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.…

This paper aims to understand how primary students use gestures to solve partition tasks and to what extent these gestures may promote fraction understanding. Analysis of six selected students' answers to partitioning tasks, classroom observation, and post-lesson interviews indicates that co-thought representational gestures play a critical role.…

We present the results of a study investigating the potential role of the generative AI GPT-4 in scaffolding students' metacognitive activities during problem-solving. The theoretical framework according to which students' interactions with GPT-4 are analysed is based on three main components: the notion of utilisation scheme within the frame of…

Research has shown that teaching mathematics through problem posing, or problem-posing based learning (P-PBL), is a student-centered instructional approach that can improve students' cognitive and affective aspects of learning. However, since textbooks continue to include very few opportunities for problem posing, researchers have been working to…

This article provides an update on the blind-variation and selective-retention theory of creativity (BVSR), beginning with an overview of its historical development. That brief narrative is then followed by a more extensive summary of recent enhancements in BVSR's conceptual foundations, including formal definitions of creative, sighted, and blind…

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

The present study aimed to describe teachers' instructional flows when implementing a mathematical problem-posing task using scriptwriting technique. With matchsticks, a growing pattern that increases by a constant unit was created and presented to the teachers as a problem-posing situation. We analyzed the instructional flows in 50 scripts,…

Despite the efforts of instructional design (ID) to solve real-life problems, it remains challenging to adapt and be flexible in such situations. In particular, problems that require simultaneous knowledge of multiple domains and contexts are more challenging to solve because real-life problems do not reconstruct the learned experience. This is…

In the context of physics education, it is imperative that educators prioritize the development of students' problem-solving abilities. Given the interdisciplinary nature of physics and its relevance to everyday life, students must possess robust problem-solving skills. However, conventional and uninspiring learning approaches have been shown to…

Many of today's educators learned math in elementary and secondary schools with approaches very different from those outlined in the current standards, and it is difficult to teach for proficiencies educators have not yet developed in themselves. How can teachers find time for this kind of professional learning with all the other responsibilities…

Undergraduate engineering students are commonly introduced to design in their first year and tackle a more authentic design challenge during senior year, with intervening courses focused on technical problem solving. Along this trajectory, students should acquire skills related to the development of engineering requirements, which are important to…

Background/purpose: This study investigates the probabilistic thinking process in solving probability problems by prospective mathematics teachers with a field-independent cognitive style. The objective is to explore how individuals with this cognitive style approach problem-solving based on the three stages of Polya's framework: understanding the…

Providing realistic solutions for word problems proves to be challenging. A possible explanation is the influence of individual's expectations and beliefs about word problems. This explanation was tested in the present study in an out-of-school context. Specifically, the study assessed effects of (1) prompting participants to make realistic…

This case study used individual interviews to investigate graduate students' sensemaking in upper-level electrostatics in the context of problems that can be efficiently solved for the electric potential using Laplace's equation. Although there are many technical mathematical issues involved in solving Laplace's equation, the focus of this…