This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

Mathematical Induction is used for direct proofs of many theorems; its logical equivalent, the Well-Ordering Property, replaced it to yield indirect proofs by contradiction. The author claims the later property is easier to comprehend and that it affords a non-geometrical example of proof by contradiction. (JP)

Describes a study in which 383 children in grades 1 through 5 were individually interviewed to find out at what point they construct unit iteration out of transitive reasoning. Indicates that most children construct unit iteration out of transitive reasoning by fourth grade. Suggests a better approach to the teaching of measurement that presents…

Discusses terminology used by teachers for the symbol "-x" which cause students to become confused. Suggested methods of avoiding this confusion are presented. (JP)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

How mathematics subject matter can be enhanced through the scientific reasoning method, how this integration can be achieved, adaptations needed for a modified approach, and resulting attainments are all considered. Prime numbers using the Sieve of Erastosthenes are the vehicle through which the approach is described. (MNS)

Examines the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems, including an experimental and control group each consisting of 34 elementary students, in Japan. The experimental group showed a significantly better performance on the retention test…

The importance of using concrete materials to teach fractions is emphasized. Suggestions for preparing inexpensive sets of such materials are given, with nine activities for their use. (MNS)

Presented are the results of two pilot studies about multidigit addition and subtraction. The results are discussed in relation to possible alternative sequences in the teaching of addition and subtraction and the relationship between basic fact mastery and numeration concept attainment. (CW)

Reports selected findings from a study of number-sense proficiency in students aged 8 to 14 years in Australia, Sweden, the United States, and Taiwan. Comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Discusses some implications for classrooms. Contains 39…

This study examined the effect of language on children's cognitive representation of number. The sample for the study consisted of 90 Arabic speaking children with a mean age of 80 months. Children were interviewed individually and asked to represent written two-digit numbers using base-10 blocks. A new approach for testing the linguistic…

Presented are several methods of introducing nondecimal numeration systems to elementary grade students. Various activities for grouping and/or visual displays are used. Games which incorporate nondecimal grouping ideas are also presented. (JP)

Sections look at: (1) Historical Perspective; (2) Naming the New System; (3) The Metric Units; (4) Measuring Larger and Smaller Amounts; (5) Advantage of Using the Metric System; (6) Metric Symbols; (7) Conversion from Metric to Customary System; (8) General Hints for Helping Children Understand; and (9) Current Status of Metric Conversion. (MP)