Discussed are number meaning and part-whole relationships concerning place value. Findings from a research study with students in grades two-five who were interviewed about place-value tasks are given. Stages of interpreting two-digit numbers are presented, with implications for the classroom. (MNS)

Some findings from research on problem solving are briefly summarized. (MNS)

Research on what elementary school students know about probability prior to instruction and what they can learn about probability is concisely reviewed. Many references are included. (MNS)

Research on direct instruction in mathematics is briefly summarized, with key procedures listed. (MNS)

Research on students' attainment on multiplication facts, common errors, and meaningful instruction is briefly cited in this review. (MNS)

Research on homework in mathematics is briefly reviewed, with the conclusion that homework may be useful since it may increase achievement but won't decrease it. Specific suggestion for planning homework are included. (MNS)

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)

Two studies on the match between test and textbook content are reviewed. The emphasis in textbooks on computation, wide variation in content, and weak matches between content in textbooks and tests were noted. (MNS)

Research on the amount of questioning and the types of questions teachers ask are briefly discussed. (MNS)

Research on the characteristics of individuals who have demonstrated a high level of ability in mathematics is presented. The importance of structure in mathematical thinking is stressed and implications for teaching are detailed. (MNS)

What research says about the learning and teaching of decimal fractions is summarized, with some instructional strategies and activities to improve learning suggested. (MNS)

After research on problem solving is briefly summarized, an in-service program on problem types and solution strategies is described. Teachers must know how pupils solve problems; they can use activities designed for both instruction and assessment. Key aspects of assessment are summarized. (MNS)

Research indicates that calculators can promote mathematics achievement. Some topics with which calculators can aid are briefly discussed: problem solving, number ideas, counting, basic facts, and computation with whole numbers and decimals. (MNS)

Research on the use of review is briefly summarized. Some guidelines for planning review work are listed, and five types of effective review are noted: outlines, questions, varied grouping, varied content, and games. (MNS)

Research on minority groups in mathematics (particularly Blacks and Hispanics) is briefly summarized. How researchers attempt to explain achievement and enrollment differences is noted. (MNS)