Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties.…

The paper describes the history of how learning trajectories (LTs) were associated with the Common Core State Standards for Mathematics (CCSS-M) and discusses the degree to which the two correspond faithfully. It reports on a website, www.turnonccmath.com, which organizes the K-8 standards into 18 LTs describing the development of big ideas over…

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

A model for fractions derived by an operation of "scattering into subunits" is hypothesized. Five stages in the model are discussed. Assumptions underlying the development of the model, features of the model, and disadvantages of the model are listed. (DT)

This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms,…

Examined were the mental processes by which elementary school students work simple multiplication exercises. Ten process models were fit to data obtained in the course of a CAI program in elementary arithmetic. The processes used by students in grade three were compared with those used by students in grade six. (CT)

A model for integer multiplication is discussed. (DT)