Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's…

This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of…

This brief presents Youth Participatory Action Research (YPAR) as a transformative exploratory tool for critical and curious educators. YPAR has been defined as a collaborative method of youth, with the support of caring adults, participating in research to explore social issues that impact them, with the end goal of taking action to improve the…

This quasi-experimental design study aimed to examine how exposure to supporting productive struggle teaching practice impacts students' conceptual understanding, procedural fluency, and strategic competence when solving high-demanding quadratic functions problem solving tasks. Results suggested that students in the supporting productive struggle…

Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models.…

This paper introduces a new mode of variational and covariational reasoning, which we call scaling-continuous reasoning. Scaling-continuous reasoning entails (a) imagining a variable taking on all values on the continuum at any scale, (b) understanding that there is no scale at which the continuum becomes discrete, and (c) re-scaling to any…

This study was to support the understanding of the set structure, binary operations, and their properties as a prerequisite of group theory material categorized as 9 structure senses. This study aimed at investigating the process of students' structure sense in recognizing the structure of mathematical properties or objects as a prerequisite of…

The present study is a systematic meta-analytic study of 38 primary sources investigating the effectiveness of algebra interventions for students who are struggling. We systematically searched and screened over 1,300 records for studies to include. We computed summary effect sizes for each of the 12 interventions included. We conducted 4 separate…

Crystalline concept is the main concept used as the reference by students in algebraic verification. This concept divided the way of solving algebraic verification into two types: symbolic and embodied compression. This research aimed to explore the students' mathematical thinking process in solving algebraic verification based on the Crystalline…

Educational research has reported different benefits related to the use of practice tests. In the case of the teaching and learning of mathematics, evidence has been found that the use of practice tests is associated with an improved performance in standardized tests. However, it is less known about the emotions that students experience during…

The topic of inequalities is one of the fundamental subject areas for the development of mathematical knowledge. Although there is a considerable body of research focused on one-variable inequalities, studies that investigate students' performance on two-variable inequalities are scarce. With this in mind, the aim of this study is twofold: first,…

This study employed the design-based research (DBR) methodology to explore how to design instructional prompts integrated into a computer-based cognitive tool, GeoGebra, for gifted mathematics education. This study was divided into two iterative research phases lasting for 3 semesters, in which differentiating the instructional prompts for gifted…

This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a…

Over the past thirty years, research on teachers' mathematical knowledge for teaching (MKT) has developed and grown in popularity as an area of focus for improving mathematics teaching and students' learning. Many scholars have investigated types of knowledge teachers use when teaching and the relationship between teacher knowledge and student…