Lee, S., Brown, R. E., & Orrill, C. H. (2011, July). Mathematics teachers’ reasoning about fractions and decimals using drawn representations. Mathematical Thinking and Learning, 13(3), 198-220.
Soo Jin Lee, Montclair State University
Rachel Eriksen Brown, Knowles Science Teaching Foundation
Chandra Hawley Orrill, University of Massachusetts Dartmouth
Mathematical Thinking and Learning, Volume 13, Issue 3, 2011, pp. 198-220
This qualitative study considers middle grades mathematics teachers’ reasoning about drawn representations of fractions and decimals. We analyzed teachers’ strategies based on their response to multiple-choice tasks that required analysis of drawn representations. We found that teachers’ flexibility with referent units played a significant role in understanding drawn representations with fractions and decimals. Teachers who could correctly identify or flexibly use the referent unit could better adapt their mathematical knowledge of fractions validating their choice, whereas teachers who did not attend to the referent unit demonstrated four problem-solving strategies for making sense of the tasks. These four approaches all proved to be limited in their generalizability, leading teachers to make incorrect assumptions about and choices on the tasks.