This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

Recent curricular reforms are following the lead of the Standards 2000 and, in diverse ways, integrating some algebraic work into primary school mathematics. Our research aims at producing a tool that will allow researchers to track the development of algebraic thinking in children as they progress through various primary programs. In this paper…

The National Council of Teachers of Mathematics recently published "Principles and Standards for School Mathematics." For the first time, these new standards include pre-kindergarten standards, while outlining the mathematics that children should learn as they progress through school. The standards present a broad view of what…

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

Because cognition is the core substance of understanding and sense making, cognition-based assessment is essential for understanding and monitoring students' development of powerful mathematical thinking. The Cognition-Based Assessment System (CBAS) project is applying the results, theories, and methods of modern research in mathematics education…

This study posits that instructional representations are viable assessment tools of subject matter knowledge within the context of lesson study. Evidence is provided and validated, suggesting that representations provide valuable insights into the depth and accuracy of the knowledge prospective teachers bring to instructional settings. It is…

This paper explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at PME-NA about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding we point to the kinds of learning and understanding we may see occurring when…

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of parabola y = (x - 3)[superscript 2] and its relationship with y = x[superscript 2]. The participants' explanations focused on…

This illustrated book examines everything having to do with the square. It begins with a basic definition of the square and continues by giving some examples of squares and other interesting historical information. Some ideas addressed include why cities are laid out in square blocks, how buildings are designed from squares and cubes, and how…

The concept of function is the single most important mathematical concept studied from kindergarten to graduate school and is critical throughout the full range of education. Thus, the goals of this book are to contribute to research in learning the concept of function and to provide a resource for mathematics teachers that could help them in…

What should constitute a preschool mathematics program for children ages 3 and a half to 5 years? What mathematical ideas could youngsters explore? This paper discusses six broad mathematical concepts for investigation by preschoolers: number, space and location, shape, patterns, measurement, and permutations. For each big idea, activities are…

Computer algebra systems (CAS) have now become much more readily accessible for use in secondary school mathematics on both hand-held and computer platforms. While the initial focus of work with CAS from the early 1980's has generally been with respect to pedagogical and curriculum issues, as familiarity with CAS in senior secondary mathematics…

This paper examines whole language and mathematical concepts implemented to incorporate reading, writing and oral-language concepts into mathematical lessons in early childhood education. After discussing the theoretical background and anecdotal observations of the use of whole language to improve math skills, the paper describes a mini study in…

Discusses application of group theory to the teaching of selection rules in electronic and vibrational spectroscopy. Indicates that acquaintance with such a mathematical concept is essential for high school students to understand molecular spectrum courses. (CC)