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A Deeper Look at Problem Solving

A Deeper Look at Problem Solving. Structures and Practices for Problem Solving in the CCSS for Mathematics Sara Donaldson and Judy Droitcour East Bay Center for Mathematics Educators. Goals of the session:. Deepen our understanding of problem types and solution methods

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A Deeper Look at Problem Solving

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  1. A Deeper Look at Problem Solving Structures and Practices for Problem Solving in the CCSS for Mathematics Sara Donaldson and Judy Droitcour East Bay Center for Mathematics Educators

  2. Goals of the session: • Deepen our understanding of problem types and solution methods • Explore connections between problem solving and the CCSS-M • Develop strategies for analyzing and tracking student thinking and achievement

  3. Goals of the session: • Deepen our understanding of problem types and solution methods • Explore connections between problem solving and the CCSS-M • Develop strategies for analyzing and tracking student thinking and achievement

  4. ResearchSuggests: • Children’s Mathematics: CGI. Carpenter, Fennema, Franke, Levy,Empson. 1999 • Key Findings: • Young children can invent strategies to solve a variety of problems given the opportunity to do so. • The most successful students had teachers who believed that students can solve problems without having a strategy provided for them. • Teachers often had intuitive knowledge of students problem solving strategies, however that knowledge was fragmented, not well connected and did not appreciate the critical role that Modeling and Counting strategies play in children’s thinking.

  5. Children’s Mathematics: CGI • Teachers knowledge of their students’ thinking was directly related to student achievement. • The most successful students had teachers who used what they learned from listening to students to make instructional decisions. (*CGI = Cognitively Guided Instruction)

  6. Activate and Connect • Where are you now? • What are your goals? • Do you agree or disagree?

  7. Quick Overview… Problem Solving = Operations and Algebraic Thinking • Addition & Subtraction • 3 Solution Methods (see p. 6) • Problem Types/Structures (see Table 1 or p. 88)

  8. Video Case Study: Ella

  9. Video Case Study: Ella • What did you notice? • What did you wonder? • What connections did you make to your own classroom and students?

  10. Connecting to the Common Core • Problem Structures Chart (p. 88)

  11. Connecting to the Common Core • Problem Structures Chart (p. 88) • Standards for Mathematical Practice (p. 6) • What do good mathematicians do?

  12. Connecting to the Common Core • Problem Structures Chart (p. 88) • Standards for Mathematical Practice (p. 6) • The Learning Progressions for Operations and Algebraic Thinking Operations and Algebraic Thinking Overview of Grades K–2

  13. Grade Level Progression:

  14. Categorizing Problem Types • Jigsaw Read: Understanding Problem Types and Children’s Strategies • Sorting Problems: Connie and Juan

  15. Reflection on the Morning…. • Classroom Applications…. • Questions….

  16. Re-Activate with Connie & Juan: • What would a solution look like at each of the 3 levels?

  17. Instructional Purpose:Balancing the Cognitive Demand Numeracy Strategy Use Problem Structure Work • Easily accessible numbers • Reword familiar problems • Teacher language • Familiar structure • Blank spots for numbers • Strategic number choice • Examples: • Carlita • Connie & Juan

  18. Differentiation: Number Range Wording Tools • Examples: • Pencils • Goldfish

  19. Assessment Implications:Knowing Where They Are • Informal Observations • CCSS-M Aligned Tasks • Tracking Progress

  20. Sharing Out • Reflections and Next Steps…. • How we can help… (ebecri.org)

  21. Sara Donaldson (swdonaldson23@gmail.com) Judy Droitcour (jdroitcour@ebecri.org)

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