Performance of 9-year-olds, 17-year-olds, and young adults on questions related to numerical estimation is reported. Implications for instruction are discussed. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Discussed is how the studies of mathematics and language can illuminate each other in areas such as symbols, sentences, substitution, and patterns. (MP)

Analyzes the concept "growth" by investigating the logic core of the concept, using systems theory, and testing it employing free definitions. Determines the associative framework using free association tests. Shows that a shift takes place in the logic core and in the associative framework from a growth in terms of geometric dimension towards a…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

An analysis of the conceptual development of children between the ages of five and six. The interrelationship of such concepts a big, long, small, and short is discussed. (JLH)

A framework for organizing instruction on the basic facts is presented. Guidelines are given for blending work with concrete materials, thinking strategies, and drill into a meaningful program. (MN)

These three brief articles concern problems students encounter in solving simple linear equations, children's conceptions of number, and the distinction between adding objects and adding numbers as illustrated by students' problems with Euler's formula. (SD)

Instructions are given for constructing and using a manipulative device which can help children to conceptualize and to comprehend the base-ten place-value system. (JT)

The use of counting sticks as a concrete manipulative material in the development of number understanding and the concept of place value is strongly urged. (JT)

Divisibility facts, greatest common divisors, least common multiples, and relative primes are explored through the use of lattice diagrams. (JT)

Discusses the relationship between geometrical and numerical concepts in the mathematical development of young children. Based upon a longitudinal field study of 224 children, findings suggest that memorization ability facilitates understanding of numerical concepts but that subsequent mathematical development is restricted until basic geometry is…

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

What are often missing for children in classroom instruction are experiences with numbers that stretch beyond computation skills and word problems. This lesson models such an experience for third graders. Students use small boxes of raisins in several problem-solving activities. Children apply whole number operations, estimate, consider…

Mathematics is considered a performing art. Examples illustrating this view are presented. Activities discussed are from the Madison Project materials and the mathematics program at University High School in Urbana, Illinois. Activities stress inventing strategies for attacking problems for elementary and secondary school mathematics. (RH)