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…

This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find…

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)

Four fifth and sixth grade students with learning disabilities were taught a strategy for comprehending word problems and devising appropriate solutions. Following instruction performance on mixed sets of addition and subtraction word problems improved. Although generalization to a different setting occurred, maintenance was mixed. (Author/DB)