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James R. Stone III

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Title: James R. Stone III


1

Making Math Work Building Academic Skills in
Context
  • James R. Stone III
  • Director
  • James.Stone_at_Louisville.edu

2
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
3
Reminder-The issue12th Grade Math Scores 2005
4
(No Transcript)
5
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

6
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.
7
Why Focus on CTE
  • CTE provides a math-rich context
  • CTE curriculum/pedagogies do not systematically
    emphasize math skill development

8
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?

9
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

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
Study Design 04-05 School Year
Sample 2004-05 69 Experimental CTE/Math teams
and 80 Control CTE Teachers Total sample
3,000 students
12
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

13
The Experimental Treatment
  • Professional Development
  • The Pedagogy

14
Professional Development
  • CTE-Math Teacher Teams occupational focus
  • Curriculum mapping
  • Scope and Sequence
  • On going collaboration CTE and math teachers

15
(No Transcript)
16
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)

17
Sample Curriculum Map
18
Sample Curriculum Map
19
What we found Map of Math Concepts Addressed by
Enhanced Lessons by SLMP
20
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

21
Ohms Law in Automotive Class
22
Auto Tech Electrical (partial)
23
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.

24
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)

25
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

26
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.

27
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).

28
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

29
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.

30
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

31
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

32
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

33
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

34
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

35
Element 6Students demonstrate understanding
  • Students now given opportunities to work on
    similar problems using this concept
  • Homework
  • Team/group work
  • Project work

36
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.

37
Element 7Formal Assessment
  • Include math questions in formal assessments...
    both embedded problems and traditional problems
    that emphasize the importance of math to
    automotive technology.

38
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

39
Analysis
Pre Test Fall Terra Nova
Difference in Math Achievement
X
Post Test Spring Terra Nova Accuplacer WorkKeys
Skills Tests
C
40
What we found All CTEx vs All CTEcPost test
correct controlling for pre-test
41
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
42
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

43
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


44
Power of the New Professional Development Model
Old Model PD
Total Surprise!
New Model PD
45
Does Enhancing Math in CTE
  • Affect Technical Skill Development?

NO!
46
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

47
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?

48
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

49
Technical Assistance
  • Replicating the Math-in-CTE approach in your state

50
Technical Assistance
  • Replicating the Math-in-CTE approach in your state

51
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

52
Staffing the Technical Assistance
53
www.nccte.org
  • James.stone_at_nrccte.org
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