james r. stone iii director linking languages for learning enhancing reading and math through career...
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James R. Stone IIIDirector
LINKING LANGUAGES FOR LEARNING
Enhancing Reading and Math through Career and Technical
EducationGrand Junction CO
LINKING LANGUAGES FOR LEARNING
Enhancing Reading and Math through Career and Technical
EducationGrand Junction CO
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.
Disclaimer:
Math-in-CTE Research Team
The Ohio State University
Morgan Lewis
University of Minnesota
James R. Stone III
Donna Pearson
Corinne Alfeld
Susan Jensen
Gregg Gross
Oklahoma State University
Craig Edwards
Brian Parr
Brent Young
Colorado
Linda Harrison
Sherrie Schneider
Michigan
Mary Fudge
Kathleen Szuminski
Penn State University
Mary Kisner Barbara Senapedis
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 PerformanceOf American Youth
300 299 302 305 307 306 307 308 307304
150170190210230250270290310330350
NAEP Scores for 17 Year olds
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.
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 - IStudents earn more credits in CTE than in math or science
97% take at least one courseNearly half earn at least 3 Specific Labor Market (SLMP) credits
One-quarter are concentrators” NAVE 2004
Characteristics of Students Enrolled in 3 or more SLMP Courses .
0
10
20
30
40
50
60
70
80
90
NativeAmerican
Black (non-Hispanic)
Hispanic Has Disability LimitedEnglish
Proficiency
GPA less than2.0
More than50% FRL
Why Focus on CTE II
Levesque, K. (2003). Public High School Graduates Who Participated in Vocational/Technical Education
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-CTEMath-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
National Research Center
AutoTech BusEd IT
Experimental
Control
Experimental
Control
Experimental
Control
Ag P&T Health
Experimental
Control
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
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
• Technical skill or occupational knowledge assessment
• General, grade level tests (Terra Nova, AccuPlacer, WorkKeys)
• NOCTI, AYES, MarkED
Building Academic Skills in Context: Math-in-CTE
Building Academic Skills in Context: Math-in-CTE
The “method” of Math-in-CTE
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
Control Inventory: order, receive, count, maintain
Ratio/PercentagesGraphing/PredictionsAlgebraic ExpressionsEquations
Manufacturing Tech: Measurement
Measure items for production
Number SenseFractionsDecimalsAngles
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
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
TIME CTE CONCEPT MATH CONCEPT MATH-IN-CTELESSON
MATHSTANDARD
MATHPARTNERMEETING
DATE
WEEK 1Aug. 17
Marketing andDECA Orientatio
n
NA NA NA NA
WEEK 2Aug. 23
DECA Orientatio
n
General Overview of
the Math-in-CTEProject
NA NA NA
WEEK 3Aug. 30(Officer
Elections)
Sales Unit Introduction to the 7
Math Concepts
Consent Forms, Student
Survey, and Math Pre
Test
NA Sept. 2
WEEK 4Sept. 7(TSLP begins)
Sales Unit Ratio/Percentages
#1 – To Market, To
Market; Lesson #25
Standards 1, 6
Sept. 9
WEEK 5Sept. 13
Sales Unit Graphing/PredictionsAlgebraic
Expressions& Equations,
PatternRecognition,Functions, DataRepresentation
#4 - What Product to
Sell
Standards 1, 2, 3, 5, 6
Sept. 16
Scope & Sequence
The Pedagogy
1. Introduce the CTE lesson2. Assess students’ math awareness3. Work through the embedded example4. Work through related, contextual
examples5. Work through traditional math examples6. Students demonstrate understanding7. 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
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 BSite 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
Data Analysis, Statistics and Probability 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
Analysis
C XPost Test Spring
Terra Nova Accuplacer WorkKeys Skills Tests
Difference in Math Achievement
Pre Test Fall
Terra Nova
What we found: Difference in % correct – All Experimental
& All Control
0
0.5
1
1.5
2
2.5
3
3.5
4
Classroom Level Student Level
TerraNova AccuPlacer Work Keysp<.05
Comparing Experimental Classrooms to Control
Classrooms by Replication Site*
0
1
2
3
4
5
6
7
Site V Site W Site X Site Y Site Z
TerraNova Accuplacer WorkKeys
*Only Significant effects shown
Comparing Experimental Students to Control Students by Replication
Site*
0
2
4
6
8
10
12
14
Site V Site W Site X Site Y Site Z
TerraNova Accuplacer WorkKeys
50thpercentile
79thpercentile
C Group
0 50th 100th
X Group
Magnitude of Treatment Effect – Effect Size
Effect SizeCohen’s d = .80the average
percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant
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 ShiftFrom 50th to:• 62nd • 56th
• 58th
• 71st• 67th
• 82nd
• 58th
• 68th
Effect Size Obtained: Classroom Analysis
Carnegie Learning Corporation Cognitive Tutor Algebra I
d= .22
Math Ability Effect: Test Score Differences
-1
0
1
2
3
4
5
Terra Nova Accuplacer Work Keys
Lower QuartileUpper Quartile
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
0
5
10
15
20
Site V Site W Site X Site Y Site Z
Difference on Occupational Skills Post Test - Classroom
Level
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 learnedWhen 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 curriculaE. CTE teachers are teachers of “math-in-
CTE” NOT math teachers
What we are and are not: A contextual continuum
• Disconnected
• Coordinated
• Context Based
• Contextual
• Algebra 1
• Academies
• Integrated math
• NRC Model
• 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
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 teacher2. Loss of CTE integrity
• What are the barriers in moving this model to pre-service education?
Bringing Math-in-CTE to your Community
1. Communities of practice A. 10+ CTE-Math Teacher teamsB. Specific occupational fociB. Regional or state C. Invite not compel
2. Administrator supportA. Professional Development – (5:3:2) – for at least one full yearB. SubstitutesC. PD support (facilities, etc.)D. Staff the structure
3. Document!!!4. Support structure