Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that…

Physical phenomena and relations can be described mathematically by functional dependencies. These are represented in the form of tables, graphs, algebraic expressions or verbal descriptions. Only the combination of different representations enables students to experience a physical phenomenon or concept in a holistic way. Therefore, students have…

In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the…

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and…

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to…

Describes a project designed to assist 12- to 14-year-old students in developing abstract reasoning skills in math and science via interactive computer programs. Examples of learning modules designed to be run on microcomputers are included. Seven references are listed. (MER)

Words are only one way of symbolizing ideas. Numbers, pictures, graphs, maps, diagrams, photographs, and other means are also used to convey information. Researchers refer to notational systems such as graphs, diagrams, and maps as "inscriptions." Inscriptions are tools that help people to perceive and to talk about spatial worlds. Spatial…

A 3-year study was conducted to determine the logical reasoning processes necessary to construct line graphs. Responses obtained from middle and high school science and mathematics students were classified into one of nine categories. These categories ranged from "no attempt to make a graph" to "complete graph with a statement of a…

Higher order cognitive development and success in the study of high school mathematics and science require an understanding of rational number concepts and facility with proportional reasoning and computation. Proportional reasoning is an essential schema for developing formal operational thought. This study involving 16 ninth-grade students was…