Using a graphical analysis of the linear best fit for a set of Cartesian data points, the drawbacks of the least-squares method for determining this best fit are discussed. The Wald Line, which utilizes a variation of the geometric mean, is proposed as the best alternative to the least-squares regression line particularly when the data contain…

Early childhood teachers need to integrate math education into the daily routine of the classroom by using counting books and physical props and also by emphasizing the mathematical aspects of play and other components of the curriculum. (MDM)

Discussed is the method of substitution of variables within the framework of precalculus level extremum problems, both maximum and minimum. Many examples with graphical representations are provided. (JJK)

Discussed are categorization schema, with elaborations about attendant epistemological obstacles, concerning the twin notions of understanding and comprehension, per se, as well as the processes affecting their attainment. Included is an example of such a schema involving the concept of the limit of a numerical sequence. (JJK)

Discusses how teachers can involve kindergarten children in learning mathematical concepts by basing such learning on the students' personal, real-world experiences. (BB)

Presents two vignettes of mathematics lessons and describes fourth-grade students' discussions of fractions, percents, decimals, time, and money while investigating the various interpretations of the word "quarter." (ASK)

Focuses on teaching in China, concentrating on two particular aspects of teaching: teaching students to prove in geometry and the details of what teachers do in classrooms. (ASK)

Presents a mathematics activity that illustrates how such adjectives as elegant, surprising, concise, and challenging can be, and in fact are, attributed to proofs by a not very expert audience. (ASK)

Presents an activity that led to the discovery of the role of ratios and percentages in discussions about triple-jump performances, and a range of tasks that provide important information about students' understanding of key mathematical concepts. (ASK)

This study examined above-grade-level abstract reasoning abilities of 150 students (grades 2-6). Understanding of abstract concepts varied by age for only four of eight subscales or concepts: probability, proportion, momentum, and frames of reference. Performance varied widely within age level for the understanding of volume, correlation,…

Presents an activity that focuses on the composition of functions in the context of jawbreakers. (ASK)

A design context for developing children's understanding of the natural world via designing, building, testing, and evaluation of models was studied. Children were asked to design models of human elbows which provided opportunities to develop their understanding of the relations between mathematics and science through the construction and…

Discussion of the use of manipulative materials in kindergartens focuses on a new generation of computationally enhanced manipulative materials, called digital manipulatives, designed to allow all students to explore mathematical and scientific concepts through direct manipulation of physical objects rather than more abstract methods of learning.…

Notes that knowing how to estimate is crucial to becoming a good problem solver. Suggests that young children be exposed to the concept as early as kindergarten in order to learn to apply the skill effectively. Discusses the values of estimation skills and how they can be developed. Outlines five classroom activities that help students develop…

Suggests an alternate way to determine the fractal dimension of bread by means of a dimensionally correct graphical analysis. (WRM)