James R. Stone III

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Making Math Work Building Academic Skills in
Context

• James R. Stone III
• Director
• James.Stone_at_Louisville.edu

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Math-in-CTE

• 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
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Reminder-The issue12th Grade Math Scores 2005
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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

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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.
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Why Focus on CTE

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

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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?

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Study Design Participants

• Participants
• Experimental CTE teacher
• Math teacher
• Control CTE teacher

• Primary Role
• Implement the math enhancements
• Provide support for the CTE teacher
• Teach their regular curriculum

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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

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Study Design 04-05 School Year
Sample 2004-05 69 Experimental CTE/Math teams
and 80 Control CTE Teachers Total sample
3,000 students
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Measuring Math Technical Skill Achievement

• Global math assessments
• Technical skill or occupational knowledge
  assessment

• General, grade level tests (Terra Nova,
  AccuPlacer, WorkKeys)
• NOCTI, AYES, MarkED

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The Experimental Treatment

• Professional Development
• The Pedagogy

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Professional Development

• CTE-Math Teacher Teams occupational focus
• Curriculum mapping
• Scope and Sequence
• On going collaboration CTE and math teachers

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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)

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Sample Curriculum Map
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Sample Curriculum Map
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What we found Map of Math Concepts Addressed by
Enhanced Lessons by SLMP
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The Pedagogy

• Introduce the CTE lesson
• Assess students math awareness
• Work through the embedded example
• Work through related, contextual examples
• Work through traditional math examples
• Students demonstrate understanding
• Formal assessment

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Ohms Law in Automotive Class
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Auto Tech Electrical (partial)
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Element 1Introduce 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.

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Element 2Find 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)

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Element 2Find 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.
• Ohms Law E I R

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Element 3Work 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.

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Element 3Work 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).

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Element 3Work through the embedded problem

• 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

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Element 3Work 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.

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Element 4Work 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

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Element 4Work 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

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Element 4Work 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

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Element 5Work 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

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Element 5Work 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

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Element 6Students demonstrate understanding

• Students now given opportunities to work on
  similar problems using this concept
• Homework
• Team/group work
• Project work

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Element 6Students 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.

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Element 7Formal Assessment

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

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The Pedagogy

• Introduce the CTE lesson
• Assess students math awareness
• Work through the embedded example
• Work through related, contextual examples
• Work through traditional math examples
• Students demonstrate understanding
• Formal assessment

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Analysis
Pre Test Fall Terra Nova
Difference in Math Achievement
X
Post Test Spring Terra Nova Accuplacer WorkKeys
Skills Tests
C
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What we found All CTEx vs All CTEcPost test
correct controlling for pre-test
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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
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Why

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

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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

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Power of the New Professional Development Model
Old Model PD
Total Surprise!
New Model PD
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Does Enhancing Math in CTE

• Affect Technical Skill Development?

NO!
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Replicating the Math-in-CTE ModelCore
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

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Challenges

• Professional development time
• Lack of fit flow of content among classes
• Resistance of some teachers to change
• Must be more than a few integrated
  activities/lesson plans
• Building communities of practice Academy (sub)
  networks?

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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
  dont understand
• Will not fix all your math problems

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Technical Assistance

• Replicating the Math-in-CTE approach in your state

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Technical Assistance

• Replicating the Math-in-CTE approach in your state

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Necessary Ingredients for Replication

• 1. Communities of practice
• A. 10 CTE-Math Teacher teams or 20-20
• B. Specific occupational foci
• C. Invite not compel
• 2. Administrator support
• A. Professional Development (532) for at
• least one full year
• B. PD support (facilities, substitutes, etc.)
• D. Staff the structure

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Staffing the Technical Assistance
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www.nccte.org

• James.stone_at_nrccte.org