Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics (CCSSM) included Model with Mathematics as one of the Standards for Mathematical Practices (SMP) and a modeling strand in the high school standards. This common aspect of standards across most states in the United States intended by CCSSM authors and…

Sometimes a student's unexpected solution turns a routine classroom task into a real problem, one that the teacher cannot resolve right away. Although not knowing the answer can be uncomfortable for a teacher, these moments of uncertainty are also an opportunity to model authentic problem solving. This article describes such a moment in Zahner's…

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

General equilibrium models now play important roles in many fields of economics including tax policy, environmental regulation, international trade, and economic development. The intermediate microeconomics classroom has not kept pace with these trends, however. Microeconomics textbooks primarily focus on the insights that can be drawn from the…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

Presents a mechanical analog designed to reduce the conceptual difficulties experienced by many students in thinking about age distribution concepts in demography. (JR)

This paper deals with an empirical study, which aims at showing the effects of the integration of modelling tasks into daily school routine in a comprehensive manner. At first the theoretical and methodological approach is explained. The main part of the paper deals with the results of the study. On the one hand the results show obstacles to the…

A three-dimensional model made from pegboard, rods, and spheres can be used to illustrate principles of multi-variate analysis. (SD)

The study sought to determine whether a teacher could efficiently and effectively develop, execute, and evaluate a mathematics program that would adequately enable pupils to learn. (Author)

Several models for problem solving are discussed, and the idea of a heuristic frame is developed. This concept provides a description of the evolution of problem-solving skills in terms of the growth of the number of algorithms available and increased sophistication in their use. The heuristic frame model is applied to two sets of physical…

A symposium of scientists and educators interested in coordinating the often parallel but separate research and development efforts in programed learning and digital-computer utilization met to define more exactly the potentialities of the computer as an instructional aid. Their papers form the basis of this book. The first section of the book…