1. LINKING LANGUAGES FOR LEARNING Enhancing Reading and Math through Career and Technical Education Grand Junction CO
James R. Stone III
Director

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. Math-in-CTE Research Team
University of Minnesota
James R. Stone III
Donna Pearson
Corinne Alfeld
Susan Jensen
Gregg Gross
The Ohio State University
Morgan Lewis
Colorado
Linda Harrison
Sherrie Schneider
Penn State University
Mary Kisner Barbara Senapedis
Oklahoma State University
Craig Edwards
Brian Parr
Brent Young
Michigan
Mary Fudge
Kathleen Szuminski

4. What do we know about CTE?
There is evidence that:
CTE does not limit postsecondary education
Math and science course taking by CTE students is increasing: amount and complexity
CTE as a function of the HS experience reduces the probability of dropping out of school
CTE is an economic value to the individual and the community (ROI)
It is possible to “major” in CTE and Academics
One conclusion is that A decade of reform (Perkins II & III, STWOA & various state efforts) is beginning to have an effect
but achievement and transition
are the challenges put forth. . .

6. The Problem: Math Performance Of American Youth
NAEP Scores for 17 Year olds

7. The number of 17-year-old students taking advanced math classes has also increased -- with 17 percent studying calculus and 53 percent studying second-year algebra --  it is unclear why that trend has not resulted in higher average math scores over all.

8. Why Focus on CTE - I
Students earn more credits in CTE than in math or science
97% take at least one course
Nearly half earn at least 3 Specific Labor Market (SLMP) credits
One-quarter are
concentrators”
NAVE 2004

9. Why Focus on CTE II
Levesque, K. (2003). Public High School Graduates Who Participated in Vocational/Technical Education

10. Why Focus on CTE - III CTE provides a math-rich context
CTE curriculum/pedagogies do not systematically emphasize math skill development
Spend a little time emphasizing each of these points

11. Alternative CTE Math Improvement Strategies
Related Math class*(e.g., Business math)
Applied Math class* (e.g., Tech Prep math)
Pull out math classes*with math teacher
Math teacher team teaches* in CTE class
The NRCCTC, Math-in-CTE model-a research based approach to improving math skills
*Note: while some of these may improve math skills of students, the evidence is lacking.

12. 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.
Emphasize it is a very simple question and a simple straight forward study

13. 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?

14. 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)
Multi-method: quantitative and qualitative
Focus of the experimental intervention was naturally occurring math (embedded in curriculum)
A model of Curriculum Integration
Intense focus on Fidelity of Treatment

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

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

17. 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

18. Building Academic Skills in Context: Math-in-CTE
The “method” of Math-in-CTE

19. The Experimental Treatment
Professional Development
The Pedagogy

20. Math-in-CTE The Method
Curriculum mapping
Enhancing the math – The Pedagogy

21. 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)

22. CTE Unit CTE Concepts Math Concepts Bus/Mkt: Distribution
Control Inventory: order, receive, count, maintain
Ratio/Percentages
Graphing/Predictions
Algebraic Expressions
Equations
Manufacturing Tech: Measurement
Measure items for production
Number Sense
Fractions
Decimals
Angles

23. Agricultural Mechanics Curriculum Mathematics Content Standards
Sample Curriculum Map
Agricultural Mechanics Curriculum
Mathematics Content Standards
PASS 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
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

24. Scope & Sequence WEEK 1 Aug. 17 Marketing and DECA Orientation NA
TIME
CTE CONCEPT
MATH CONCEPT
MATH-IN-CTE
LESSON
MATH
STANDARD
PARTNER
MEETING
DATE
WEEK 1
Aug. 17
Marketing and
DECA Orientation NA
WEEK 2
Aug. 23
General Overview of
the Math-in-CTE
Project
WEEK 3
Aug. 30
(Officer
Elections)
Sales Unit
Introduction to the 7
Math Concepts
Consent Forms, Student
Survey, and Math Pre
Test
Sept. 2
WEEK 4
Sept. 7
(TSLP begins)
Ratio/Percentages
#1 – To Market, To
Market; Lesson #25
Standards 1, 6
Sept. 9
WEEK 5
Sept. 13
Graphing/
Predictions
Algebraic Expressions
& Equations, Pattern
Recognition,
Functions, Data
Representation
#4 - What Product to Sell
Standards 1, 2, 3, 5, 6
Sept. 16

