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

Stone003@umn.edu

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

The Experimental Treatment

• Professional Development• The Pedagogy

Math-in-CTEThe 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

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

Building the Enhanced CTE Lesson

Building the Enhanced CTE Lesson

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

What did we find?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 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

Does Enhancing Math in CTE

Does Enhancing Math in CTE

Affect Technical Skill Development?

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?

Conclusion: The NRC Model

(Process)(Pedagogy)=Mathachievement

Core Principles

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