Measuring middle grades teachers' understanding of rational numbers with the mixture rasch model

Andrew Izsák, Chandra Hawley Orrill, Allan S. Cohen, Rachael Eriksen Brown

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to a convenience sample of 201 middle grades teachers and used the mixture Rasch model to uncover 2 distinct subgroups. Further analyses of the test data and follow-up interviews with 16 of the same teachers revealed that group membership provided 2 important pieces of information. First, teachers in Group 1 understood the role of multiplying or dividing by 1 in standard computation procedures much better than teachers in Group 2. Second, teachers in Group 1 identified appropriate referent units for numbers and appropriate parts-of-parts of quantities more consistently across situations than teachers in Group 2. Capturing such information extends recent advances in measuring mathematical knowledge for teaching.

Original languageEnglish (US)
Pages (from-to)279-300
Number of pages22
JournalElementary School Journal
Issue number3
StatePublished - Mar 2010

All Science Journal Classification (ASJC) codes

  • Education


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