25. Building the Enhanced CTE Lesson

26. 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

27. Professional Development
CTE-Math Teacher Teams; occupational focus
Curriculum mapping – derived from the workplace
Scope and Sequence
CTE and math teachers professional development
On going collaboration CTE and math teachers

28. What did we find?
What did we learn?

29. Map of Math Concepts Addressed by Enhanced Lessons in each SLMP
Number of Corresponding CTE Math Lessons Addressing the Math Concept
Site A
Site B
Site C
Site D
Site E
Number and Number Relations 8 4 10 2
Computation and Numerical Estimation 7 6 12
Operation Concepts 1
Measurement 5 3
Geometry and Spatial Sense
Data Analysis, Statistics and Probability 11 9
Patterns, Functions, Algebra
Trigonometry
Problem Solving and Reasoning
Communication

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

31. What we found: Difference in % correct – All Experimental & All Control
NOTE: Compared to the semester length test, we have “hits” on Accuplacer AND TerraNOVA. Also explain that this is the level of randomization = a random assignment test
p<.05
*Controlling for pre-test measures of math ability

32. Comparing Experimental Classrooms to Control Classrooms by Replication Site*
NOTE: the apparent small effects for site A are a function of the large pre-test difference favoring the control classes. No tests were significant in site C at the classroom level.
*Only Significant effects shown

33. Comparing Experimental Students to Control Students by Replication Site*
NOTE: Controlling only for pre-test scores. Students in enhanced classes significantly outperformed their counterparts in one or more tests in each of the test sites.

34. Magnitude of Treatment Effect – Effect Size
Cohen’s d = .80
the average percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant
50th percentile
X Group
C Group
79th percentile
50th
100th

35. Effect Size Obtained: Classroom Analysis
Effect size (Cohen’s d)
All Classes
Terra Nova (d=.28)
Accuplacer (d=.11)
By Site
Site V –WorkKeys (d=.20)
Site W-AccuPlacer (d=.54)
Site X –Terra Nova (d=.43)
Site Y-Terra Nova (d=.87)
Site Z – AccuPlacer (d=.18)
-TerraNova (d=.45)
Carnegie Learning Corporation Cognitive Tutor Algebra I
Percentile Shift
From 50th to:
62nd
56th
58th
71st
67th
82nd
68th
d= .22

36. Math Ability Effect: Test Score Differences
Evidence of the “Matthew Effect” – Higher Ability Students Gained more than Lower Ability Students with this Approach BUT both gained more than the Control Students

37. Does Enhancing Math in CTE
Affect Technical Skill Development?

38. *
No difference in four sites; experimental students scored significantly higher in one site
*p<.10

39. Time invested in Math Enhancements
Average of 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%
Average total school time investment (assume 6 classes per day) = 1.7%
Modest investment for major payoff

40. What we learned When We Began the Study A box of curriculum
Teacher training
Replicable by individual teachers
As a Result of the Study
A curriculum development process
Building and sustaining a community of practice
Replicable by teams of committed teachers working together over time
Core Principles

41. 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

42. What we are and are not: A contextual continuum
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
Disconnected
Coordinated
Context Based
Contextual
Algebra 1
Academies
Integrated math
NRC Model

43. Issues
How much math can be enhanced in CTE before it is no longer a CTE class? (The “tipping” point issue)
Crisis Immediacy – we want a fix and we want it now
System investment (teacher time and PD costs)
Should math credit be provided for enhanced CTE classes – are we teaching math or providing a venue for students to learn how to use math?
1. Highly qualified teacher
2. Loss of CTE integrity
What are the barriers in moving this model to pre-service education?

44. Conclusion: The NRC Model
(Process)(Pedagogy)=Mathachievement
Core Principles

45. Bringing Math-in-CTE to your Community
Communities of practice
A. 10+ CTE-Math Teacher teams
B. Specific occupational foci
B. Regional or state
C. Invite not compel
2. Administrator support
A. Professional Development – (5:3:2) – for at least one full year
B. Substitutes
C. PD support (facilities, etc.)
D. Staff the structure
3. Document!!!
4. Support structure