A teacher introduced mathematical concepts into six year olds' stories about losing and growing teeth. Results demonstrated that children's authentic mathematical experiences are derived from the children's knowledge and experience, are multimodal, and are open ended. Calls for open-ended activities that allow children to explore ways to use…

Describes a seven-year-old boy's activity of drawing pictures of his favorite sport of basketball. The boy's drawing involved the use of proportional reasoning, which requires an understanding of how relationships between objects vary systematically. (BB)

Hypermedia provides an easy-to-use option for adding visualization, via the computer, to the classroom. Some examples of this medium are presented, including applications in basic linear algebra and calculus, and a tutorial in electromagnetism. (Author)

Discussed is a method of approximating the roots of a quadratic that allows the discovery of relationships between parabolas and circles and between the use of geometry and algebra. Included are the procedure and justification of the method. (KR)

Discussed is the type of evidence children find to be convincing using either empirical or deductive methods to justify propositions which they consider to be true. Included are the problem, research design, and the conclusion. (KR)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…

Describes how an eight year old devised a part-whole schema during a school mathematics process involving the development of a geometric model to conceptualize fractions. Provides examples that utilize this schema in dealing with the relative size of fractions, as well as addition and subtraction, multiplication, and division of fractions.…

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…

A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)

Long-documented gaps between male and female performance on tests of spatial mathematics ability are discussed. Possible explanations are offered, and suggestions are put forth for cultivating spatial relationships ability in girls through sports and other activities. (PB)

The difficulties and misconceptions that many students experience when learning to visualize graphs of functions are discussed. Specifically, the inability to make accurate connections between symbolic and graphical representations, the lack of understanding about scale and scaling, and the confusion caused by transformations are examined with…

Presents a method for demonstrating addition and subtraction of integers on the number line in a way that distinguishes between subtraction and negative numbers. The model depicts the sign of the number by forward or backward movement on the number line. Subtraction is illustrated by a turning around movement. (MDH)

To examine the effect of motivational manipulated conditions on students' mathematics scores, elementary students received either ordinary standardized test instructions or special instructions (do as well as possible for themselves, parents, and teachers). Those given special instructions scored significantly higher in the test, implying that…

Two geometry problems generated from a design problem involving a shuttle return mechanism in a weaving machine are presented. The solutions to these problems are detailed. (CW)