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Schüler-Meyer, Alexander – Educational Studies in Mathematics, 2017
After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Design
Kontorovich, Igor' – Educational Studies in Mathematics, 2018
This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…
Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematical Formulas, Algebra
Hackenberg, Amy J.; Lee, Mi Yeon – Educational Studies in Mathematics, 2016
To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…
Descriptors: Mathematics Instruction, Mathematical Logic, Fractions, Algebra
Influence of Additive and Multiplicative Structure and Direction of Comparison on the Reversal Error
González-Calero, José Antonio; Arnau, David; Laserna-Belenguer, Belén – Educational Studies in Mathematics, 2015
An empirical study has been carried out to evaluate the potential of word order matching and static comparison as explanatory models of reversal error. Data was collected from 214 undergraduate students who translated a set of additive and multiplicative comparisons expressed in Spanish into algebraic language. In these multiplicative comparisons…
Descriptors: Error Patterns, Undergraduate Students, Spanish, Algebra
Wittmann, Michael C.; Flood, Virginia J.; Black, Katrina E. – Educational Studies in Mathematics, 2013
We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of…
Descriptors: Figurative Language, Algebra, Mathematics, Mathematics Education
Jiang, Chunlian; Hwang, Stephen; Cai, Jinfa – Educational Studies in Mathematics, 2014
This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…
Descriptors: Foreign Countries, Grade 6, Problem Solving, Mathematics Instruction