Discusses a framework for assessing middle school students' thinking in conditional probability and independence. Establishes four levels of thinking from subjective to numerical reasoning for both constructs. Students (n=15) from grades 4-8 were interviewed. Profiles reveal that levels of probabilistic thinking were stable across the two…

The performance of sixth and seventh graders on a variety of tasks involving estimation and reasonableness of results were studied. Also examined was the effect of a short unit of activities on these two topics. Correct answers approximately doubled after instruction. (MNS)

Insights from both cognitive psychology and learning disabilities intervention research are presented to improve understanding of the processes by which number fact fluency develops. Discussion includes assessment guidelines and learning strategies such as counting all, counting on, and alternative groupings. (Author/JDD)

This article presents the "concrete semiconcrete abstract" (CSA) teaching sequence for teaching basic math skills to students with and without learning disabilities. Guidelines include providing a minimum of nine instructional lessons (three at each level), each with four lesson steps. Validation of the CSA sequence and lesson format with 15…

Presents a series of hands-on activities for grades K-2, 3-4, 5-6, and 6-8 using the common theme of kites to develop number sense in basic operations and fractions. Teachers' guides and worksheets are provided. (MDH)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Discusses duality between process and concept in mathematics, ambiguity of symbolic notation, and flexibility in thought processes of successful students. Content analysis and empirical evidence suggest a qualitatively different kind of mathematical thought in more able compared to less able elementary students (n=72) in arithmetic. (Contains 42…

The influence that number naming grammar has on the understandings of two-digit numbers and place value of kindergarten children of European and Asian background was examined. Results indicate that Asian verbal/numerical representation patterns naming tens and units in order may be associated with distinctive place value concepts that support…

Effects of 3 different types of instruction (use of manipulatives, use of diagrams, and use of symbols only) of rational number content and teaching techniques were compared for 75 preservice teachers in a course in elementary mathematics. Only the manipulatives group showed significant improvement pretest to posttest. Implications are discussed.…

Research on cognitive representation of numbers and understanding of place value of U.S. and Japanese first graders was extended to France, Sweden, and Korea (118 subjects; approximately 24 from each of the 5 countries). Basic differences in children's cognitive representations of number are influenced by characteristics of their languages. (SLD)

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

The abacus is a calculating tool that has been used in Asia for thousands of years. Mental abacus calculation is a skill in which an abacus image in the mind is used without the actual physical manipulation of the abacus. Using this method, people can perform extremely rapid and accurate mental calculations. Research indicates that abacus training…

In this article, the author reports findings from a project designed to explore approaches for improving students' mathematical learning outcomes in relation to the base ten number system. The project explored the role of a commonly used teaching activity, referred to in the project as the "base ten game," in developing children's…

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis…