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

3.  94% of workers reported using math on the job, but, only 1  22% reported math “higher” than basic  19% reported using “Algebra 1”  9% reported using “Algebra 2”  Among upper level white collar workers 1  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 job 2 1.M. J. Handel survey of 2300 employees cited in “What Kind of Math Matters” Education Week, June 12 2007 2.Carnevale & Desrochers cited in “What Kind of Math Matters” Education Week, June 12 2007

4.  43% of ACT-tested Class of 2005 1 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. 1. What we did 2.What we found 3.What we learned

6.  CTE provides a math-rich context  CTE curriculum/pedagogies do not systematically emphasize math skill development

7.  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. National Research Center AutoTech Experimental Control BusEd Experimental Control IT Experimental Control Ag P&T Experimental Control Health Experimental Control Sample 2004-05:69 Experimental CTE/Math teams and 80 Control CTE Teachers Total sample: 3,000 students* Study Design 04-05 School Year

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

10.  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

12.  Professional Development  The Pedagogy

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

15. Math Concept Number of Corresponding CTE Math Lessons Addressing the Math Concept Site A Site B Site C Site D Site E Number and Number Relations 84410 2 Computation and Numerical Estimation 87612 Operation Concepts00100 Measurement 573 0 12 Geometry and Spatial Sense01002 Data Analysis, Statistics and Probability 1194 1 4 Patterns, Functions, Algebra 7 1 35 2 Trigonometry00002 Problem Solving and Reasoning010 3 0 Communication11000

16.  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)

17. Agricultural Mechanics CurriculumMathematics Content StandardsPASS Standards NCTM Standards Determining sprayer nozzle size given flow rate and speed Problem solving involving cross-sectional area, volume, and related rates PASS Process Standard 1: Problem Solving NCTM Problem Solving Standard for Grades 9-12 Determine pipe size and water flow rates for a water pump Problem solving involving cross-sectional area, volume, and related rates Determine amount of paint needed to paint a given surface (calculate surface area, etc) Problem solving involving surface area, ratio and proportions Determine the concrete reinforcements and spacing needed when building a concrete platform or structure Problem solving involving cross-sectional area, volume, and related rates

18. Health Standards Identification Health SkillMathematics Content Standards Michigan Content Standard Analyze methods for the control of disease. Prognosis and diagnosis Body planes Range of motion Pharmacy calculations (for pharmacy techs Solve linear equations Read and interpret graphs and charts Problem solving involving statistical data Ratio and Proportion 1.2 Students describe the relationships among variables, predict what will happen to one variable as another variable is changed, analyze natural variation and sources of variability to compare patterns of change. Analyze changes in body systems as they relate to disease, disorder and wellness Cultures and sensitivity Lab techniques Blood sugar and user failure versus accurate sample collection C & S of wounds, collection contamination process and outcome Calculate time, temperature, mass measurement and compare to known standards Interpretation of measurement results Calculate accurate measurement in both metric and English units 2.3 Students compare attributes of two objects or of one object with a standard (unit) and analyze situations to determine what measurement(s) should be made and to what level of precision

19. 1.Introduce the CTE lesson 2.Assess students’ math awareness 3.Work through the embedded example 4.Work through related, contextual examples 5.Work through traditional math examples 6.Students demonstrate understanding 7.Formal assessment

21. Lesson TopicCTE ConceptsMath Concepts NCTM Standards Voltage, Current, Resistance and Ohm’s Law Whole numbers; decimals and fractions (adding, subtracting, multiplying and dividing); solving linear equations; ratio proportion; system of equations; metric to metric conversions; metric prefixes; reading and writing percents N8, N9, A2, M0, M1, P15, P16 Series and Parallel Circuits Decimals and fractions (adding, subtracting, multiplying and dividing); solving linear equations; ratio proportion; system of equations; metric to metric conversions; substituting data into formulas; working with reciprocals N8, N9, A7, A8, A9, A11, P2, P15 Electrical Components Solving linear equations; percents; temperature; comparing numbers; linear measurement N8, N9, A2, M0, M1, P2, P15

22.  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.

23.  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 )

24.  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

25.  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.

26.  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).

27.  We need to isolate the variable.  We do that by dividing IR by R, which leaves I by 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

28. I = 12 / 0.4 I = 30 amps  The student needs a 30 amp fuse to handle the lights.

29.  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

30.  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

31. 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

32.  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

33.  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

34.  Students now given opportunities to work on similar problems using this concept: Homework Team/group work Project work

35.  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.

36.  Include math questions in formal assessments... both embedded problems and traditional problems that emphasize the importance of math to automotive technology.

37. 1.Introduce the CTE lesson 2.Assess students’ math awareness 3.Work through the embedded example 4.Work through related, contextual examples 5.Work through traditional math examples 6.Students demonstrate understanding 7.Formal assessment

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

39. *Controlling for pre-test measures of math ability p=.03 p=.02 p=.08

40. 50th percentile 71st C Group 050th100th X Group Terra Nova the average percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant Accuplacer 67th Carnegie Learning Corporation Cognitive Tutor Algebra I d=.22

41.  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%

42. Old Model PD New Model PD Total Surprise!

43. Affect Technical Skill Development? NO!

44. A. Develop and sustain a community of practice B. Begin with the CTE curriculum and not with the math curriculum C. Understand math as essential workplace skill D. Maximize the math in CTE curricula E. CTE teachers are teachers of “math-in-CTE” NOT math teachers

45.  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

46. James.stone@louisville.edu