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)

Describes the teaching of geodesic-dome concepts to students in grades 3-5 through the trial use of Energetic and Synergetic Geometry as well as the undertaking of a workshop designed to prepare elementary and secondary school teachers to conduct further experiments. (CC)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

Tape counters on recording equipment indicate the number of revolutions made by the take-up reel as magnetic tape is wound on it. Relating the number of minutes of play of the machine to counter values poses interesting problems. Five problems are presented as well as background information for their solution. (JN)

An Apple LOGO program is provided which results in the creation of a cat's face. Discusses program commands, indicating that, although they are never mentioned, various mathematical/geometrical concepts are involved. Indicates that LOGO provides an environment where one can play comfortably with these basic concepts. (JN)