The inclusion of probability in the school curriculum is argued to be justified on mathematical, psychological, and social grounds. Contemporary teaching approaches are suggested as sufficient. (MP)

Three components of a curriculum organized to facilitate a concept acquisition process are discussed. These are concrete experiences related to a concept, skill development activities and applications. (MP)

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)

Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

Discussed is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

Presents the use of manipulatives in the three stages of concept learning called concrete, bridging, and symbolic. Examines the three stages in developing the concept of rounding two-digit numbers. (MDH)

Advocated is the use of everyday games and situations instead of the traditional use of textbooks, workbooks, and worksheets. New goals and principles for the beginning arithmetic student are presented. Modifications of activities that promote the constructivist ideal are included. (KR)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Argues that "student talk" is an important developmental activity in mathematics. Gives suggestions that will facilitate student talk. (PK)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Argues that, though considerable difference of view is evident between Montessori and Piaget about the importance of certain concepts and level of cognitive development necessary for genuine understanding, the ideas and methods first presented by Montessori 80 years ago stand up well when evaluated through the lens of current research. (PK)

Proposes that teachers should examine the elements of mathematical understandings that precede conservation and one-to-one correspondence and tailor classroom instruction to benefit both conserving and nonconserving students. (PK)

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)