In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

Solving word problems is challenging in elementary schools, both for the teacher in teaching students to solve word problems and for the student in learning to solve them. This paper examines how the ideas of learning trajectory and variation pedagogy could be integrated as an instructional principle for teaching this content in the context of…

This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…

This paper reports an intervention phase of a design study aimed to assist second-grade Filipino children in solving addition word problems in English, a language they primarily encounter only in school. With Filipino as the medium of instruction, an out-of-school pedagogical intervention providing linguistic and representational scaffolds was…

This paper is aimed at depicting the quality of functions of some of the aspects of attention in children with mild intellectual disabilities and their influence on the mastering of arithmetic operations, including addition and subtraction. The sample used in this study encompasses 60 pupils, both males and females. The criteria used in the…

The 2011 study, "Benefits of Practicing 4 = 2 + 2: Nontraditional Problem Formats Facilitate Children's Understanding of Mathematical Equivalence," examined the effects of addition practice using nontraditional problem formats on students' understanding of mathematical equivalence. In nontraditional problem formats, operations appear on…

A multiple-baseline design across math-fact sets was used to evaluate the effects of a taped-problems intervention on students' performance with addition facts and their inverses in an intact, rural, second-grade classroom. Results suggested that the procedure was effective in improving fluency on math facts as well as their inverses. Across 3…

The purpose of this study was to investigate the effectiveness of using the concrete-representational-abstract (CRA) teaching sequence with integrated strategy instruction for developing addition with regrouping competence among students with learning difficulties in mathematics. A total of 16 lessons were provided to 24 students during a six-week…

Demonstrates the merging of cognitive psychology, psychology of mathematics, and special education. Various models of children's addition strategies are reviewed and critiqued. Addition strategy with poor learners should be comprehensive and include interactions between strategies, knowledge, metacognition, motivation, and social factors. (MAK)