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Math in Career and Technical Education. 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

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Math in career and technical education

Math in Career and Technical Education


Math in cte research team
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


What do we know about cte
What do we know about CTE?

There is evidence that:

  • CTE does not limit postsecondary education

  • Math and science courses taken 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. . .


Background framework for improving cte

Programmatic

Classroom learning

Work based learning

CTSO learning

Professional Development (Pre and in-service)

Structural

Traditional:

Tech Prep/Dual Credit/ Articulation

Career magnets

Regional Centers

As School Reform:

MCHS

Career academies

Career pathways

Background: Framework for Improving CTE


The Problem: Math PerformanceOf American Youth

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.

http://nces.ed.gov/nationsreportcard/ltt/results2004/


Why focus on cte

Students earn more credits in CTE than in math or science 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.

97% take at least one course

Nearly half earn at least 3 Specific Labor Market (SLMP) credits

One-quarter are

concentrators”

Why Focus on CTE

NAVE 2004


Alternative cte math improvement strategies
Alternative CTE Math Improvement Strategies 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.

  • 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

Math-in-CTE 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.

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
Key Questions of the Study 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.

  • 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
Study Design: Key Features 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.

  • 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 04-05 School Year 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.

Sample 2004-05: 63 Experimental CTE/Math teams and 71 Control CTE Teachers

Total sample: 3,000 students*


Study design participants

Participant 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.

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

Study Design: Participants


Measuring math technical skill achievement

Global math assessments 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.

Technical skill or occupational knowledge assessment

General, grade level tests (Terra Nova, AccuPlacer, WorkKeys)

NOCTI, AYES, MarkED

Measuring Math & Technical Skill Achievement


The experimental treatment
The Experimental Treatment 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.

  • Professional Development

  • The Pedagogy


Professional development
Professional Development 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.

  • CTE-Math Teacher Teams; occupational focus

  • Curriculum mapping

  • Scope and Sequence

  • CTE and math teachers professional development

  • On going collaboration CTE and math teachers


Curriculum maps
Curriculum Maps 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.

  • 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)


Scope & Sequence 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.


Curriculum map linking to standards
Curriculum Map-Linking to Standards 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.


Experimental treatment the pedagogy
Experimental Treatment: The Pedagogy 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.

  • Introduce the CTE lesson

  • Assess students’ math awareness

  • Work through the embeddedexample

  • Work through related,contextual examples

  • Work through traditional math examples

  • Students demonstrate understanding

  • Formal assessment


What did we find

What did we find? 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.

What did we learn?



Analysis
Analysis SLMP

Pre Test Fall

Terra Nova

Difference in Math Achievement

Post Test Spring

Terra Nova Accuplacer WorkKeys Skills Tests

X

C


What we found difference in correct all experimental verses all control
What we found: SLMPDifference in % correct – All Experimental verses All Control

p<.05


Math ability effect test score differences
Math Ability Effect: Test Score Differences SLMP

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 SLMP

Affect Technical Skill Development?



Time invested in math enhancements
Time invested in Math Enhancements significantly higher in one site

  • 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 significantly higher in one site

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

What we learned


Replicating the math in cte model core principles
Replicating the Math-in-CTE Model: significantly higher in one siteCore 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


Replicating the math in cte model core principles1
Replicating the Math-in-CTE Model: significantly higher in one siteCore Principles

  • Maximize the math in CTE curricula

  • CTE teachers are teachers of “math-in-CTE” NOT math teachers


What we are and are not a contextual continuum

Disconnected significantly higher in one site

Coordinated

Context Based

Contextual

Algebra 1

Academies

Integrated math

NRC Model

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


Issues
Issues significantly higher in one site

  • 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) – there is no cheap or quick fix

  • 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


Conclusion the nrc model
Conclusion: The NRC Model significantly higher in one site

(Process)(Pedagogy)=Mathachievement

Core Principles


Math in cte1

Math-in-CTE significantly higher in one site

Making it happen

in your community


Necessary ingredients
Necessary Ingredients significantly higher in one site

  • Communities of practice

    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!!!


Core principle a develop and sustain a community of practice
Core Principle A significantly higher in one siteDevelop and sustain a community of practice

  • Cohorts of math-CTE teacher teams (10+)are formed around specific occupational foci or CTE content (e.g. business, auto technology, health).

  • Communities of practice participate together in professional development several times during the academic year

  • External “stimuli” to help maintain focus


Core principle b begin with the cte curriculum and not with the math curriculum
Core Principle B significantly higher in one siteBegin with the CTE curriculum and not with the math curriculum

  • Math-CTE teacher teams interrogate the curriculum, identifying the math that occurs creating curriculum maps that identify the intersection of occupational content and math constructs/concepts.

  • The CTE related math is mapped onto the curriculum using a scope and sequence


Teach the math when it occurs

Teach the math when it occurs: significantly higher in one site

"Placement of the lesson is an integral part of the students understanding the math concepts. I taught this lesson to two separate groups; the group studying electrical circuits got "IT" immediately as a normal part of the CTE lessons. The group taught out of context had a much more difficult time with the lesson. When taught again "in" context, group two had a better understanding of the math application and its relevance."


Core principle c understand math as essential workplace skill
Core Principle C significantly higher in one siteUnderstand math as essential workplace skill

  • Teacher teams generate math examples in which students solve authentic workplace problems.

  • Math is a “tool” used in the workplace.

  • CTE teachers bridge CTE and math vocabulary as they develop and teach the lessons.


Core principle d maximize the math in cte curricula
Core Principle D significantly higher in one siteMaximize the math in CTE curricula

  • CTE teachers build on students’ prior math knowledge and skills.

  • Math-CTE teacher teams continue to locate as much math as possible in the CTE curricula throughout the school year.

  • CTE teachers capitalize on teachable moments that follow the math enhanced lessons.


Core principle e cte teachers are teachers of math in cte not math teachers
Core Principle E significantly higher in one siteCTE teachers are teachers of “math-in-CTE” NOT math teachers

  • CTE teachers participate in professional development activities that enable them to teach the math as it occurs in their content.

  • CTE teachers learn more about the math concepts in their CTE curriculum.

  • CTE teachers learn math formulas and vocabulary.

    • CTE teachers are given opportunities to practice teaching the math in their curriculum.


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