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Making Math Work

Making Math Work. A Pedagogic and Professional Development Strategy for Success. Dr Sherrie Schneider Mary Fudge. Disclaimer:.

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Making Math Work

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  1. Making Math Work A Pedagogic and Professional Development Strategy for Success Dr Sherrie Schneider Mary Fudge

  2. Disclaimer: The work reported herein was supported under the National Dissemination for Career and Technical Education, PR/Award (No. VO51A990004) and /or under the National Research Center for Career and Technical Education, PR/Award (No. VO51A990006) as administered by the Office of Vocational and Adult Education, U. S. Department of Education.However, the contents do not necessarily represent the positions or policies of the Office of Vocational and Adult Education or the U. S. Department of Education, and you should not assume endorsement by the Federal Government.

  3. CTE: What do we know? • CTE keeps kids in school • CTE helps kids focus their PS education plans • CTE is an economic benefit to participants and to states • CTE-based structures (e.g.,dual enrollment, career academies) can affect achievement and transition of youth to college and work. • But what more value can CTE provide as part of the high school experience?

  4. Perkins IV requires . . . • Develop challenging academic and technical standards and related challenging, integrated instruction

  5. Here is the Problem: Math Performance of American Youth NAEP Scores for 17 Year olds

  6. Despite the fact, students are taking more math and science

  7. Why Focus on CTE • CTE provides a math-rich context • CTE curriculum/pedagogies do not systematically emphasize math skill development

  8. The Math-in-CTE Study A study to test the possibility that enhancing the embedded mathematics in Technical Education coursework will build skills in this critical academic area without reducing technicalskill development.

  9. Key Questions of the Study • Does enhancing the CTE curriculum with math increase math skills of CTE students? • Can we infuse enough math into CTE curricula to meaningfully enhance the academic skills of CTE participants (Perkins III Core Indicator) • . . . Without reducing technical skill development • What works?

  10. Study Design • Random assignment of teachers to experimental or control condition • Five simultaneous study replications • Three measures of math skills (applied, traditional, college placement) • Multi-method: quantitative and qualitative • Focused on naturally occurring math (embedded in curriculum) • Test a model of Curriculum Integration • Intense focus on Fidelity of Treatment

  11. Global math assessments Technical skill or occupational knowledge assessment General, grade level tests (Terra Nova, AccuPlacer, WorkKeys) NOCTI, AYES, MarkED Measuring Math & Technical Skill Achievement

  12. 1. Professional Development Summer PD (5 days) – Mapping and lesson creation Late fall PD (2-3 days) - Lesson creation Early Spring PD (2-3 days) – Lesson creation On-going direct and indirect math support 2. The Math Enhancement Process (The 7 Element Pedagogic Model) What we tested:

  13. Map of Math Concepts Addressed by Enhanced Lessons in each SLMP

  14. Time invested in Math Enhancements • Average of 18.55 hours across all sites devoted to math enhanced lessons (not just math but math in the context of CTE) • Assume a 180 days in a school year; one hour per class per day • Average CTE class time investment = 10.3%

  15. Why • Ebbinghaus effect – refreshing or relearning previously learned material • Vocabulary effect – math as a foreign language • Spillover effect – math skills developed in one area improve performance in others

  16. Replicating the Math-in-CTE Model:Core Principles • Develop and sustain a community of practice • Begin with the CTE curriculum and not with the math curriculum • Understand math as essential workplace skill • Maximize the math in CTE curricula • CTE teachers are teachers of “math- in-CTE” NOT math teachers

  17. Old Model A box of curriculum Short term “training” Little or no support after the “sage on the stage” goes away Replicable by individual teachers (assumed) New Model Process not an event Built on communities of practice On-going support – the learning curve Requires teams of committed teachers working together over time The Professional Development Paradigm in Practice

  18. Power of the New Professional Development Paradigm Old Model PD Total Surprise! New Model PD

  19. Disconnected Coordinated Context Based Contextual Algebra 1 Academies Integrated math NRC Model Math-in-CTE in Context • Traditional academic class (e.g. Algebra 1) • CTE & Academic teachers coordinate around themes (e.g. ‘health’) • Occupation is the context for delivery of traditional academics (Related or applied math) • Academics emerge from occupational content

  20. Remaining Issues • Class impact vs. program impact • Tipping point (how much math) • Other academic areas (e.g., science, literacy) • Pre-service options • Potential impact of other approaches (e.g., context based)

