Ga. Jones et al., MULTIDIGIT NUMBER SENSE - A FRAMEWORK FOR INSTRUCTION AND ASSESSMENT, Journal for research in mathematics education, 27(3), 1996, pp. 310-336
This research extended the validation of a framework for assessing and
describing children's thinking in multidigit number situations and us
ed this framework to generate and evaluate different versions of an in
structional program. The key constructs of the framework-counting, par
titioning, grouping, and number relationships-appeared to be highly st
able within each of the five levels and across the full range of think
ing exhibited by 12 case studies. Results suggest that the levels may
generate a hierarchy of thinking. Teachers were effective in implement
ing two versions of the framework-driven instructional program. Any di
fferences could be attributed to the quality of problem-solving experi
ences, the level of student interactions, and, in essence, to differen
ces in teachers' familiarity with the program.