Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

Describes a credit-card-debt activity that allows students to increase their awareness of underlying mathematical concepts relevant to the world of commerce and personal finance through learning geometric and arithmetic sequences. (KHR)

Draws on data from 1988 National Education Longitudinal Study to estimate the impact of block-scheduled mathematics course on 10th-grade student achievement and teachers' use of class time. Findings suggest that while block scheduling is positively associated with teachers' use of multiple instructional methods and more individualized instruction,…

Genetics is a difficult topic as it involves abstract concepts, which are not directly observable. Studies on using simulations to support the learning of genetics have largely been confined to the use of quantitative simulations to replace experimentation. This study describes the use of a new type of simulation built using an iconic modelling…

We first discern three different sources to describe the non-modelling-friendly environment in Taiwan: the background of mathematics teachers and students, examinations and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis…

To help mathematics educators realise the power of computer-based applications and modelling, this paper deals with four questions: (a) What implications does technology have for the range of applications and modelling problems that can be introduced? (b) In what cases does technology facilitate the learning of applications and modelling? (c) When…

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

This study examined the role and development of applied problem solving in mathematics education in the Finnish comprehensive school. The development during the 1980s of applied problem solving in schools was positive in many ways: the changes were cautious and took place more slowly than had been planned; and many obstacles related to the…

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)

It has been 25 years since the publication of J. B. Carroll's (1963) seminal work on the model of school learning (MSL) and its subsequent identification by B. S. Bloom (1968) as the theoretical basis underlying mastery learning. Carroll's model of school learning is a theoretical formulation asserting that the degree of learning attained on a…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…