This paper describes a development and evaluation process used to create teacher education materials that help prepare middle and secondary mathematics teachers to teach data analysis and probability concepts with technology tools. One aspect of statistical reasoning needed for teaching is the ability to coordinate understandings of center and…

In this article I report on a study of the cognitive tools that research mathematicians employ when developing deep understandings of abstract mathematical definitions. I arrived at several conclusions about this process: Examples play a predominant role in understanding definitions. Equivalent reformulations of definitions enrich understanding.…

There is a dearth of research on the mechanisms for preservice teachers' development of the pedagogical knowledge necessary for effective use of such technologies. We explored the emergent Technological Pedagogical and Content Knowledge (TPACK) (Niess 2005, 2006, 2007) of a group of secondary mathematics preservice teachers in a methods course as…

In this article, we argue that the debates about mathematics education that have arisen in the United States over the past decade are the result of a major shift in how we conceptualize mathematical knowledge and mathematics learning. First, we examine past efforts to change mathematics education and argue they are grounded in a common traditional…

Since the advent of the NCTM "Standards" (1989), mathematics educators have been faced with the challenge of assessing the impact of "Standards"-based (or "reform") curricula. Research on the impact of "Standards"-based curricula has predominantly focused on student achievement; here we consider an alternative: Students' epistemological…

Reviews the article, "Can Mathematics Education and History of Mathematics Coexist?" (M.N. Fried) which appeared in "Science and Education". Challenges Fried's assertion that combining history of mathematics with mathematics education is inherently difficult. The assertion is considered flawed in terms of both its view of history and a limited…

Reviews the historical development of subtraction algorithms used in the United States. Indicates that the algorithms used to teach subtraction have not changed much in the last 40 years, but in the late 1800s and early 1900s, different algorithms were developed that had a great impact. Contains 22 references. (DDR)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

Considers four language arts--speaking, listening, reading, and writing--as activities that enhance the development of mathematical concepts. Suggests ways language arts can be used in learning difficult concepts as missing addends, algorithms, number facts, and problem solving. (39 references) (MDH)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…