Over the last five years, interest in the role of history in teaching mathematics has grown markedly. A National Science Foundation–supported Mathematical Association of America Institute on the History of Mathematics and Its Use in Teaching was founded in summer 1995 to explore how the history of mathematics can be used in the classroom. It has produced modules for use in high school and college mathematics teaching. A study on this topic has been authorized by the International Commission on Mathematics Instruction and was the centerpiece of the most recent International Congress in Mathematics Education (ICME), which was held in Japan in the year 2000.
This research extended the validation of a framework for assessing and describing children's thinking in multidigit number situations and used this framework to generate and evaluate different versions of an instructional program. The key constructs of the framework—counting, partitioning, grouping, and number relationships—appeared to be highly stable within each of the five levels and across the full range of thinking exhibited by 12 case studies. Results suggest that the levels may generate a hierarchy of thinking. Teachers were effective in implementing two versions of the framework-driven instructional program. Any differences could be attributed to the quality of problem-solving experiences, the level of student interactions, and, in essence, to differences in teachers' familiarity with the program.
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