data set consisted of textbooks that are currently in use in public schools…

Collaborative problem solving (CPS) has been shown to both engage and benefit students' learning of mathematics. However, there is evidence that group work is not always easy to facilitate, in part because educators lack details about learners' engagement during group work: the processes of problem solving involved, and how these are engaged. In…

This commentary raises and discusses questions based on some of the agreements, disagreements, and themes found in the four chapters on fractions. It considers (1) the importance of tasks that are based in perception and readily available activity in light of an emphasis on problem solving in mathematics education, and the role that theories about…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…

This study examined how two small-group discourse types (Reflective and Exploratory) supported the inclusion and enacted levels of cognitive demand of students who typically struggle with mathematics in real-world, task-based assessment activities. The study focused on 11 fifth-grade students within a larger study involving 97 fifth-grade students…

In this paper, we offer a theoretical account of the emotion-cognition dialectic (i.e. the unit of feeling and cognition in thought) in identity formation (or identification), focusing on early childhood and mathematics. We consider how contradictory (emotional-cognitive) experiences which arise in different forms of mathematical activity (a…

Embodied cognition is growing in theoretical importance and as driving a set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to connect with inspired colleagues in this growing community of discourse…

In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

In this paper, we emphasize the methodological challenges of analyzing data with/in an enactivist framework in which (1) all knowing is doing is being, while focusing on, (2) how an entry by the observer transforms usual ways of analyzing data. In this sense, the association of knowing with doing suggests a shift in attention away from what…

The aim of this paper is to build up an argument about the importance of a mathematical analysis of young children's activity in relevant for the age educational tasks. Most of current approaches (psychological, social, and pedagogical) are limited to the study of the development of children's thinking, paying less attention to the involved…

In this paper, we trace the development of our theorizing about students' mathematical understanding, showing how the adoption of an enactivist perspective has transformed our gaze in terms of the objects of our studies and occasioned for us new methods of data analysis. Drawing on elements of Pirie-Kieren (P-K) Theory for the Dynamical Growth of…