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Math and the Gifted Learner

Math and the Gifted Learner. CLIU 21 – Gifted Symposium Unwrapping the Potential. Agenda. Goals Why Alternatives to Acceleration? What Works Open Questions Parallel Tasks. Challenge vs Acceleration. Common Core Standards Research Gifted Students Brain and Learning.

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Math and the Gifted Learner

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  1. Math and the Gifted Learner CLIU 21 – Gifted Symposium Unwrapping the Potential

  2. Agenda • Goals • Why Alternatives to Acceleration? • What Works • Open Questions • Parallel Tasks

  3. Challenge vs Acceleration • Common Core Standards • Research • Gifted Students • Brain and Learning

  4. Common Core Standards • Much more rigorous • Shift in when concepts are introduced • Most noticeable in K – 8 • More depth, fewer concepts in most grades • Progressions across grade levels more coherent • Standards for Mathematical Practice

  5. Common Core Standards for Mathematical Practice #1 Make sense of problems and persevere in solving them. Can the student • Consider analogous problems? • Monitor and evaluate their progress, changing course if necessary? • Explain correspondences between the different mathematical representations? • Identify correspondences between different approaches?

  6. Common Core Standards for Mathematical Practice #2 Reason abstractly and quantitatively. Can the student • Decontextualize AND Contextualize? • Create a coherent representation of the problem? • Attend to the meaning of quantities, not just compute them?

  7. Common Core Standards for Mathematical Practice #3 Construct viable arguments and critique the reasoning of others. Can the student explain • What his/her solution is? • Why his/her solution works? • How someone else’s solution works and why?

  8. Common Core Standards for Mathematical Practice #4 Model with mathematics. Can the student • Apply the mathematics to solve problems in real-world situations? • Can they use tools such as diagrams, two-way tables, graphs, flowcharts and formulas? • Routinely interpret their results in context, reflect on whether the results make sense and revise model if necessary?

  9. Common Core Standards for Mathematical Practice #5 Use appropriate tools strategically. Can the student • Make sound decisions about which mathematical to use in the situation? • Use technology to • help visualize the results to analyze, explore, and compare • to explore and deepen understanding of mathematical concepts

  10. Common Core Standards for Mathematical Practice #6 Attend to precision. Can the student • Communicate precisely to others? • Use clear definitions in discussions and their own reasoning? • Use symbols, units of measure, labels consistently and appropriately?

  11. Common Core Standards for Mathematical Practice #7 Look for and make use of structure. Can the student • Discern patterns or structure? • Can they see complicated things as being one and as being composed of simpler things?

  12. Common Core Standards for Mathematical Practice #8 Look for and express regularity in repeated reasoning. Can the student • Notice repetition in calculations and look for general methods and shortcuts? • Maintain oversight of the process while attending to the details? • Evaluate reasonableness of intermediate results?

  13. Pause and Reflect • How do our current practices in mathematics instruction for gifted students align with these expectations? • What questions do these Standards raise?

  14. What Does the Research Say?

  15. Research – Differences • Pace at which they learn • Depth of their understanding • Their interests

  16. Research – Needs • Unable to explain their solution • De-emphasis on right answers • Uneven pattern of development: concepts vs computation • Individual attention AND opportunities to work in groups

  17. Research – What Works • Explain their reasoning orally & in writing • Flexible grouping • Inquiry-based, discovery learning • Open-ended problems • Problems with multiple solutions or multiple paths to a solution • Higher level questioning

  18. Research – What Works Cont’d. • Differentiated assignments • Activities completed individually & in groups • Use of manipulatives and “hands-on” activities • Analyzing errors • Technology

  19. Research – Curriculum • Consider • Depth • Breadth • Pacing • ALL Students • Reasoning • Real-world Problem Solving • Communication • Connections

  20. Two Specific Examples Open Questions and Parallel Tasks • Provide tasks within each student’s zone of proximal development • Each student has opportunity to make a meaningful contribution • On topic, addressing same standards; level of depth or complexity changes • Common Core: Standards for Mathematical Practice (especially #1 & 3)

  21. Math Experience #1 A problem Replace the boxes with values from 1 to 6 to make each problem true. You can use each number as often as you want. You cannot use 7, 8, 9, or 0.

  22. Reflection • How did you chose your numbers? • Think about your students. • What would their answers tell you about their weaknesses or strengths? • How might you challenge a strong student who picks ‘easy’ numbers? • What supports could you give students who are struggling with this task??

  23. Math Experience #2 • A task - Choose one of the following tasks and use the grid of dots given. • Option 1 – Make as many shapes as you can on the grid with an area of 12. The corners of the shapes must be dots on the grid. • Option 2 – Make as many rectangles as you can on the grid with an area of 12. The corners of the rectangles must be dots on the grid.

  24. Reflection • Which option did you choose? Why? • Think about your students. • What would their choice tell you about their weaknesses or strengths? • How might you challenge your stronger students with this task? • What adaptations or supports could you give students who are struggling with this task??

  25. Key Elements • Big Ideas • The focus of instruction must be on the big ideas being taught so that they are all addressed, no matter at what level. • Choice • There must be some aspect of choice for the student, whether in content, process, or product. • Pre-assessment • Prior assessment is essential to determine what needs different students have. Small, Marian. Great Ways to Differentiate Mathematics Instruction. Teachers College Press. 2009

  26. Open Questions • Mathematically meaningful • Variety of responses and approaches possible • Richer mathematical conversations • All students can participate • Build mathematical reasoning, communication, and confidence

  27. Creating Open Questions • Convert conventional questions to open questions by: • Turning around a question • Asking for similarities and differences • Replacing a number with a blank • Asking for a number sentence • Changing the question

  28. Parallel Tasks • Sets of two or three tasks • Same ‘big idea’, standards • Close enough in context that they may be discussed simultaneously – questions asked fit both tasks • Lead to discussion of important underlying mathematical ideas

  29. Creating Parallel Tasks • Identify the big idea and standards • Identify developmental differences • Develop similar contexts and common follow up questions • Can use a task readily available and alter it for a different development level (up or down)

  30. Things to Remember • Deeper learning is important • Open questions must allow for correct responses at a variety of levels • Parallel tasks allow struggling students to succeed and challenge proficient students • Both should be constructed so all students can participate in follow up discussions

  31. Other Simple Possibilities • Give students problems with errors in the solution. Students need to find error, correct it and explain why the error occurred. • Require students to find more than one solution to a problem.

  32. Resources for Math • NCTM Illuminations • http://illuminations.nctm.org/ • Inside Mathematics • http://insidemathematics.org/ • NRICH • http://nrich.maths.org/public/ • HoodaMath • http://www.hoodamath.com/

  33. Resources for Math • CLIU Content Networking Groups Wiki • http://cliu21cng.wikispaces.com/ • Print Resources • Van De Walle, John A., Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams. Teaching Student-centered Mathematics. Second ed. Vol. I, II & III. New York: Pearson. • Small, Marian. Good Questions: Great Ways to Differentiate Mathematics Instruction. New York: Teachers College, 2009. Print.

  34. Thank you! Cathy Enders Carbon Lehigh Intermediate Unit #21 Curriculum & Instruction/Educational Technologies Department endersc@cliu.org

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