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Research conducted in grades K-8 on activity-based teaching approaches, including studies on the use of manipulative materials, is reviewed and synthesized in this report. On the basis of the synthesis, it was concluded that lessons using manipulative materials have a higher probability of producing greater mathematical achievement than do non-manipulative lessons. Use of both manipulative materials and pictorial representations is highly effective; symbolic treatments alone are less effective. The use of materials appears to be effective with children at all achievement levels, ability levels, and socioeconomic levels. Activity-oriented programs and the use of mathematic laboratories can be expected to result in achievement at least as high as when activities are not emphasized. Other conclusions are also presented, plus implications for further research. Implications for classroom practice and five guidelines for those planning projects or selecting programs are presented. (MS)

Suggestions for using four-function calculators, programmable calculators, and microcomputers are considered in this collection of 36 articles. The first section contains articles considering general implications for mathematics curricula implied by the freedom calculators offer students from routine computation, enabling them to focus on results and relationships, and is balanced by Section Two, exploring inappropriate ways calculators can be used. Freedom from thinking about routine calculations provides freedom for thinking about problem solving is the theme of Section Three. Articles in Section Four include some specific lesson ideas for using calculators in the classroom. Section Five focuses on programmable calculators. Section Six contains articles which consider ways in which microcomputers can be introduced into schools, addressing physical, economic, and political issues. Section Seven explores implications of the computer on mathematics curricula, considering both new topics and new approaches to old topics (such as computer assisted instruction). Computer literacy is the theme of Section Eight, suggesting that although all students need to know about computers, "what" they need to know is debatable. The ability to simulate real-world events (computer simulations) is considered in the final section, suggesting that this ability opens new areas for mathematical exploration. (Author/JN)