Metacognition is described and suggestions for teachers about developing and improving metacognitive skills in performing mathematical tasks are given. (MNS)

Discusses how teachers can help students make the transition from using manipulative materials to abstract mathematical symbols. Includes: (1) a definition of the transition state; (2) ways to bridge the gap (by asking questions and by using activities); and (3) a specific example (teaching place value). (JN)

A brief description is presented of a curriculum offered in one school system that applies much of the available research on how children learn. Materials used, goals for instruction, concepts emphasized, and intellectual processes engaged in each of grades kindergarten through third are noted. (MP)

Discusses developmentally appropriate activities for teaching counting skills for kindergarten and early first-grade programs. Describes four activities: (1) counting on; (2) counting back; (3) auditory patterning; and (4) visual patterning based on the 10-frame. (YP)

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)

Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)

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…

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

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)

Described is an activity where base-10 blocks are used to develop students' skills in reading, writing, and visualizing large numbers. An activity sheet that helps students with decimal points is included. (KR)

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

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)