LINKING LANGUAGES FOR
LEARNING
Enhancing Reading and Math
through Career and Technical
Education
Grand Junction CO
James R. Stone III
Director
[email protected]
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.
Math-in-CTE Research
Team
University of Minnesota
The Ohio State University
James R. Stone III
Morgan Lewis
Penn State University
Mary Kisner
Barbara Senapedis
Colorado
Donna Pearson
Linda
Harrison
Corinne Alfeld
Sherrie
Schneider
Gregg Gross
Susan Jensen
Michigan
Oklahoma State
University
Mary Fudge
Craig Edwards
Kathleen
Szuminski
Brian Parr
Brent Young
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. . .
The Problem: Math Performance
Of American Youth
NAEP Scores for 17 Year olds
304
300
299
302
305 307 306 307
308
307
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
04
350
330
310
290
270
250
230
210
190
170
150
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.
http://nces.ed.gov/nationsreportcard/ltt/results2004/
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
Why Focus on CTE II
Characteristics of Students Enrolled in 3 or more SLMP Courses .
90
80
70
60
50
40
30
20
10
0
Native
American
Black (nonHispanic)
Hispanic
Has Disability
Limited
English
Proficiency
Levesque, K. (2003). Public High School Graduates Who Participated in Vocational/Technical Education
GPA less than
2.0
More than
50% FRL
Why Focus on CTE III
• CTE provides a math-rich context
• CTE curriculum/pedagogies do not
systematically emphasize math skill
development
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.
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.
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?
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
Study Design 0405 School Year
AutoTech
National Research Center
BusEd
Ag P&T
IT
Health
Experimental
Experimental
Experimental
Experimental
Experimental
Control
Control
Control
Control
Control
Sample 2004-05:
69 Experimental CTE/Math teams and 80 Control CTE Teachers
Total sample: 3,000 students*
Study Design: Participants
Participant
• 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
Measuring Math & Technical
Skill Achievement
• Global math
assessments
• General, grade
level tests (Terra
Nova, AccuPlacer,
WorkKeys)
• Technical skill • NOCTI, AYES,
or
MarkED
occupational
knowledge
assessment
Building Academic Skills in
Context: Math-in-CTE
The “method” of Math-in-CTE
The Experimental
Treatment
• Professional Development
• The Pedagogy
Math-in-CTE
The Method
• Curriculum mapping
• Enhancing the math – The Pedagogy
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)
CTE Unit CTE Concepts Math
Concepts
Bus/Mkt:
Distribution
Manufacturing
Tech:
Measurement
Control Inventory:
order, receive, count,
maintain
Ratio/Percentages
Graphing/Predictions
Algebraic Expressions
Equations
Measure items for
production
Number Sense
Fractions
Decimals
Angles
Sample Curriculum Map
Agricultural Mechanics
Curriculum
Mathematics Content
Standards
Determining sprayer nozzle size
given flow rate and speed
Problem solving involving
cross-sectional area,
volume, and related rates
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
PASS
Standards
PASS
Process
Standard
1:
Problem
Solving
NCTM
Standards
NCTM
Problem
Solving
Standard
for
Grades 912
Scope & Sequence
TIME
CTE CONCEPT
MATH CONCEPT
MATH-IN-CTE
LESSON
MATH
STANDARD
MATH
PARTNER
MEETING
DATE
WEEK 1
Aug. 17
Marketing and
DECA
Orientation
NA
NA
NA
NA
WEEK 2
Aug. 23
DECA
Orientation
General Overview
of
the Math-in-CTE
Project
NA
NA
NA
Sales Unit
Introduction to
the 7
Math Concepts
Consent Forms,
Student
Survey, and Math
Pre
Test
NA
Sept. 2
Sales Unit
Ratio/Percentages
#1 – To Market, To
Market; Lesson
#25
Standards 1, 6
Sept. 9
Graphing/
Predictions
Algebraic
Expressions
& Equations, Pattern
Recognition,
Functions, Data
Representation
#4 - What Product
to Sell
Standards 1,
2, 3, 5, 6
Sept. 16
WEEK 3
Aug. 30
(Officer
Elections)
WEEK 4
Sept. 7
(TSLP
begins)
WEEK 5
Sept. 13
Sales Unit
Building the Enhanced
CTE Lesson
The Pedagogy
1.
2.
3.
4.
5.
6.
7.
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
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
What did we find?
What did we learn?
Map of Math Concepts Addressed
by Enhanced Lessons in each SLMP
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
8
4
4
10
2
Computation and Numerical Estimation
8
7
6
12
12
Operation Concepts
0
0
1
0
0
Measurement
5
7
3
0
12
Geometry and Spatial Sense
0
1
0
0
2
11
9
4
1
4
Patterns, Functions, Algebra
7
1
3
5
2
Trigonometry
0
0
0
0
2
Problem Solving and Reasoning
0
1
0
3
0
Communication
1
1
0
0
0
Data Analysis, Statistics and Probability
Analysis
Pre Test
Fall
Terra Nova
Difference in Math Achievement
C
Post Test
Spring
Terra Nova
Accuplacer
WorkKeys
Skills Tests
X
What we found:
Difference in % correct – All Experimental &
All Control
4
3.5
3
2.5
2
1.5
1
0.5
0
Classroom Level
TerraNova
Student Level
AccuPlacer
Work Keys
p<.05
Comparing Experimental
Classrooms to Control
Classrooms by Replication Site*
7
6
5
4
3
2
1
0
Site V
Site W
TerraNova
Site X
Accuplacer
*Only Significant effects shown
Site Y
Site Z
WorkKeys
Comparing Experimental Students to
Control Students by Replication
Site*
14
12
10
8
6
4
2
0
Site V
Site W
TerraNova
Site X
Accuplacer
Site Y
Site Z
WorkKeys
Magnitude of Treatment
Effect – Effect Size
the average
percentile standing of
the average treated
(or experimental)
participant relative to
the average untreated
(or control)
participant
Effect Size
Cohen’s d = .80
50th
percentile
X Group
C Group
79th
percentile
0
50th
100th
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)
Percentile Shift
From 50th to:
• 62nd
Carnegie
• 56th Learning
Corporation
Cognitive
• 58th Tutor
Algebra I
•
•
•
•
•
71st
67th
nd .22
82d=
58th
68th
Math Ability Effect: Test
Score Differences
5
Lower Quartile
Upper Quartile
4
3
2
1
0
-1
Terra Nova
Accuplacer
Work Keys
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
Does Enhancing Math in
CTE
Affect Technical Skill
Development?
Difference on Occupational
Skills Post Test - Classroom
Level
20
15
10
5
0
Site V
Site W
Site X
Site Y
Site Z
No difference in four sites; experimental students scored significantly
higher in one site
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%
• Average total school time investment
(assume 6 classes per day) = 1.7%
•
Modest investment for major payoff
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
Replicating the Math-in-CTE
Model:
Core Principles
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
What we are and are not: A
contextual continuum
• Traditional academic class
(e.g. Algebra 1)
• Disconnected
• Algebra 1
• Coordinated
• Academies • CTE & Academic teachers
• Context Based
• Contextual
coordinate around themes
(e.g. ‘health’)
• Integrated • Occupation is the context
for delivery of traditional
math
academics
(Related or applied math)
• NRC Model • Academics emerge from
occupational content
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?
Conclusion: The NRC
Model
(Process)(Pedagogy)=Math
achievement
Core Principles
Bringing Math-in-CTE to
your Community
1. 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
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Curriculum Mapping - Colorado State Plan