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James R. Stone III Director James.Stone@Louisville.edu

Making Math Work: Building Academic Skills in Context. James R. Stone III Director James.Stone@Louisville.edu. Reminder-The issue 12 th Grade Math Scores 2005. A cautionary note. 94% of workers reported using math on the job, but, only 1 22% reported math “higher” than basic

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James R. Stone III Director James.Stone@Louisville.edu

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  1. Making Math Work: Building Academic Skills in Context James R. Stone III Director James.Stone@Louisville.edu

  2. Reminder-The issue12thGrade Math Scores 2005

  3. A cautionary note • 94% of workers reported using math on the job, but, only1 • 22% reported math “higher” than basic • 19% reported using “Algebra 1” • 9% reported using “Algebra 2” • Among upper level white collar workers1 • 30% reported using math up to Algebra 1 • 14% reported using math up to Algebra 2 • Less than 5% of workers make extensive use of Algebra 2, Trigonometry, Calculus, or Geometry on the job2 • M. J. Handel survey of 2300 employees cited in “What Kind of Math Matters” Education Week, June 12 2007 • Carnevale & Desrochers cited in “What Kind of Math Matters” Education Week, June 12 2007

  4. Taking more math is no guarantee • 43% of ACT-tested Class of 20051 who earned A or B grades in Algebra II did not meet ACT College Readiness Benchmarks in math (75% chance of earning a C or better; 50% chance of earning a B or better in college math) • 25% who took more than 3 years of math did not meet Benchmarks in math (NOTE: these data are only for those who took the ACT tests) ACT, Inc. (2007) Rigor at Risk.

  5. 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 technical skill development. Math-in-CTE 1. What we did 2. What we found 3. What we learned

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

  7. 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?

  8. Study Design 04-05 School Year Sample 2004-05: 69 Experimental CTE/Math teams and 80 Control CTE Teachers Total sample: 3,000 students*

  9. Participants Experimental CTE teacher Math teacher Control CTE teacher Liaison Primary Role Implement the math enhancements Provide support for the CTE teacher Teach their regular curriculum Administer surveys and tests Study Design: Participants

  10. Study Design: Key Features • Random assignment of teachers to experimental or control condition • Five simultaneous study replications • Three measures of math skills (applied, traditional, college placement) • Focus of the experimental intervention was naturally occurring math (embedded in curriculum) • A model of Curriculum Integration • Monitoring 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. The Experimental Treatment • Professional Development • The Pedagogy

  13. Professional Development • CTE-Math Teacher Teams; occupational focus • Curriculum mapping • Scope and Sequence • On going collaboration CTE and math teachers

  14. What we found: Map of Math Concepts Addressed by Enhanced Lessons by SLMP

  15. Developing the Pedagogy: Curriculum Maps • Begin with CTE Content • Look for places where math is part of the CTE content • Create “map” for the school year • Align map with planned curriculum for the year (scope & sequence)

  16. Sample Curriculum Map

  17. Sample Curriculum Map

  18. 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

  19. Ohm’s Law in Automotive Class

  20. Auto Tech – Electrical (partial)

  21. Element 1:Introduce the Automotive lesson • A student brought this problem to class: • He has installed super driving lights on a 12 volt system. His 15 amp fuse keeps blowing out. He has 0.4 Ohms of resistance.

  22. Element 2:Find out what students know: • Discuss what they know about voltage, amperes, and resistance. Volt is a unit of electromotive force (E) Ampere is a unit of electrical current (I) Ohm is the unit of electrical resistance (R)

  23. Element 2:Find out what students know: • What is an Ohm? • Where did the name come from? • Georg Ohm was a German physicist. In 1827 he defined the fundamental relationship between voltage, current, and resistance. • Ohm’s Law: E = I R

  24. Element 3:Work through the embedded problem: • The student has installed super driving lights on a 12 volt system. His 15 amp fuse keeps blowing. He has 0.4 Ohms of resistance.

  25. Element 3:Work through the embedded problem: • Continue bridging the automotive and math vocabulary. • The basic formula is: E = I R We know E (volts) and R (resistance). We need to find I(amps).

  26. Element 3:Work through the embedded problem: • We need to isolate the variable. • We do that by dividing IR by R, which leaves Iby itself. • What you do to one side of the equation you must do to the other...therefore E is also divided by R. I = E / R

  27. Element 3:Work through the embedded problem: I = E / R I = 12 / 0.4 I = 30 amps • The student needs a 30 amp fuse to handle the lights.

  28. Element 4:Work through related, contextual examples • A 1998 Ford F-150 needs 180 starting amps to crank the engine. What is the resistance if the voltage is 12v? R = E / I R = 12 / 180 R = .066... Ohms

  29. Element 4:Work through related, contextual examples • If the resistance in the rear tail light is 1.8 Ohms and the voltage equals 12v, what is the amperage? I = E / R I = 12 / 1.8 I = 6.66 amps

  30. Element 4:Work through related, contextual examples A 100-amp alternator has 0.12 Ohms of resistance. What must the voltage equal? E = I R E = 100(0.12) E = 12 volts

  31. Element 5:Work through traditional math examples • The formula for area of a rectangle is A = LW where A is the area, L is the length and W is the width. • Find the area of a rectangle that has a length of 8 ft. and an area of 120 sq. ft. A / L = W 120 sq ft / 8 ft = W 15ft = W

  32. Element 5:Work through traditional math examples • The formula for distance is D = RT where D is the distance, R is the rate of speed in mph and T is the time in hours. • If a car is traveling at an average speed of 55 mph and you travel 385 miles, how long did the trip take? D = RT T = D / R T = 385 / 55 mph T = 7 hours

  33. Element 6:Students demonstrate understanding • Students now given opportunities to work on similar problems using this concept: Homework Team/group work Project work

  34. Element 6:Students demonstrate understanding • A vehicle with a 12 volt system and a 100 amp alternator has the following circuits: 30 amp a/c heater 30 amp power window/seat 15 amp exterior lighting 10 amp radio 7.5 amp interior lighting 1. Find the total resistance of the entire electrical system based on the above information. 2. Find the unused amperage if all of the above circuits are active.

  35. Element 7:Formal Assessment • Include math questions in formal assessments... both embedded problems and traditional problems that emphasize the importance of math to automotive technology.

  36. 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

  37. Analysis Pre Test Fall Terra Nova Difference in Math Achievement Post Test Spring Terra Nova Accuplacer WorkKeys Skills Tests X C

  38. What we found: All CTExvs All CTEcPost test % correct controlling for pre-test p= .08 p= .03 p= .02 *Controlling for pre-test measures of math ability

  39. Magnitude of Treatment Effect – Effect Size Accuplacer Terra Nova the average percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant 50thpercentile X Group C Group 71st 0 50th 100th 67th Carnegie Learning Corporation Cognitive Tutor Algebra I d=.22

  40. What we found: 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%

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

  42. Affect Technical Skill Development? NO! Does Enhancing Math in CTE

  43. 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

  44. Final thoughts: Math-in-CTE • A powerful, evidence based strategy for improving math skills of students; • A way but not THE way to help high school students master math (other approaches – NY BOCES) • Not a substitute for traditional math courses • Lab for mastering what many students learn but don’t understand • Will not fix all your math problems

  45. James.stone@louisville.edu www.nccte.org

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