This classroom-based action research investigates the impact of teaching problem-solving heuristics on preservice teachers' mathematical creativity, self-efficacy, and problem-solving beliefs. The study was conducted with seven preservice teachers at a state university in the Philippines, using a Plan-Do-Study-Act (PDSA) cycle. Participants were…

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…

This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by…

Mathematical beliefs and metacognitive knowledge play significant roles in solving mathematical problems; thus, this study aims to investigate the influence of middle school students' beliefs on their metacognitive knowledge when solving geometry problems. This study utilizes both quantitative and qualitative research methods. A linear regression…

This paper examined the ability of students to pose a problem in a free posing situation about sets in terms of the problem text, compatibility with mathematics principles, the problem type and structure, solvability, and mathematical complexity. Additionally, students were probed to determine the difficulties they encountered during the problem…

This research examined the impact of the Cognitive-Communicative (C-C) model as a pedagogical strategy for teaching algebraic word problems (AWPs). The C-C model integrates structured dialogue, concept clarification, and systematic problem-solving steps to enhance students' comprehension and reasoning. Employing a mixed-methods framework, the…

Proficiency in solving mathematical problems is essential for preservice elementary teachers, as they will teach foundational math concepts and foster problem-solving abilities among young learners. However, many studies found low problem-solving performance among preservice teachers. In line with this, the present study examined how…

This article presents a set of "work-sharing routines," which teachers can use to broaden their repertoire of using student work, with an eye toward cultivating students' belonging. The authors define work-sharing as using actual mathematical student work, ideally from students in the class, to facilitate learning. Although there are…

The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive…

The aim of this study is to understand teacher education students' experience with an introduction to use of escape room as a didactic tool in mathematics, and to gain insight on the impact of such an introduction on teacher education students' development as mathematics teachers. Escape room is a new, game-based, didactic tool in school that…

In the present study, we explored whether future teachers considered spatial skills to be built up slowly and incrementally (incremental view) or considered spatial skills to be an innate, static aptitude (entity view). We also examined whether these views were associated with personal spatial skills, confidence in spatial problem-solving, or…

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…

The purpose of this study was to explore the effect of visually assisted guided discovery learning strategy on grade 10 students' problem solving skills of learning plane geometry in Woldia City, North Wollo, and Ethiopia. A nonequivalent quasi-experimental pretest-posttest-control group design and a case study design were used. The population of…

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…