Measuring Shifts in Reasoning about Fraction Arithmetic in a Middle Grades Number and Operations Content Course

The present study extends recent advances developing and applying measures of mathematical content knowledge for teaching. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct but related components necessary for reasoning in terms of quantities when solving fraction arithmetic problems. The present study adds a new component of validity for the survey by examining the extent to which one pre-service teacher's growth in reasoning about fraction arithmetic, as indicated by assessments she completed for a middle grades numbers and operations course, was reflected in her performance on the survey. Results provide an existence proof that the survey is sensitive to shifts towards more proficient reasoning. [For the complete proceedings, see ED583608.]