Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

Discusses ways to incorporate language into the teaching of mathematics and involve students more fully in mathematical processes. Describes classroom teaching practice with and without writing. Lists 11 references. (YP)

This article reviews briefly some of the research related to the development of automaticity for recall of basic math facts, reports on a research project with six fourth- and fifth-grade students, and gives teaching suggestions for the development of automaticity. (PB)

Seventy-seven children (ages 5-13) with mild to moderate mental retardation were presented with addition problems. The patterns of strategies used were found to be similar to those used by intellectually normal children, though counting-on and memory strategies were used by subjects with greater frequency. Strategies became more sophisticated with…

Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)

The errors and strategies made by students who consistently use the incorrect-addition strategy on "hard" ratio tasks were investigated. The characteristics of these "adders," such as awareness of noninteger multiples, the use of fractions and decimals, awareness of both within and between ratios, and distinguishing nonratio…

Discusses the contributions in each chapter of the book, highlighting the textbook analyses for each arithmetic topic presented. (MDH)

Six fifth-grade children participated in a four-day teaching experiment on complex additively structured problems to investigate difficulties in concurrently holding in mind situations in which items play multiple roles. Difficulties included distinguishing take-away difference from comparison difference and indirect evaluation of an additive…

Discusses the use and construction of "fact fans," fun and easy-to-make manipulatives that provide elementary school students with the opportunity to explore mathematics operations being studied in the classroom and to practice addition, subtraction, multiplication, and division facts. (BB)

Presents student comments as they explain their mathematical reasoning and thinking about place value in addition and subtraction. (ASK)

Examines the scope and nature of upper elementary school pupils' difficulties with modeling and solving nonroutine additive word problems. Concludes that many errors result from the superficial, stereotyped approach of adding or subtracting two given numbers without considering the appropriateness of that action in relation to the problem context.…

Describes a mathematics lesson using digital sums that allows teachers to assess third grade students' understanding of reasoning, arithmetic, and geometry. (ASK)

One of the major goals in mathematics education is to teach the ability to solve word problems. This study compared the word problem solving abilities of second-grade students from Taiwan (N=24) with those of American students (N=24). Two tests were used in the problem solving interviews. The comparisons between the performance of the groups on…

The objective of the Easy Math Program is to give all students (not just those with mathematical talent) an intuitive grasp of the quantitative principles on which mathematics is based, so they will be able to execute its basic operations with insight, and move on to its higher concepts with confidence. The program approaches this objective by a…

Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice,…