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…

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

This action research study explores the interplay between language acquisition and high school mathematics education, particularly for multilingual learners. The study challenges conventional, segregated approaches to math and language learning that emphasize formulaic memorization and algorithmic methods, contributing to the "math…

The introduction of digital artefacts for the teaching/learning of mathematics raises the issue of "transitioning" between the mathematical knowledge built in digital contexts and that built in a more traditional, non-digital context, and vice versa. In this article, we address this issue by presenting a teaching experiment aimed at…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

A primary goal of ethnomodeling is to value, sustain, and in some instances introduce cultural practices and traditions that have often been lost or overshadowed because of an emphasis on modern methods (Orey & Rosa, 2010). Through an ethnomodeling task focusing on geometric transformations, the authors share a Model It! activity to engage…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

In this study, it was aimed to examine the argumentation structures of 5th-grade middle school students, while they were structuring geometric concepts in argumentation-based activities of geometric shapes. To this end, 7 fifth-grade students studying in a public middle school were included in the study. In the study, five geometry tasks involving…

Mathematical spaces extend far beyond the classroom and physical environments into virtual spaces. Today's students have more to consider than just their face-to-face experiences with mathematics inside or outside the classroom; they have the online perspectives of others to consider as well. To gain critical insight, we conducted this research…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

In this article, the authors present variants to the classic problem the Prisoner's Dilemma. They discuss how senior secondary school students can use these variations to explore basic game theory concepts and develop mathematical proficiencies and practices. They also suggest how students can apply these concepts to decision-making processes in…

This study investigated the effects of (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

This study investigated the effects of: (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…