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…

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…

Doubly robust (DR) estimators that combine regression adjustments and inverse probability weighting (IPW) are widely used in causal inference with observational data because they are claimed to be consistent when either the outcome or the treatment selection model is correctly specified (Scharfstein et al., 1999). This property of "double…

The aim of this study is to evaluate factors contributing to poor academic performance of students in higher education. Data was collected in 2017 from 216 students enrolled in different programmes at a higher education provider in New Zealand. The effect of factors relating to family obligations, work and social commitments, and financial…

Pronouns encouraging a second-person perspective (e.g., "you/your") affect peoples' mental representations constructed while reading and improve learning. The present study applied these insights to a domain in that such pronoun effects have yet been unexplored: mathematical word problem solving. Specifically, we encouraged a…

This research has been conducted to analyze students' problem-solving abilities in direct current electricity in STEM-based learning. The implementation of STEM in this research is to train the domain of scientific practices and engineering practices that are associated with model problems and project-based learning. The research method used was…

In recent years, grand challenge initiatives have emerged nationally with the goal of addressing large, multidisciplinary public problems. The advent of university-led grand challenge initiatives offers an important opportunity to reflect on how institutions of higher education design, implement, and orient externally relevant activities at a time…

While members of the academy are particularly adept at complaining and poking holes in most proposals that cross their paths, we are less comfortable with offering solutions. This essay asks members of the honors community to consider some of the major challenges facing honors education today and propose solutions that might be adapted on a…