the nature of our collaborative research project
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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 CollectionAS A STARTING POINT Literature review Diagnostic student assessment (pre) Preliminary exploratory lessons (with
video for further analysis)
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
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
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
FRACTIONS Digital Paper
We explored linear, area and set models…
We asked: Which representation is helpful in which situations?
Tad Watanabe, 2002 TCM article
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
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
What We Found Out
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0%
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Growth in Achievement
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The project was a benefit to students
Other challenges & misconceptions we encountered with Grade 4-7 Students
Some Common Misconceptions Translates to…
Area Models: Size of the partitioned areas doesn’t matter when using an area model, just the number of pieces
Approximations in drawings (is it good enough? Understanding the need for equal parts, but approximating equal parts in area model drawings)
Set Models: Fractions cannot represent ‘parts of a set’. All representations of fractions must show the ‘parts’ as attached or touching, and all parts must be exactly the same no matter how the set might be named
Inability to see the following as a fraction relationship:
Equivalent Fractions: Always involve doubling
1/2 then 2/4 then 4/8 then 8/16(5/10ths would not be considered in this scenario)
The numerator and denominator in a fraction are not deeply related: (that the fraction has two numbers that represent a value because the numbers have a relationship)
2/5ths is equal to 1/10th because 2 fives are 10 and 1 ten is 10Note - Use of fraction language by educators may contribute to this problem: When we show a fraction, but don’t say it, the students seem to have multiple ways of naming it themselves, some of which are confusing (e.g., one over ten)
Implications for teachingExpose 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.
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