Missing-value proportion problems: The effects of number structure characteristics

ABSTRACT

This study explores the effects of number structure characteristics on student thinking in solving missing-value proportion problems. Prior research has documented that the presence of an integer ratio is beneficial, particularly if the integer relationship is within the same measure space. Less information on student performance is available, however, on shrink problems, in which the value to be found is smaller than the given value. In the current work, we systematically investigate student success rates and strategy use on problems that vary in the presence/absence of integer ratios in either measure space and in both enlarge and shrink problems. This study provides evidence and direction to educators seeking to advance their students’ proportional reasoning via judiciously chosen tasks. We start from a distribution analysis of student strategies, which allows us to propose a hierarchy of problem difficulty. We then discuss apparent differences in student thinking based on these number structure characteristics and identify problem types for which more sophisticated proportional reasoning is needed. Directions for further research and implications for teaching are discussed.

KEYWORDS:

• Missing-value problem
• proportion
• proportional reasoning
• ratio
• rational number

Funding

This research was supported in part through a Professional Development Assignment from the University of Northern Iowa for Suzanne Riehl.

Additional information

Funding

This research was supported in part through a Professional Development Assignment from the University of Northern Iowa for Suzanne Riehl.