Math in Career and Technical Education

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Math in Career and Technical Education
James R. Stone III Stone003_at_umn.edu
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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
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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
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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. . .

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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

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The Problem Math PerformanceOf American Youth
NAEP Scores for 17 Year olds
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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/results20
04/
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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
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Why Focus on CTE II
Levesque, K. (2003). Public High School Graduates
Who Participated in Vocational/Technical Education
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Why Focus on CTE - III

• CTE provides a math-rich context
• CTE curriculum/pedagogies do not systematically
  emphasize math skill development

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Alternative CTE Math Improvement Strategies

• Related Math class(e.g., Business math)
• Applied Math class (e.g., Tech Prep math)
• Pull out math classeswith 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.

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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.

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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?

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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

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Focus of Math Interventions

• Higher Level Math

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Study Design 04-05 School Year
Sample 2004-05 63 Experimental CTE/Math teams
and 71 Control CTE Teachers Total sample
3,000 students
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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

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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

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The Experimental Treatment

• Professional Development
• The Pedagogy

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Professional Development

• CTE-Math Teacher Teams occupational focus
• Curriculum mapping
• Scope and Sequence
• CTE and math teachers professional development
• On going collaboration CTE and math teachers

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Curriculum Maps

• Begin with CTE Content
• Look for places where math is part of the CTE
  content (V-Tecs, AYES, MarkED, state guides, last
  years maps)
• Create map for the school year
• Align map with planned curriculum for the year
  (scope sequence)

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Scope Sequence
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Curriculum Map-Linking to Standards
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Scope Sequence/Planning Grid
Lesson Plan Designator
Two to Three will be scheduled each semester
Three scheduled during the year
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Experimental Treatment 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

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Enhancing the CTE Curriculum

• Auto Technology Health

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Larrys Truck Improvements

• Larry put a 6 lift kit on his Ford F-150 and a
  set of 33s Super Swamper Thornbird Tires
• The Suspension System has been modified but the
  Brake System has not.
• Do You See Any Problems?

GIT-R-DONE
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What Parts Control the Stopping of the Truck?

• Master Cylinder
• Brake Hoses/Lines
• Wheel Cylinders
• Brake Calipers

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Larry has a Problem!

• What changes could you make to fix the problem?
• Bigger parts
• Such as Master Cylinder, Brake lines, Wheel
  Cylinders, and/or Brake Calipers

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Pascals LawUnlock the mechanics of the
Hydraulic Braking System
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Before we apply Pascals Law

• We must first review and be familiar with
• Diameter of a Piston
• Radius of the Piston
• Area of the top surface of the Piston
• Mathematically speaking
• Diameter The width of a circular or cylindrical
  object.
• Radius The radius of a circle is half the
  diameter
• Area Any particular extent of space or surface

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Pascals Law

• In the 1600's, the French scientist Blaise Pascal
  discovered a fact now known as Pascal's Law. It
  states that pressure at any point in a body of
  fluid is the same in every direction, exerting
  equal force on equal areas. This works for gases
  and liquids (both are fluids).

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Pascals Formula

• This brings us to a very important formula
• P Pressure, F Force and A Area
• This expresses that Pressure is Force per Unit
  Area. This is why pressure is usually expressed
  in pounds per square inch (psi).

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F Force
F P A
P Pressure
A Area
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Alices Areas

• Your patient, Alice, came into the Emergency
  Department with partial and full thickness burns
  to her entire right (R) leg after falling into a
  camp fire. You are to calculate the area of the
  burn and determine the percentage of her body
  that is burned.

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• We will break her body into different geometric
  shapes. For example, her head will be a sphere,
  her arms and legs will be cylinders, her thorax
  will be a rectangular solid and her perineal area
  will be a triangle.

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Alices areas

• We will figure the surface area of each part of
  Alices body separately and then find the total
  by adding all the parts together.
• r 12.62cm

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Solution
SA4pr2
4(3.14)( 12.62cm)2
2000cm2
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Alices Arms

• r4cm
• h75.62cm

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Solution

• SA2pr2 2prh
• 2(3.14)(4cm)2 2(3.14)(4cm)(75.62cm)
• 100.48cm2 1899.58cm2
• 2000cm2
• Two arms so 2(2000cm2)

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Alices Thorax

• 40.9cm
• 50.9cm
• 20.9cm

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Solution

• There are six sides!
• Front and Back
• SA2lw
• (2)(50.9cm)(40.9cm)
• 4163.6cm2
• top and bottom
• SA2lw
• 2(40.9cm)(20.9cm)
• 1709.6cm2
• Two sides
• SA2lw
• 2(50.9cm)(20.9cm)
• 2127.62cm2
• Total8000cm2

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What did we find?

• What did we learn?

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Map of Math Concepts Addressed by Enhanced
Lessons in each SLMP
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Analysis
Pre Test Fall Terra Nova
Difference in Math Achievement
X
Post Test Spring Terra Nova Accuplacer WorkKeys
Skills Tests
C
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What we found Difference in correct All
Experimental All Control
plt.05
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Comparing Experimental Classrooms to Control
Classrooms by Replication Site
Only Significant effects shown
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Comparing Experimental Students to Control
Students by Replication Site
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Magnitude of Treatment Effect Question 2
Effect Size Cohens d .80
the average percentile standing of the average
treated (or experimental) participant relative to
the average untreated (or control) participant
50thpercentile
C Group
X Group
79thpercentile
0
50th
100th
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Effect Size Obtained Classroom Analysis
Effect size (Cohens 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
• 56th
• 58th
• 71st
• 67th
• 82nd
• 58th
• 68th

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Effect Size Obtained Classroom Analysis
Effect size (Cohens 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
d .22
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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
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Does Enhancing Math in CTE

• Affect Technical Skill Development?

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No difference in four sites experimental
students scored significantly higher in one site
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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

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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

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Replicating the Math-in-CTE ModelCore
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

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Replicating the Math-in-CTE ModelCore
Principles

• Maximize the math in CTE curricula
• CTE teachers are teachers of math-in-CTE NOT
  math teachers

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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

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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)
  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

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Conclusion The NRC Model
(Process)(Pedagogy)Mathachievement
Core Principles
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Math-in-CTE

• Making it happen
• in your community

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Necessary Ingredients

• Communities of practice
• 2. Administrator support
• A. Professional Development (532) for at
  least one full year
• B. Substitutes
• C. PD support (facilities, etc.)
• D. Staff the structure
• 3. Document!!!

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Core Principle A Develop 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

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Core Principle BBegin 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

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Teach the math when it occurs

• "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."

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Core Principle CUnderstand 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.

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Core Principle DMaximize 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.

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Core Principle E CTE 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.