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