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The Nature of our Collaborative Research Project

The Nature of our Collaborative Research Project. Funded by KNAER Principal Investigator Dr. Cathy Bruce (Trent University) In partnership with the Ministry of Education – Lead: Shelley Yearley KPRDSB, SMCDSB, OCDSB. Data Collection. AS A STARTING POINT Literature review

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The Nature of our Collaborative Research Project

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  1. The Nature of our Collaborative Research Project • Funded by KNAER • Principal Investigator Dr. Cathy Bruce (Trent University) • In partnership with the Ministry of Education – Lead: Shelley Yearley • KPRDSB, SMCDSB, OCDSB

  2. Data Collection AS A STARTING POINT • Literature review • Diagnostic student assessment (pre) • Preliminary exploratory lessons (with video for further analysis)

  3. Data Collection and Analysis THROUGHOUT THE PROCESS • Gathered and analysed student work samples • Documented all team meetings with field notes and video (transcripts and analysis of video excerpts) • Co-planned and co-taught exploratory lessons (with video for further analysis after debriefs) • Cross-group sharing of artifacts

  4. Data Collection and Analysis TOWARD THE END OF THE PROCESS • Gathered and analysed student work samples • Focus group interviews with team members • 30 extended task-based student interviews • Post assessments

  5. Findings • Students had a fragile and sometimes conflicting understanding of fraction concepts when we let them talk and explore without immediate correction • Probing student thinking uncovered some misconceptions, even when their written work appeared correct • ‘Simple’ tasks required complex mathematical thinking and proving

  6. FRACTIONS Digital Paper

  7. We explored linear, area and set models… We asked: Which representation is helpful in which situations? Tad Watanabe, 2002 TCM article

  8. Number Lines So we looked closely at linear models… How do students: -think about numbers between 0 and 1 -partition using the number line -understand equivalent fractions and how to place them on the number line

  9. Why Number Lines? • Lewis (p.43) states that placing fractions on a number line is crucial to student understanding. It allows them to: • PROPORTIONAL REASONING: Further develop their understanding of fraction size • DENSITY: See that the interval between two fractions can be further partitioned • EQUIVALENCY: See that the same point on the number line represents an infinite number of equivalent fractions

  10. What We Found Out • The project was a benefit to students

  11. Other challenges & misconceptions we encountered withGrade 4-7 Students

  12. Implications for teaching • Expose students to a careful selection of representations that further student understanding. • Consider how representations can act as the site of problem solving/reasoning. • Think more about how to teach equivalent fractions. • Think more about the use of the number line.

  13. 2012-2013 • 5 teams (5 teachers – 5 release days) • 3 teams engaged in Collaborative Action Research on addition and subtraction of fractions • KPRDSB, SCDSB, TLDSB • 2 teams field testing lessons from last year on compare, order, represent • YCDSB, SMCDSB

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