In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

Real-time collaborative programming (RCP), which allows multiple programmers to work concurrently on the same codebase with changes instantly visible to all participants, has garnered considerable popularity in higher education. Despite this trend, little work has rigorously examined how undergraduates engage in collaborative programming when…

This study aims to determine the effect of using STEAM digital teaching materials on increasing creative problem-solving skills. This study has a quasi-experimental research design with a nonequivalent control group. This study employed a random sampling technique and obtained Class 8-F as the experimental class and Class 8-H as the control class.…

This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

Case-based learning (CBL) is a learner-centric educational approach that fosters independent learning and exploration through case analysis, guided by teachers' heuristic instruction. The study aimed to evaluate the efficacy of CBL versus traditional teaching methods in advanced breast cancer education for residents. In this randomized controlled…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

Background and Context: Productive failure (PF) is a learning paradigm that flips the order of instruction: students work on a problem, then receive a lesson. PF increases learning, but less is known about student emotions and collaboration during PF, particularly in a computer science context. Objective: To provide insight on students' emotions…

Developing students' scientific literacy is the most important educational goal and challenge of the 21st century. Many studies have confirmed that flipped learning has significantly impacted learning science. Researchers indicate that the lack of an appropriate learning guidance strategy in the pre-class stage for flipped learning will influence…

Students' experience errors in solving proportional problems and prospective teachers' experience were the same thing. Research that explained the wrong strategy for understanding proportional problems still needed to be completed. Objectives to describe the wrong strategies chosen by prospective teachers in solving proportional questions and the…

Metacognitive instruction supports L2 listening learners to enhance their listening comprehension skill. To date, some review studies have investigated this topic; however, none of them has reported quantitative and qualitative findings in the form of a systematic literature review. This research addresses this gap by collecting, analyzing, and…

Fostering creative thinking and promoting metacognitive processes are two major goals of 21st -century education. Recent research has pinpointed the essential role of meta-creativity in the process of creative thinking. Nevertheless, the concept of meta-creativity has not been widely adopted. The purpose of the present study is, therefore,…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

Gamification, including game-based learning (GBL), is a widely recognized pedagogical approach used for imparting and reinforcing cybersecurity knowledge and skills to learners. One innovative form of GBL gaining popularity across various educational levels, from secondary schools to professional development, is escape room-style education. This…

The importance and benefits of teamwork in the university context have been widely recognized in recent decades. However, there is little evidence that analyzes the effects of the combination of collaborative learning strategies and gamification methodologies for the improvement of transversal skills and academic performance. In this sense, in…

Educational digital escape games (EDEGs) are digital versions of escape rooms where players solve puzzles and complete challenges to achieve educational goals. This study investigates the effects of EDEGs on the academic achievement and motivation of elementary school students in mathematics. Using an explanatory sequential mixed-method design, 45…