Professional Development Resources: Research-Based Practices for K-6 Mathematics

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1 Professional Development Resources: Research-Based Practices for K-6 Mathematics

2 Today s Session Introduction to resources and K-6 mathematics topics Focus on K 6 Mathematics Content Problem Solving and Persistence

3 Translate research-based practices into examples and practical tools that support and improve classroom instruction.

4 U.S. Department of Education Institute of Education Sciences (IES) What Works Clearinghouse (WWC) Practice Guides DWW Library

5 DWW Library Resources in: Literacy Mathematics and Science Quality Teaching Data-Driven Improvement Comprehensive Support

6 Mathematics Topics Encouraging Girls in Math and Science National Math Panel: Critical Foundations for Algebra Major Topics of School Algebra Developing Effective Fractions Instruction for K-8 Improving Mathematical Problem Solving in Grades 4 through 8 Response to Intervention in Elementary- Middle School Mathematics

7 IES What Works Clearinghouse Practice Guides

8 IES What Works Clearinghouse Practice Guides

9 Newest IES Practice Guide (November 2013)

10 How Practice Guides are Developed Expert Panel - Researchers - Practitioners Research Recommendations Broad Search Assess Quality Identify Examples Peer Review

11 Practice Guides Levels of Evidence Strong: High confidence (multiple rigorous studies in a variety of contexts) Moderate: Some evidence (may not work in all settings) Low or Minimal: Hasn t been proven with rigorous research (but panel still thinks it is important)

12 Other Sources National Mathematics Advisory Panel

13 For Each Practice Research base and key concepts Expert interviews School site videos and slideshows Interviews and sample materials from schools Ideas for action Tools and templates to implement practices

14 All media and materials are accessible in the DWW Library from: WestEd box for DWW Materials: Professional Development package Research-Based Practices for K-6 Mathematics As well as: Adolescent Literacy Improving K-3 Reading Comprehension Increased Learning Time Research-Based Practices for Secondary Schools Using Student Achievement Data to Support Instructional Decision Making

15 Research-Based Practices for K-6 Mathematics Module 1: Introduction to K-6 Mathematics Topics Module 2: Focus on Mathematics Content Module 3: Problem Solving and Persistence Module 4: Assessments and Interventions

16 Practice Guides used in Modules Module 2: Focus on Mathematics Content National Math Panel: Critical Foundations for Algebra Developing Effective Fractions Instruction for K 8 Module 3: Problem Solving and Persistence Module 4: Assessments and Interventions Improving Mathematical Problem Solving in Grades 4 8 Response to Intervention in Elementary/Middle Mathematics Encouraging Girls in Math and Science

17 K-6 Mathematics Content 17

18 Part 1: Overview of Math Content

19 Simultaneously Teaching Conceptual Understanding, Computational Fluency, and Problem-Solving Skills Dr. Joan Ferrini-Mundy National Science Foundation and Michigan State University The interrelations among conceptual understanding, computational fluency, and problem-solving skills, and how teachers can develop lesson plans to integrate these areas into their instruction.

20 Part 2: Teaching Fractions

21 Practice Guide

22 Recommended Practices Initial Fraction Concepts Build basic fraction concepts from students informal understandings of sharing and proportion. Fractions as Numbers Use number lines to develop student understanding of fractions as numbers. Operations With Fractions Help students understand why computational procedures with fractions make sense. Ratio, Rate, Proportion Develop understanding of proportional relationships before teaching computational procedures.

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24 Recommendation 2 Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.

25 Number Lines: A Key Representational Tool Dr. Yukari Okamoto University of California, Santa Barbara The misconceptions that students have about fractions and how to help them understand fractions place in the number system.

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28 Resource Inventories for Focus on Mathematics Content

29 QUESTIONS

30 Problem Solving and Persistence 30

31 Part 1: Problem-Solving Teaching Strategies

32 Practice Guide

33 Practice Guide Recommendations Prepare problems and use them in whole-class instruction. Assist students in monitoring and reflecting on the problem-solving process. Teach students how to use visual representations. Expose students to multiple problem-solving strategies. Help students recognize and articulate mathematical concepts and notations.

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36 Instructional Strategies Teach students to use visual representations, employ multiple problem-solving strategies, and relate mathematical concepts and notation to problem solving. Asha Jitendra Mark J. Driscoll Ken Koedinger

37 Research Findings Students who visually represent mathematical information prior to writing an equation are more effective at problem solving. Using visual representations is most effective when students design their own representations. More successful problem solvers are more efficient in selecting approaches to problems because they know how to use multiple strategies. Using worked examples and asking students to explain the process improves problem solving.

38 Representing a Problem Visually Joe Corigliano Madison Elementary School Spokane, WA A fifth-grade teacher invites student groups to present their solutions to Frank s Fresh Farm Produce problem deciding whether there is enough gas in the truck s tank before going to pick up produce at two farms.

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44 Part 2: Persistence and Problem Solving

45 Effort and Persistence Research Findings Effort and persistence pays off in mathematics achievement. Implications for Instruction Teachers and parents must be conscious of the messages they provide to students about the importance of effort. Teachers should model how they solve difficult problems, including that it takes time and may be puzzling. Teachers should encourage and reward effort in addition to achievement.

46 Messages on Effort and Persistence Brent Perdue Rita Hadley Joanne Hagen Madison Elementary School Spokane, WA Elementary principal and teachers demonstrate strategies to encourage students to apply effort in learning mathematics.

47 Ability is Expandable Teach students that the brain grows when they practice and learn new material. There are two ways to view intelligence: that it is fixed and can t be changed, or that it is expandable and that with effort, abilities can improve or expand.

48 Two Mindsets

49 Resource Inventories for Problem Solving and Persistence

50 QUESTIONS

51 Professional Development Package DWW Materials: