Writing is a key component in developing mathematics thinking and understanding. Four strategies to encourage student writing to describe thinking and reasoning are offered. Teachers can use this writing to verify student understanding of mathematical concepts. (MT)

The intercorrelations among the 11 subtests second edition of the Detroit Tests of Learning Aptitude (DTLA-2) for a portion of the standardization sample were subjected to both factor analysis and cluster analysis. None of the factors or clusters corresponded exactly to any of the eight DTLA-2 composities. (Author/LMO)

Computer algebra systems are described. Features of such systems and information on MACSYMA, Maple, muMath, REDUCE, and SMP are given. (MNS)

After discussion of the equivalency of the information laws of Bradford, Leimkuhler, Lotka, and Mandelbrot, aberrations from Leimkuhler's law (including "Groos droop" as encountered in practice) are studied. Other aberrations of Leimkuhler's law are explained, starting from generalization of verbal formulation of Bradford's Law. (18…

Compares a conventional method of basic mathematics instruction (mastery learning) with a structuralist approach using analogical reasoning. Pretest posttest results from three adult education classes show that analogical teaching is more effective in developing ability to think numerically. (SK)

Investigates effects of a long-term, systematic effort to teach a relational meaning of "equals" to children before they reach the transitional age of 13. Data obtained from 15 first, second, and third graders indicated teachers need not wait until junior high school to introduce a relational view. (RH)

Forty students from the first, second, fourth, and sixth grades (10 from each), equally balanced for sex and representing a middle class SES, were individually administered mathematical tasks of matching, equality, cardination, and measure and Piagetian conservation task of number, length, and surface or area. (NQ)

The purpose of this study was to examine the effect on student understanding of Newton's Third Law in an introductory calculus-based physics class when a new graphical representational tool called a system schema was used throughout instruction to help visualize objects and interactions between them explicitly. The system schema serves as an…

As part of a larger investigation of preservice teachers' use of, and movement amongst, various modes of representing exponential relationships, this report focuses on one case study, that of Mike, whose facility in moving amongst representational registers was not matched by conceptual understanding of the underlying mathematical ideas as he…

The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

Learning mathematics with understanding is the vision of school mathematics recommended by the National Council of Teachers of School Mathematics (NCTM). In order to design and develop learning environments that promote understanding efficiently, teachers need to be aware of student difficulties in learning mathematics. Drawing from the research…

This book, written for students of calculus, is designed to augment the explanations of concepts covered in a calculus class. It consists of an overview of calculus divided into basic ideas and vocabulary, the process of differential calculus, and integral calculus. The book is intended as a resource to explain the concepts of calculus in everyday…

Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)