Suggests that mathematical modeling is "a way of life for everyone." Describes the M's of mathematics which include methods, models, and modeling; and the R's of mathematics which are reasoning, reading, 'riting and 'rithmetic. Outlines their role in promoting "the way of life" and discusses implications for the 16-19 curriculum. (Author/ASK)

Addresses the role that so-called emergent models can play in the process of constituting formal mathematics. Describes how the use of these models became more explicated over time and developed into the notion of emergent models. Uses the design of instructional sequence for flexible mental strategies for addition and subtraction as an example…

Contrasting instructional approaches were used to introduce mathematical modeling to two sets of students with weak content skills and no prior modeling experience. One group was exposed to examples of models for a particular contextual problem; the other group was asked to construct their own model for the same situation. In less than three…

Flowing granular mixtures in rotating cylindrical drums arise in numerous industrial settings and are of great technological significance worldwide. To date, the development of a robust mathematical model for this process remains an open research problem. However, simple mathematical models may be developed that capture some of the underlying…

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and…

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…

This paper examines the effects of learning time on student achievement. It begins by reviewing what is known about how time is allocated and utilized in schools and the effects of differing amounts of exposure to schooling on achievement. Several theoretical perspectives concerning how time spent affects achievement are briefly discussed. The…

This study investigated the impact of four student characteristics and the instructors on the relative abilities of a simulation-gaming method and the lecture-discussion method to increase the economic knowledge, retention of economic knowledge, and interest toward economics of college students enrolled in an introductory economics course.…

Methods of formulating mathematical models are discussed and problems, insights, and solutions are given. (PK)

An approach is described for teaching formulation of mathematical models to undergraduates with no modeling experience. Instruction is based on observation of successful patterns of behavior. (MP)

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)

Illustrates how modeling and other non-deductive forms of reasoning as employed by a highly creative mathematician can be productive as important conceptual innovations and, by the same token, can serve as effective tools for stimulating conceptual development in the process of learning mathematics. Characterizes Klein's model-based practice and…