This article examines what constitutes a 'good' mathematical problem and proposes to conceptualize the notion of "collective mathematical problems" as phenomena that arise through and by way of the inter-actions enabled by the collective itself. The author examines how these collective mathematical problems can emerge in the classroom…

This systematic review and meta-analysis synthesised evidence on teaching problem-solving skills to children in early childhood education and care settings (ECEC) in the domain of science, technology, engineering and mathematics (STEM). Given the foundational nature of early cognitive development and the growing emphasis on STEM competencies, this…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Contribution: This article proposes a task-driven ADDIE-Twist design model with a double-helix structure, which introduces intelligent teaching tools and lightweight collaboration platforms to design a knowledge-sharing and group collaboration model with two layers of teaching task driven and learning task driven, providing inspiration for the…

Previous studies have emphasised that play can promote children's learning of mathematics. However, little research has been directed towards understanding how collective imaginary play motivates children's mathematical learning. Informed by the cultural-historical conception of play and motives, this paper examines how Conceptual PlayWorld (CPW)…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

Purpose: Being "literate" is well established as key to active civic participation, right from the earliest years of life. Young children's natural curiosity and motivation to understand the world and their places within it through playful explorations offers rich opportunities for learning. Reported here are findings from a STEAM…

Mathematics plays a crucial role in engineering education. Students who are good at math are often advised to consider engineering as a career. In this study, engineers, mathematics teachers, and engineering professors were asked about the type of mathematics representative of engineering, whether the engineering problems created by math…

This teaching note illustrates how escape rooms can be utilized as a tool to teach or review business law concepts, encourage student collaboration, and provide an opportunity for gameplay. Escape rooms can be adapted to any topic, made asynchronous, and scaled up to accommodate larger groups. This note also describes the value of incorporating…

Instructors traditionally lecture on new content before providing practice problems, but learning is often superficial. Exploratory learning before instruction deepens conceptual understanding by giving students a novel activity to explore before direct instruction. We examined how increasing the salience of contrasting cases in exploration versus…

We present example assessments featuring spectroscopic unknown puzzles, where the solution to the puzzle is the outcome of a known chemical reaction. These spectroscopic exercises engage students in a substantially more authentic manner than the conventional structure elucidation puzzles that are ubiquitous in organic chemistry instruction.…

In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

Taking into account the profound impact of technology on modern education, especially during the COVID-19 pandemic, increasing academic interest has focused towards the design and application of such tools on different learning contexts. A specific area of Human-Computer Interaction, called affordance theory, focuses on the perception, design and…

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…