  21. Study Design 04-05 School Year Sample 2004-05: 57 Experimental CTE/Math teams and 74 Control CTE Teachers Total sample: 3,000 students*

  22. The Research Design The Experimental Treatment X X Difference Difference C C On-going fidelity of treatment measures

  23. * No difference in four sites; experimental students scored significantly higher in one site. *p<.10

  24. What we found: All CTEx vs All CTEcPost test % correct controlling for pre-test p= .02 p= .03 p=ns

  25. Percentile “Shift” From 50th to: 71st 67th 99th 76th 81st 74th 66th What we found: Magnitude of effect Effect size (Cohen’s d) All Classes Terra Nova (d=.55) Accuplacer (d=.42) By Site Site A –WorkKeys (d=2.8) Site B- TerraNova (d=.69) Site C –Accuplacer (d=.85) Site E- Terra Nova (d=.64) Site F – AccuPlacer (d=.39) Carnegie Learning Corporation Cognitive Tutor Algebra I d= .22

  26. Use of Method/Lessons in School Year Following Study

  27. Math-in-CTE Model Professional Development Sessions • Curriculum mapping (math/CTE nexus) • Scope & sequence (map the year) • Development of math-enhanced lessons • On-going math support Teaching the Lessons

  28. The Seven Elementsof a Math-Enhanced Lesson • Introduce the CTE lesson • Assess students’ math awareness • Work through the embeddedexample • Work through related,contextual examples • Work through traditional math examples • Students demonstrate understanding • Formal assessment

  29. Curriculum Mapping Mary Fudge

  30. Curriculum Maps • Begin with CTE Content • Look for places where math is part of the CTE content (V-Tecs, AYES, MarkED, state guides, last year’s maps) • Create “map” for the school year • Align map with planned curriculum for the year (scope & sequence)

  31. CURRICULUM MAPPING

  32. CURRICULUM MAPPING

  33. Sample Curriculum Map

  34. Sample Curriculum Map

  35. Curriculum MappingExercise Curiculum Map Template.pdf

  36. The Pedagogy Mary Fudge

  37. The Pedagogy • The “seven elements” provide the pedagogic framework for creating and teaching math-enhanced lessons.

  38. The Pedagogy • Introduce the CTE lesson • Assess students’ math awareness • Work through the embeddedexample • Work through related,contextual examples • Work through traditional math examples • Students demonstrate understanding • Formal assessment

  39. Element 1: Introduce the CTE lesson • Explain the CTE lesson. • Identify, discuss, point out, pull out the math embedded in the CTE lesson.

  40. Element 2: Assess students’ math awareness • Begin “bridging” between the CTE and math. • Introduce math vocabulary through the math embedded in the CTE. • Use methods and techniques to assess the whole class.

  41. Element 3: Work through the math example embeddedin the CTE lesson • Work through the steps or processes of the embeddedmath example. • Continue to bridge the CTE and math vocabulary.

  42. Element 4: Work through related, contextual math-in-CTE examples Using the same embedded math concept: • Work through similar problems in the same occupational context. • Use examples of varying levels of difficulty; order from basic to advanced. • Continue to bridge CTE and math vocabulary. • Check for understanding.

  43. Element 5: Work through traditional math examples Using the same embedded math concept: • Work from applied to abstract problems. • Work through examples as they may appear on standardized tests. • Move from basic to advanced problems. • Continue to bridge CTE-math vocabulary. • Check for understanding.

  44. Element 6: Students demonstrate understanding • Provide students with opportunities to demonstrate their understanding of the math concepts embedded in the CTE. • Connect the math back to CTE context. • Conclude the lesson with CTE.

  45. Element 7: Formal Assessment • Include math questions in formal assessments, for example: • CTE unit exams • CTE project assessments

  46. Some Final Thoughts… 1 math concept ≠ 1 lesson ≠ 1 class period Lessons can address one or more concepts and/or last longer than one class period.

  47. PEDAGOGY:The “Seven Elements” in brief • Introduce the CTE lesson • Assess students’ math awareness • Work through embedded example • Work through related,contextual example • Work through traditional example • Students demonstrate understanding • Formal assessment

  48. Math in CTE Health Lesson Alices Areas Health Lesson

  49. Making It All Work:The Math-in-CTE ModelFinal Thoughts

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