This study investigated 45 undergraduate students' mathematical problem posing based on four problem situations. This study was designed to better understand the kinds of problems they pose, and the kinds of mathematical ideas exhibited when problem posing. The findings of this study support that underprepared college students can pose…

While much research has been done on Critical Thinking (CT) skills, the "disposition toward CT" has not been adequately investigated. The paucity of literature regarding technology teachers' disposition toward CT is particularly problematic as these teachers have to assist learners with the designing and making of solutions (artefacts)…

For too long, problem solving has been studied as a solitary and isolated activity where individuals make progress based on personal resources acquired from knowledge, previous experiences or moments of illumination; however, in society, and indeed amongst mathematicians, problem solving can be highly collaborative and occurs in spaces where…

In this paper, we explore how science textbook authors reconciled their personal hopes with disciplinary and societal demands in their writing. Using a qualitative narrative storytelling research method, we interviewed four Canadian science textbook authors about their hopes and the challenges they encountered in their writing. To understand their…

Ultraviolet (UV)-visible (Vis) spectroscopy is widely used in all modern laboratories as a routine method of analysis. The monitoring of chemical reactions in an aqueous solution involving a gas product is a demanding task but particularly for oscillatory reactions which are obtainable in a narrow concentration range. In this work, the…

Friedel-Crafts alkylation reactions using a curated set of alcohols provide students with the opportunity to combine the study of electrophilic aromatic substitution with carbocation rearrangements. In this experiment students may be presented with up to nine alcohols that yield six products, all synthesized under identical reaction conditions.…

Since the beginning of the 21st century, evaluability assessments have experienced a resurgence of interest. However, little is known about how evaluability assessments have been used to improve future evaluations. In this article, we identify characteristics, challenges, and opportunities of evaluability assessments based on a scoping review of…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

Problem-solving skills in a digital environment are a prerequisite to a better future for all citizens in the Fourth Industrial Revolution era. To investigate the relationship between age, gender, computer use, and adult learners' problem-solving skills in a digital environment, this study analyzed the 4,540 Korean participants' problem-solving…

The response process of problem-solving items contains rich information about respondents' behaviours and cognitive process in the digital tasks, while the information extraction is a big challenge. The aim of the study is to use a data-driven approach to explore the latent states and state transitions underlying problem-solving process to reflect…

Despite the importance of teachers' conceptions of and competency in problem solving, limited attention is given to this area in the current literature. We examined 96 preservice elementary teachers' problem-solving conceptions and performances by having them define and create metaphors for problem solving and then investigated the relationships…

This paper discusses methodological challenges in researching practice. The primary challenge discussed arises from the view that practice is inextricable from its performance, and that performance is embedded in social relations, material infrastructures and historical context. The paper argues for a philosophical hermeneutics approach that works…

As a follow-up to their article, "Emojis and Their Place in the Mathematics Classroom" (EJ1358586), the authors examine how emojis can be used as bridging representations to support student understanding of proof and algebra in upper primary school. They take a problem from reSolve, Level 3, (AAMT, 2020), look at it from the perspective…

Managing communications have effectively been a key leadership and management skills of a teacher. Many problems, in and out of the educational institutions, can be directly traced to whether the information was communicated, how it was communicated, and who communicated it. This paper reviews and discusses effective communication in educational…

This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…