Introduces an introductory module for analysis. Describes stock of basic functions and their graphs as part one and three methods as part two: transformations of simple graphs, the sum of stock functions, and upper and lower bounds. (YP)

Summarizes the history of the mathematical idea of function and presents questionnaire data from (n=117) mathematics teachers. Results showed that teachers had a tendency to think only in terms of continuous functions, yet had little skill in constructing continuous functions. They scarcely considered discontinuous functions. (14 references) (MKR)

Deals with the issue of visualization as it is related to the learning of mathematics in multicultural classrooms. Discusses the importance and the role of visualization in multicultural classrooms. (YP)

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Tests of (n=107) third through sixth graders' basic addition facts found that 34% of errors involved the addition of zero and 83% of the remaining errors involved at least one of the digits 7, 8, or 9 when the other addend was 4 or more. (20 references) (MKR)

Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

Reports a study to examine careless errors fifth-grade students (n=58) make while solving mathematical word problems and explores the type of student who frequently makes such errors. Results indicated that frequency of these errors was significantly related to the noncognitive variables of the study. Discusses implications for remediation. (20…

Investigates children's cognitive structures with respect to concepts one-half, one-quarter, and one-third as these apply to continuous circular and triangular regions. Examines the effect of an intervention program with 21 children in grades three through six. (YP)

Discusses students' use of visual considerations in doing geometrical proofs. Studies ninth-grade students (n=17) in an academically-selective high school in Jerusalem. Concludes that only three out of 16 students who turned in their papers chose symmetry considerations when working on a proof. Contains 16 references. (ASK)

Examines selected first-grade mathematics textbooks used in Japanese and American schools. Focus points of analysis include size and volume, repetition, length of explanations, mathematics content, gender issues, and the relevance of the pictures to the mathematics content. Contains 16 references. (DDR)

Assessment of general reasoning processes, elementary algebraic understanding, and novel problem solving of (n=147) seventh- and eighth-grade students found that abilities to generalize from patterns and tables of data and understanding variable constructs contributed significantly to application of algebraic concepts and processes. Questions…

Interview and questionnaire responses of students in grades K-10 completing common and decimal fraction tasks suggested the existence of 2 sequential unistructural-multistructural-relational learning cycles within the concrete symbolic mode. (46 references) (MKR)

Attempts to reveal students' (N=800) misconceptions regarding quadratic functions, and identifies conceptual obstacles that may impede students' understanding. Findings indicate that the conceptual obstacles identified were fairly pervasive. Discusses the educational implications of the findings. Contains 34 references. (JRH)

Analyzes the problem-solving process and presents the dominance of the conjecture or theoretical aspect as a subtle relation between the data and the conjecture. Argues that conjectures are not necessarily subordinate to the data but play active roles in mathematical problem solving. Discusses the meaning of this dominance in the context of…

Questionnaires involving attitudes towards mathematics and achievement in mathematics given to (n=1,082) high school seniors found that the means of each attitudinal variable were not much different among the 3 groups, but that high- achieving students consistently showed a small deviation on each attitudinal variable. Includes mathematics…