This booklet summarizes the mathematics chapter from "Handbook of Research on Improving Student Achievement", published by the Educational Research Service (ERS). The Handbook is based on the idea that, in order to succeed, efforts to improve instruction must focus on the existing knowledge base with respect to effective teaching and learning. The…

Examples are given of the variety of mathematical concepts and problems being studied by psychologically oriented researchers in France. Work on decimals, circles, natural numbers, decimal and real numbers, and didactic transposition are included. Comments on designing research on mathematics concept formation conclude the article. (MNS)

The activity provides practice plotting points in the Cartesian plane, develops inductive skills in pattern recognition, develops verbal and translation skills, and acquaints students with some properties of linear relations. Three worksheets are included. (MNS)

Difficulties that entering college freshmen showed on a mathematics assessment test are discussed. More students can perform decimal computation than can order decimals. The concept of equivalent decimals should be taught more carefully at every level. (MNS)

An approach to teaching multiplication and division with negative numbers that focuses on graphs to illustrate concepts is revealed. The material and problems used are presented with comments on the teaching methods applied with 11-year-olds. (MP)

Presented are activities which give practice in making estimates, gathering data, and checking the reasonableness of results. (TG)

Examines the effects of cultural and educational variables on the development of number conservation among Baoule (agricultural group) children and Dioula (merchant group) children. Results suggest that both school and a merchant culture provide for acquisition of a mature number concept, supporting the "functional learning systems"…

Analyzes the solution of additive problems involving negative numbers by prospective primary school teachers using surveys. Concludes that students feel no need to use negative numbers in the solution of additive problems and compares results of this study to another study of same content done on secondary school students. (ASK)

Validates a framework for assessing children's thinking in multidigit number situations and uses the framework to evaluate instructional programs. Key constructs--counting, partitioning, grouping, and number relationships--appear stable within each of 5 levels across 12 case studies, suggesting a possible hierarchy of thinking. (DF)

Described is an activity where base-10 blocks are used to develop students' skills in reading, writing, and visualizing large numbers. An activity sheet that helps students with decimal points is included. (KR)

Described are activities involving higher order thinking skills developed for gifted students that can be used for all students. Discussed is a framework for designing activities using Bloom's Taxonomy of the Cognitive Domain and William's Student Behaviors. Sample activities are included. (KR)

Discussed is the importance of incorporating calculators and computers into the primary grades. Number concepts, counting skills, place-value, basic operations, problem-solving, and higher order thinking skills can be reinforced by using calculators and computers along with manipulatives. (KR)

Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Interviews with (n=55) children and their teachers in years one, two, and three showed a closer association between knowledge of place value and levels of counting than between levels of counting and the ability to explain the counting sequence. (13 references) (MKR)