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…

Mathematical problem posing, generally defined as the process of interpreting given situations and formulating meaningful mathematical problems, is academically important, and thus several interventions have been used to enhance this competence among students and teachers. Yet little is known about the interventions' various components and their…

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…

A college participant with a learning disability in the area of mathematics completed a strategy instruction intervention regarding mathematical problem-solving items. The participant responded to innovative interview questions regarding their approach to the mathematical problem-solving items (i.e., planning and reflecting) and their motivational…

This study addresses the critical issue of mathematical underperformance among preschoolers in Yopal Casanare, Colombia, through the perspective of an action research project. It focuses on the design and implementation of a didactic unit aimed at promoting numerical thinking, specifically seriation and structured counting, in preschool students.…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

This article reports two primary school teachers' perceptions of the effectiveness of lessons based on a problem-solving intervention. The intervention included enabling and extending prompts, independent student struggle time initially and time to share problem-solving strategies at the end. The intervention had two versions: one included whole…

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K-Grade 12 to develop flexibility in students' mathematical understanding and to provide them…

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for…

Researchers have repeatedly found schematic diagrams, both as part of Modified Schema Based Instruction and outside of this problem-solving approach, effective for teaching students with disabilities, including intellectual and developmental disabilities (IDD), to solve math word problems. The current study was a systematic replication of Bouck,…

This study examined the effect of comprehension strategy instruction on third-grade English Learners' word-problem-solving performance. The supplemental intervention included modeling how to read the word problem to identify and restate the question, distinguishing relevant from irrelevant information, and collaborating with peers on applying the…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…

This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…