This study assessed whether a sample of two hundred seven 3- to 7-year-olds could interpret multidigit numerals using simple identification and comparison tasks. Contrary to the view that young children do not understand place value, even 3-year-olds demonstrated some competence on these tasks. Ceiling was reached by first grade. When training was…

There were 120 pupils in years 1 to 5 from two schools which were interviewed using specially prepared tasks to study the variety of interpretations given to letters by adolescents. Results indicate that two distinct conceptual understandings of the role played by a letter in relation to geometrical data exist in pupil's thinking. (Author/TG)

Students were measured on eleven aptitudes from Guilford's structure-of-intellect cube, and randomly assigned to symbolic or figural instructional modes for a unit on functions. Achievement was measured and compared for students with different aptitudes. (SD)

Children learned two linear function rules under varying conditions: presence vs. absence of pointing; visual cues (context vs. weight vs. both pictured); and a verbal-only baseline condition. A complex rule was learned as a transfer task. Visual cues aided both learning and transfer; pointing helped initial learning, but retarded transfer.…

The author emphasizes the importance of concepts and mathematical form in a discussion of understanding mathematics. (MN)

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

TO DETERMINE THE EFFECT OF INSTRUCTIONAL APPROACHES FOR SUBTRACTION AND/OR TIME OF SYMBOLIZATION UPON (1) ACHIEVEMENT IN ARITHMETIC, (2) ATTAINMENT OF NUMBER CONCEPTS, (3) ATTITUDES TOWARD ARITHMETIC IN GRADES ONE AND TWO, THIS REPORT ASSESSES FOUR EXPERIMENTAL CLASSES, THERE WERE TWO FIRST GRADE CLASSES OF 20 PUPILS EACH AND TWO SECOND GRADE…

Explores two hypotheses about the effect of symbolic systems on psychological functions: (1) culturally elaborated systems of signs affect psychological functioning in a general way; and (2) systems of signs, when used to support skilled action, affect the organization of human activity. Reviews research that supports the second hypothesis. (LB)

In a study of mathematics learning, taking a rule-oriented approach, students were taught to trade objects of type A for objects of types B and C. Children ranging from ages 7 to 9 were given rules for converting A to B and B to C and were then presented with the task of converting A to C. Of the 30, 6 succeeded. Of the 24 who failed, half were…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

This paper examines sixth-grade children's thinking related to solving ratio and proportion problems before these children had received any instruction in the domain. It explores unitizing and norming, one of the processes identified by both content analyses (Behr, Harel, Post, & Lesh, 1990); Harel, Behr, Post & Lesh, 1990) and research in…

This document reports on a study into the relationships between cognitive preferences, achievement, and ethnicity of first year algebra students. The sample consisted of 175 students from two high schools in the Denver (Colorado) metropolitan area. The two schools were chosen because of the diversity of ethnic groups in the student populations.…