Curriculum Mapping

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					          LINKING LANGUAGES FOR
                    LEARNING
            Enhancing Reading and Math
           through Career and Technical
                     Education
                     Grand Junction CO
James R. Stone III
Director

                               Stone003@umn.edu
           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
                             Colorado         Donna Pearson

                              Linda            Corinne Alfeld
   Penn State University
                             Harrison          Susan Jensen
       Mary Kisner
                              Sherrie          Gregg Gross
    Barbara Senapedis
                             Schneider

                                    Oklahoma State
                 Michigan             University
                Mary Fudge           Craig Edwards
                 Kathleen                 Brian Parr
                Szuminski
                                         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
350
330   304               302   305 307 306 307   308   307
310         300   299
290
270
250
230
210
190
170
150
  73

  75

  77

  79

  81

  83

  85

  87

  89

  91

  93

  95

  97

  99

  01

  04
19

19

19

19

19

19

19

19

19

19

19

19

19

19

20

20
                         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           Black (non-          Hispanic        Has Disability          Limited         GPA less than   More than
        American           Hispanic)                                                   English              2.0        50% FRL
                                                                                     Proficiency
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-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 04-
05 School Year                           National Research Center




            AutoTech             BusEd           IT               Ag P&T             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               Primary Role
• Experimental CTE      •   Implement the math
  teacher                   enhancements
• Math teacher          •   Provide support for
                            the CTE teacher
• Control CTE teacher   •   Teach their regular
                            curriculum
• Liaison
                        •   Administer surveys
                            and tests
Measuring Math & Technical
    Skill Achievement
  • Global math   • General, grade
    assessments     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
                                         Ratio/Percentages
Bus/Mkt:        Control Inventory:       Graphing/Predictions
Distribution    order, receive, count,   Algebraic Expressions
                maintain                 Equations

                                         Number Sense
                                         Fractions
Manufacturing
                Measure items for        Decimals
Tech:           production               Angles
Measurement
          Sample Curriculum Map
    Agricultural Mechanics           Mathematics Content           PASS        NCTM
            Curriculum                     Standards             Standards   Standards
Determining sprayer nozzle size   Problem solving involving      PASS        NCTM
   given flow rate and speed         cross-sectional area,       Process     Problem
                                     volume, and related rates   Standard    Solving
                                                                 1:          Standard
Determine pipe size and water     Problem solving involving      Problem     for
   flow rates for a water pump       cross-sectional area,       Solving     Grades 9-
                                     volume, and related rates               12

Determine amount of paint         Problem solving involving
   needed to paint a given           surface area, ratio and
   surface (calculate surface        proportions
   area, etc)
Determine the concrete            Problem solving involving
   reinforcements and spacing        cross-sectional area,
   needed when building a            volume, and related rates
   concrete platform or
   structure
                Scope & Sequence
  TIME        CTE CONCEPT        MATH CONCEPT           MATH-IN-CTE           MATH           MATH
                                                          LESSON            STANDARD        PARTNER
                                                                                            MEETING
                                                                                              DATE
 WEEK 1      Marketing and             NA                    NA                 NA            NA
 Aug. 17        DECA
               Orientation
WEEK 2            DECA         General Overview              NA                 NA            NA
Aug. 23          Orientation            of
                               the Math-in-CTE
                                   Project
 WEEK 3      Sales Unit         Introduction to        Consent Forms,           NA          Sept. 2
  Aug. 30                             the 7                 Student
 (Officer                       Math Concepts         Survey, and Math
Elections)                                                     Pre
                                                            Test
WEEK 4       Sales Unit        Ratio/Percentages      #1 – To Market, To   Standards 1, 6   Sept. 9
Sept. 7                                                Market; Lesson
(TSLP                                                          #25
  begins)
WEEK 5         Sales Unit      Graphing/              #4 - What Product    Standards 1,     Sept. 16
Sept. 13                       Predictions                   to Sell          2, 3, 5, 6
                               Algebraic
                                   Expressions
                               & Equations, Pattern
                               Recognition,
                               Functions, Data
                               Representation
Building the Enhanced
      CTE Lesson
          The Pedagogy
1.   Introduce the CTE lesson
2.   Assess students‟ math awareness
3.   Work through the embedded example
4.   Work through related, contextual examples
5.   Work through traditional math examples
6.   Students demonstrate understanding
7.   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
                                             Number of Corresponding CTE Math
                                            Lessons Addressing the Math Concept
                     Math Concept
                                                              Site   Site
                                            Site A   Site B                 Site E
                                                               C      D
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

              Pre Test
               Fall
             Terra Nova

    Difference in Math Achievement

             Post Test
C             Spring                 X
             Terra Nova
             Accuplacer
             WorkKeys
             Skills Tests
            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                 Student Level
                                                  p<.05
        TerraNova       AccuPlacer   Work Keys
        Comparing Experimental
         Classrooms to Control
    Classrooms by Replication Site*
7
6
5
4
3
2
1
0
    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*

14
12
10
8
6
4
2
0
     Site V   Site W     Site X     Site Y   Site Z

      TerraNova        Accuplacer     WorkKeys
          Magnitude of Treatment
           Effect – Effect Size
                                         Effect Size
the average                              Cohen’s d = .80
percentile standing of
the average treated                   50th
(or experimental)                   percentile
participant relative to
the average untreated                                      X Group
                          C Group
(or control)
participant
                                               79th
                                             percentile

                  0                   50th                      100th
         Effect Size Obtained:
          Classroom Analysis
      Effect size (Cohen‟s d)      Percentile Shift
All Classes                        From 50th to:
   Terra Nova           (d=.28)    • 62nd
  Accuplacer            (d=.11)   Carnegie Learning
                                   • 56th
By Site                           Corporation
     Site V –WorkKeys (d=.20)     Cognitive Tutor
                                   • 58th
    Site W-AccuPlacer (d=.54)     Algebra I
                                   •   71st
    Site X –Terra Nova (d=.43)     •   67th
    Site Y-Terra Nova (d=.87)      •   82d= .22
                                         nd

    Site Z – AccuPlacer (d=.18)    •   58th
            -TerraNova (d=.45)     •   68th
     Math Ability Effect: Test
        Score Differences
5

4                                                          Lower Quartile
                                                           Upper Quartile
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      As a Result of the Study
• A box of curriculum        • A curriculum
                               development process
• Teacher training           • Building and sustaining a
                               community of practice
• Replicable by individual   • Replicable by teams of
  teachers                     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
• Disconnected    • Algebra 1    • Traditional academic class
                                   (e.g. Algebra 1)

• Coordinated     • Academies • CTE & Academic teachers
                                 coordinate around themes
                                 (e.g. „health‟)

• Context Based   • Integrated • Occupation is the context
                    math         for delivery of traditional
                                 academics
                                 (Related or applied math)
• Contextual

                  • 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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posted:11/2/2011
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