Despite the increasing amount of research into mathematical problem posing, research shows that much is still unknown about students' cognitive processes when engaged in problem posing. In this study, 16 undergraduate students' problem-posing products and processes are examined in order to shed light on the forms of mathematical reasoning that the…

The purpose of this mixed-method study is to investigate and compare students' problem-solving and higher order thinking skills. This study involves two contexts: a traditional teaching program and a Lesson Study program. In qualitative phase, seven mathematics lecturers, a physics lecturer and the researcher forms the Lesson Study group and they…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

Purpose: This paper aims to describe the statistical arguments produced by third-grade students (8-9 years old) and to identify the teaching support for collective argumentation in a lesson based on data comparison. A Lesson Study Group researched and planned the lesson around a problem from the official mathematics textbook.…

The purpose of this study was to quantify the relationship between pre-service teachers' spatial visualisation skills and their mathematical creativity through problem-posing tasks. A group of 62 pre-service teachers completed the Purdue Spatial Visualisation test and took the mathematical creativity test through problem-posing tasks. Pearson's…

This convergent mixed methods study investigated the relationship between the assessment-capable learning (ACL) instructional model, John Hattie's influence referred to as "students driving their own learning," and math achievement in kindergarten. While Visible Learning literature has focused on secondary and higher education, this…

The issue of low math performance, particularly in schools serving historically marginalized communities, requires immediate attention. Despite implementing various interventions, including leadership changes, curriculum updates, and hiring consultants, student achievement in math has remained stagnant at Ida B. Wells Academy (Wells). This case…

Background: Educational technologies typically provide teachers with analytics regarding student proficiency, but few digital tools provide teachers with process-based information about students' variable problem-solving strategies as they solve problems. Utilising design thinking and co-designing with teachers can provide insight to researchers…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…

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…

The increasing use of complex machine learning models in education has led to concerns about their interpretability, which in turn has spurred interest in developing explainability techniques that are both faithful to the model's inner workings and intelligible to human end-users. In this paper, we describe a novel approach to creating a…

The aim of this study is to investigate the production and dissemination of mathematical modeling-based projects by gifted students, intended to solve real-life problems, over the four-year Project Production and Management Program (PPMP). The longitudinal research methodology was utilized to examine the project production process among…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

The purpose of the present study was to gather data regarding the implementation of Prodigy in elementary schools in a mid-sized school district in the southern United States. Prodigy is a free, adaptive mathematics game provided by Prodigy Education. The program integrates curriculum-aligned mathematics content (Grades 1-8) in a game-based…