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)

Three experiments examined the ability of 4- and 5-year- olds and adults to identify correspondences in spatial ratios. Results suggested that young children made accurate spatial proportionality judgments based on relational information and not on the exact form of the stimuli. Findings pose implications for theories of mathematical development…

Describes a study that explores secondary school students' conceptions of division by zero. Examines whether students identify expressions involving division by zero as undefined or tend to assign them numerical values. Studies students' justifications and analyzes the effects of age and level of achievement in mathematics on students' responses…

Presents a problem and its solution on generating the complete set of triples of given sides of a triangle. Determines that students who work through the problem stand to learn a great deal more than just which particular triangles fit the given requirements. (ASK)