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California Educational Research Association
Disneyland Hotel – Anaheim, CA
December 1, 2011
Terry Vendlinski
Julia Phelan
Improving Middle School Math Instruction: Formative
Assessment, PD and Big Ideas
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Background
• Math instruction seldom builds on the prior knowledge of students and doesn’t account for student misconceptions.
• Math is often presented as a list of facts to be memorized and procedures to be implemented.
• Students often see these facts and procedures as random or disorganized.
• Students have little understanding of how math relates to or is useful in the “real” world.
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Method
• Organize instruction around key foundational ideas (unlike many textbooks)
• Develop formative assessments, instructional materials and professional development around these foundational ideas.
• Measure the way teachers conceptually organize content and choose exemplary problems to illustrate a concept.
• Compare pre / post maps to experts
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Concept Maps
Links
•applies to
•can represent
•is a
•property of
•type of
•used to
Concepts
•Additive Identity
•Additive Inverse
•Distributive Property
•Equivalence
•Factoring
•Fractions
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Exemplary Problems
Solve for the unknown:15 + 17 + c = 40
Evaluate the expression y + 3 when y = 2
The two triangles are similar, what is the length of side AB?
Solve for the unknown:15=15
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Knowledge (Concept) Map Example
Can represent
repeatedundoes
Division
Multiplication
Addition
SubtractionFind the
mean of 3, 6, 9, 15
1
Find the product of
12 x 3
2
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Our Research Questions
• Through professional development, can teachers change their conceptual organization of the mathematics domain they teach to become more like experts?
• Do teachers in different grades respond differently to professional development?
• Do teachers with different levels of experience respond differently to professional development?
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The study
• 144 teachers from seven public school districts in Southern California and Arizona.
• 8+ hours of professional development in three conceptual areas that involved conceptual understanding and analysis of student work.
• Phased-in approach from 6th to 7th to 8th grade teachers.
• Randomized Control Trial using both within and between-school groups.
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Do teachers change in their ability to organize math concepts?
• 6th grade teachers showed marginally significant differences in their ability to organize math concepts after one year of PD
• 6th grade teachers showed significant differences in their ability to connect problems and concepts after two years of PD.
• 7th grade teachers showed significant differences in their ability to organize math concepts after two years of PD.
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Conclusions
• The way teachers organize conceptual thinking does change, but the rate appears to differ by grade.
• The way teachers connect problems and concepts appears to take longer to develop.
• These changes also appear to be related to experience. Sixth grade teachers had significantly more math teaching experience and MS math teaching and were significantly more likely to have a single subject credential.
Find this report at: http://www.cse.ucla.edu/products/reports/R794.pdf
For more information: vendlins@ucla.edu
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