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Representation: Getting at the heart of mathematical understanding. Wisconsin Mathematics Council Green Lake Annual Conference Thursday, May 6, 2010 Sarah Burzynski, Math Teacher Leader, Longfellow School MPS Melissa Hedges, Math Teaching Specialist, MPS. WALT and Success Criteria.
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Wisconsin Mathematics Council
Green Lake Annual Conference
Thursday, May 6, 2010
Sarah Burzynski, Math Teacher Leader, Longfellow School MPS
Melissa Hedges, Math Teaching Specialist, MPS
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation.
What does it mean to know how to compare fractions?
What does it mean to understand how to compare fractions?
What’s the difference?
1. Turn over one card at a time. On your own study the fractions you see. No talking!
2. Decide…Which is larger? About by how much?
3. Estimate the difference.
4. Be prepared to share the estimated difference as a unit fraction. (A unit fraction has a one in the numerator.e.g.: ½, ⅓, ¼.)
No common denominators please!
Tap into your first “life line.”
Which is larger? About by how much?
2/3 or 1/4
3/8 or 3/4
5/3 or 7/4
As you reasoned through this task:
As children move between and among these representations for concepts, there is a better chance of a concept being formed correctly and understood more deeply.
Lesh, Post & Behr (1987)
National Research Council. (2001). Adding it up. Mathematics Learning Study Committee, Center for Education, Division of Behavioral Sciences and Education, National Research Council. Washington, DC: National Academy Press.
National Research Council. (2002). Helping Children Learn Mathematics. Mathematics Learning Study Committee, J. Kilpatrick & J. Swafford, Editors. Center for Education, Division of Behavioral Sciences and Education. Washington, DC: National Academy Press.
Wisconsin Department of Public Instruction. (1998). Wisconsin’s model academic standards for mathematics. Madison, WI: Author.
In reviewing the student work, what are you noticing?
What does the representation being used by the student tell us about his/her understanding of the mathematics?
How do the children use representations to clarify thinking and make sense of the task?
How does their use of representations surface misconceptions?
Grade K5 – Grade 8
Students will effectively use mathematical knowledge, skills and strategies related to reasoning, communication, connections, representations, and problem solving.
Descriptors, such as but not limited to: