Study supported by research grant 1-K03-Hd36971 and by training grant 1-T01-Hd00203 from the National Institute of Child Health and Human Development.

The article suggests that Belcastro rods, which retain the basic properties of Cuisenaire rods but allow instant identification by touch, may be useful in teaching mathematical concepts to blind children. Drawings illustrate use of the rods in teaching such concepts as addition and subtraction. (Author/DB)

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…

Examined is the notion of "representation" as it is used in mathematics education. The first section explains what appears to the current "received view" of representation within mathematics education. The second section describes the constructivist view of representation, especially as this view is related to Piaget's theory. The third section…

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)

The development of the place value system and its universal use demonstrate the elegance and efficiency of mathematics. This paper examines the concept of place value by: (1) presenting the historical development of the concept of place value in the Hindu-Arabic system; (2) considering the evolution of the number zero and its role in place value;…

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)

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

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)

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

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)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…

Proposed is a model for basic preconditions for "the design of effective programs in developmental learning." Such a program should include (1) a continuous psychocognitive diagnosis and assessment of each child; (2) a structured, coherent, sequential approach to content area; (3) a focus on symbolic manipulation and the essentials of a concept;…