Ben, a good mathematics student, participated in a seven-week study. Describes three tasks that reflect impact of textbooks, real-life connections, and mathematical symbols. Shows that Ben's notion of one-half was task-dependent, concrete, and based on physical actions. (NI)

How physiological disciplines can contribute to the study of how people learn mathematics is considered. Manipulative and experiential learning, sequential versus hierarchical organization, declarative versus procedural knowledge, and short-term versus long-term memory are among the points discussed. (MNS)

Outlines one teacher's questioning of the understanding of computational processes by her students in mathematics class. Points out the importance of teaching the context of meaning and its application in mathematics. (MD)

The rationale and description of a game situation used as an introduction to the system of coordinates and the development of proportional reasoning are given. Reactions and answers of second-; fourth-; and sixth-grade children are analyzed. (MN)

Describes the use of a graphic organizer--webs--to help students learn to connect concepts in mathematics. (MKR)

A general discussion of cognitive development as it relates to measurement is presented. Suggested measurement activities are given. (MK)

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

Discusses the rationale and a method for the instructional use of graphing calculators as an intermediary step between the intuitive notion of the concept of a limit and its formal epsilon-delta definition. (JJK)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

Here are some ideas that the nursery-school teacher might suggest to parents as ways to set the stage for learning in mathematics for their children. (MN)

The discussions of the theme group on Technology and Cognitive Development at the Fifth International Congress on Mathematical Education are summarized. How computers can be used to engage students actively, to promote problem-solving skills, and to achieve better understanding is discussed. (MNS)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

Pattern recognition is viewed as a fundamental cognitive skill that lays the groundwork for the ability to form abstractions and generalizations. Incorporating patterning into the curriculum of young children is encouraged. (MP)

This document suggests ways of using children's intuitive ideas about mathematics as a starting point for an elementary curriculum. Ways are discussed to capitalize on what children already know: to cultivate rather than discourage students' intuitive mathematical sense, and to help students make connections between what they know and what they…