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)

Responses to area and preimeter questions asked of 9-, 13-, 17-year-olds and young adults in the National Assessment are summarized. Recommendations for instruction aimed at improving these results are described. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Results of National Assessment problems on area are used to highlight the difficulties elementary students have with area and volume concepts. Recommendations for instruction include the provision for substantial practice with coverings before the introduction of computational short-cuts. (SD) Aspect of National Assessment (NAEP) dealt with in…

The performance of 13 and 17-year-olds on National Assessment items involving computation with fractions is reviewed, together with findings from related research. Recommendations for improving instruction are offered. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Results of the National Assessment of Education Progress (NAEP) related to subtraction are summarized and interpreted. Implications for instruction are discussed. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Performance of 9-year-olds, 17-year-olds, and young adults on questions related to numerical estimation is reported. Implications for instruction are discussed. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Performance on several word problems used in the National Assessment of Educational Progress is discussed. Errors are analyzed for different age groups, and the overall findings are compared with results of related research. Implications for instruction are derived. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results…

Various algorithms used in addition, subtraction, and division problems were identified. The percentages of people in the National Assessment survey populations using each method are reported, as are the percentages of those using the most popular methods who answered correctly. Implications for instruction are discussed. (SD) Aspect of National…

The results of the National Assessment of Educational Progress concerning students' recognition of the names of solid objects are summarized. Implications for the teaching of elementary school mathematics are discussed. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Twenty first-grade teachers' use of knowledge from research about mathematical thinking of children was compared with that of 20 teachers who did not participate in an analysis of research. Implications for teacher education and practice are discussed. (SLD)