The relationships between three types of tasks were investigated with 428 children from kindergarten through grade 6 showing that correspondence, seriation, and transitivity reflected different underlying concepts. Thus, it was concluded that neither correspondence nor transitivity tasks can serve as replacements for traditional seriation tasks in…

In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional…

Hispanic students are notably behind their white counterparts in the core academic skills. Although the precise size of the gap depends on the subject area, age or grade, and the assessment, by all measures, a significant gap in mathematics, reading skills and science exists between Hispanic and white students. Educational achievement, or…

Working with his daughter and her friend on a problem-solving task gave Graham Jones the opportunity to reconsider how best he might help. This document describes how he went about assisting the girls in solving the problem. In assisting, Graham decided to present the girls with a three part lesson, which would lead to the solution. He stresses…

This book is a teacher's resource guide designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four…

This paper suggests that logic consists of a collection of propositions and operations of negation, conjunction, disjunction, implication, and equivalence. It points out that the operations on dispositions depend upon the truth-value of the propositions involved. This raises the questions, How do we know whether a proposition is true or false? and…

Numeracy can be defined as having the competence and disposition to use mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life (Willis 1992). An important aspect of developing the capacity to use mathematics in everyday life is, for students at school, to use mathematics to meet the…

Efforts to develop a mathematics curriculum that meets the needs of a modern society are reflected in reform recommendations across the developed world. A common requirement is for students to understand the calculation procedures they are taught and to develop "number sense". This paper will analyse students' strategies for calculating…

This book has as its major focus the comprehensive assessment of children's early numerical knowledge and strategies and their advancement. Practical and theoretical aspects of assessment are explained in detail. A major feature of the book is a learning framework in early number that is applied in analyzing the results of assessment and planning…

This paper describes a collaborative research study designed to determine whether well-constructed tasks in mathematical inquiry with the use of methods in dialogic discourse help students' retention of mathematical concepts in probability. The paper reports on an experiment conducted in two classrooms in an urban school district in the Pacific…

Eighty-seven pupils in grades 4-6 completed five multiplication examples and wrote a problem for another example. They were reasonably proficient, with mean scores of 82 percent in grade 4, 75 percent in grade 5, and 97 percent in grade 6. They did less well on developing a problem. (MNS)

Problems involving record-setting events are presented, with comments on both the mathematics skills and the reading skills that are involved with each. (MNS)

According to responses from 166 of 600 management faculty, most believe that incoming students are deficient in writing, verbal, and math skills and are not as motivated as their predecessors. Opinions were similar for public/private and accredited/nonaccredited institutions and for tenured/nontenured and senior/junior faculty. (SK)

Comments on current reform in mathematics teaching. Changes include getting students actively involved in their mathematics studies and encouraging them to see the larger picture. College teaching has involved more technology as well as ensuring that a broader spectrum of students benefit than in the past. Reform movements need to more closely…

Investigates the effects of instructional environment on students' conceptual understanding and procedural knowledge of calculus. Uses multiple achievement measures to determine the degree to which students from different instructional environments had mastered the concepts and procedures inherent to first semester calculus. Indicates no…