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David Stevens, Ed.D.

How Math Learning Difficulties Develop. David Stevens, Ed.D. Developmental Psychologist. 01 Developmental Readiness. Some students arrive in kindergarten and first grade without having the necessary foundation for math instruction. Robbie Case & Sharon Griffin. Number Knowledge Test.

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David Stevens, Ed.D.

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  1. How Math Learning Difficulties Develop David Stevens, Ed.D. Developmental Psychologist

  2. 01 Developmental Readiness Some students arrive in kindergarten and first grade without having the necessary foundation for math instruction. Robbie Case & Sharon Griffin

  3. Number Knowledge Test Have a candy. Here are 2 more. How many do you have? Which pile has more? (Show two piles of chips) How many triangles are there? (Show mixed array) If you had 4 candies and received 3 more, how many would you have? What comes two numbers after 7? Which number is bigger/smaller? (Show twoarabicdigits) Robbie Case & Sharon Griffin

  4. 02 Mile Wide Inch Thick The large number of required topics does not allow some students the time they need to understand foundational concepts. Schmidt, McKnight, & Raizen 1997

  5. Number of Topics per Grade Grade Center for Research in Math & Science Education, Michigan State University

  6. Grade 4 International Test Question “There are 600 balls in a box, and 1/3 of the balls are red. How many red balls are in the box?” Percent Correct Center for Research in Math & Science Education, Michigan State University

  7. 03 Teacher Training Programs Teacher training programs traditionally emphasize Language Arts instruction.

  8. Colleges Providing Sufficient Training www.nctq.org

  9. 04 Memorization over Understanding Some students move forward in the early grades only by using counting and memorization strategies.

  10. How Many cookies? Which is larger 8 or 9? 5 + 3 = ? 4 x 6 = ? 328 + 486

  11. 2 + 3 = ? 3 + 2 = ? 2 + ? = 5 5 = 3 + ? 5 - 3 = ? 5 - 2 =?

  12. 05 Curriculum Becomes More Complex As the curriculum becomes more complex the counting and memorization strategies are not effective.

  13. The whole is divided The parts are of equal size There are a specific number of parts The parts equal the whole

  14. The complexity of fractions make it more likely that students will forget that fractions represent quantities. This leads to memorization without understanding: “Find the common denominator, then add” “Flip it and multiply” “The bigger the denominator the smaller the fraction”

  15. 06 Outcomes Many Students are not developing the foundation they need for long-term success in mathematics.

  16. Grade 8 Passing Rate National Center for Educational Statistics -- 2009

  17. 07 Solutions Recent research documents recognize these problems and agree on proven solutions.

  18. Changing Course “Teachers face long lists of learning expectations to address at each grade level, with many topics repeating from year to year. Lacking clear, consistent priorities and focus, teachers stretch to find the time to present important mathematical topics effectively and in depth.” www.nctm.org/focalpoints

  19. NCTM Now Recommends Instruction should devote “the vast majority of attention” to the most significant mathematical concepts. Focus on developing problem solving, reasoning, and critical thinking skills. Develop deep understanding, mathematical fluency, and an ability to generalize. www.nctm.org/focalpoints

  20. National Math Panel Report “The manner in which math is taught in the U.S. is "broken and must be fixed." www2.ed.gov/about/bdscomm/list/mathpanel/reports.html

  21. National Math Panel Recommendations Math curricula should: Be "streamlined and should emphasize a well-defined set of the most critical topics in the early grades." Emphasize "the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic recall of facts." Teach with "adequate depth." Have an "effective, logical progression from earlier, less sophisticated topics into later, more sophisticated ones." Have teachers regularly use formative assessment. www2.ed.gov/about/bdscomm/list/mathpanel/reports.html

  22. Screen all students and provide interventions to students identified as at-risk. Instructional materials for students should focus intensely on in-depth treatment of whole numbers. Instruction during the intervention should be explicit and systematic. Include instruction on solving word problems that is based on common underlying structures. Students should work with visual representations. Devote ten minutes in each session to fluent retrieval of basic arithmetic facts. Monitor student progress. Include motivational strategies. ies.ed.gov

  23. For over a decade, research studies of mathematics education in high performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.” These Standards are a substantial answer to that challenge. www.corestandards.org

  24. Kindergarten Standards www.corestandards.org

  25. The Best Practices 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Streamlinethe curriculum to emphasize the big ideas of mathematics. Individualizelearning experiences to each student’s developmental level. Adaptto the learning style of each student. Bridgefrom the concrete to the abstract. Provideconcrete feedback and levels of scaffolding to provoke thinking. Develop knowledge of concepts AND math facts. Promotecognitive flexibility and problem solving. Drawon intrinsically motivating aspects of mathematics to inspire learning. Teachfor mastery. Introduceconcepts at the simple level and build to the complex level. Helpstudents make connections between concepts. Guideinstruction with formative assessment.

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