This theoretical paper outlines a conceptual framework for examining growth in prospective teachers' mathematical understanding as they engage in thinking about and planning for the mathematical learning of others. The framework is based on the Pirie-Kieren (1994) Dynamical Theory for the Growth of Mathematical Understanding and extends into the…

The purpose of this study was to describe how middle school students physically arrange and organize statistical data. A case-study analysis was used to define and characterize the styles in which students handle, organize, and group statistical data. A series of four statistical tasks (Mooney, Langrall, Hofbauer, & Johnson, 2001) were given…

When students confront arithmetic or algebraic word problems, they develop ideas and notations during the processes of solving them by using various arithmetic strategies. Those ideas and notations are the basis for solving that type of problems. Is it possible to aid the development of students' algebraic thinking during their transition from…

This paper describes three fundamental principles, dictated by Wilhelm von Humboldt, that were widely adapted as the basic philosophy of higher education in the United States, and proposes to revise the unfulfilled dream of von Humboldt to make it come true. This paper stresses the achievements of humanity not only in technology, health, or the…

This digest provides a guide to improving student achievement in mathematics education and suggests resources for further study. It provides recommendations for the classroom and is a companion piece to "Improving Student Achievement in Mathematics, Part I: Research Findings." Recommendations include that students can learn both concepts…

The purpose of the study is to compare the effectiveness of conceptual change text oriented instruction and traditional instruction on students' understanding of cellular respiration concepts and their attitudes toward biology as a school subject. The sample of this study consisted of 84 eleventh-grade students from the 4 classes of a high school.…

This book looks at how teachers implement national math and science standards in their classrooms. Teacher-authored chapters provide insights into how children think and reason as they pose questions, collect data, and build data models to answer their questions. While the spotlight is primarily on student understanding and its development over…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

The Blue Planet program aims to develop an understanding of and insight into the environment among students by introducing environmental problems such as pollution. This paper presents a study investigating junior high school students' previous knowledge and understanding of environmental issues and perceptions on the nature of the water cycle.…

Cognitive conflict has been used as an effective teaching method since the 1980s, although the effects of this method are unclear. According to some researchers, cognitive conflict does not consistently lead to conceptual change. This paper describes a study investigating answers for the questions, What is the definition of cognitive conflict in…

The concepts of "learning community" and "community of practice" may hold value to researchers, but questions exist as to how well they help in organizing and clarifying the type of critical thinking involved in investigative work. This paper approaches the problem from two directions. One is to deconstruct the two concepts…

The purpose of this study was to investigate the nature of students' responses to an innovative curriculum unit in which I attempted to help students build bridges between traditional practices and beliefs about aspects of health and conventional western science concepts. This paper reports on the responses of one articulate student, who has given…

This paper focuses on student understanding and learning of the algebraic concept--rate of change. Teachers' knowledge about their students and current literature on students' understanding is used to design and assess the instruments. Data were obtained as part of two-year research program that focused on how the study of students' understanding…

This digest summarizes research findings on best teacher practices in mathematics education. Among the findings are: students can learn both concepts and skills by solving problems; whole-class discussion following individual and group work improves student achievement; and using calculators in the learning of mathematics can result in increased…

Based on a summary of research findings on best teacher practices in mathematics education, which is presented in Part 1, the companion to this digest, recommendations are given to improve mathematics teaching practices. Among the recommendations are: students can learn both concepts and skills by solving problems; whole-class discussion following…