Multidigit number sense: A framework for instruction and assessment

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.