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…

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.…

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…

Posing problems in the mathematics classroom can enhance students' learning experiences and allow them to produce problems in a realistic context. Students do not always associate positive feelings with mathematics. Problem-posing activities can positively impact students' mathematical understanding while allowing for freedom of expression.…

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…

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…

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…

The OECD's Programme for the International Assessment of Adult Competencies (PIAAC) represents a comprehensive international comparative assessment of the information processing skills of adults vital for the full participation in social and economic life in the 21st century. PIAAC is now in its second cycle and continues a series of international…

This study aimed to examine the effect of using the flipped classroom model on students' proportional reasoning. In this context, the study focused on students' achievement and solution strategies for proportional reasoning problems. The participants of the study were 56 seventh-grade students, who were determined by convenience sampling method.…

The purpose of this study was to identify the the factors that influenced pre-service teachers' perceptions of their abilities to solve structured physics problems. 1185 pre-service teachers from different disciplines, enrolled in physics courses in one Turkish University from 2008 to 2017 participated in a descriptive survey. The factors…

Agency is a core pedagogical goal of the maker education movement. However, there are still many unknowns about how agency is identified in maker settings. To document maker educator professional visions of agency, we conducted video-cued interviews with eleven U.S-based maker educators using video clips of families making in a drop-in…

Many empirical studies about STEM (science, technology, engineering, and mathematics) curriculum present problems for students to solve. This paper draws upon the data collected from the enactment of an integrated STEM curriculum to discuss problems as constitutive of problem spaces where four Grade 5 Singapore students engage with the…