1. A Pedagogic and Professional Development
Making Math Work
A Pedagogic and Professional Development
Strategy for Success
Dr Sherrie Schneider
Mary Fudge
Math-in-CTE

2. 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

3. CTE: What do we know? CTE keeps kids in school
CTE helps kids focus their PS education plans
CTE is an economic benefit to participants and to states
CTE-based structures (e.g.,dual enrollment, career academies) can affect achievement and transition of youth to college and work.
But what more value can CTE provide as part of the high school experience?
Math-in-CTE

4. Perkins IV requires . . .
Develop challenging academic and technical standards and related challenging, integrated instruction
What is new is that every time you see CTE you also see academics!
Math-in-CTE

5. Here is the Problem: Math Performance of American Youth
NAEP Scores for 17 Year olds
Math-in-CTE

6. Despite the fact, students are taking more math and science
Math-in-CTE

7. Why Focus on CTE CTE provides a math-rich context
CTE curriculum/pedagogies do not systematically emphasize math skill development
Spend a little time emphasizing each of these points
Math-in-CTE

8. The Math-in-CTE Study
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.
Emphasize it is a very simple question and a simple straight forward study
Math-in-CTE

9. 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?
Math-in-CTE

10. Study Design
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
Focused on naturally occurring math (embedded in curriculum)
Test a model of Curriculum Integration
Intense focus on Fidelity of Treatment
Math-in-CTE

11. Measuring Math & Technical Skill Achievement
General, grade level tests (Terra Nova, AccuPlacer, WorkKeys)
NOCTI, AYES, MarkED
Global math assessments
Technical skill or occupational knowledge assessment
Math-in-CTE

12. What we tested: 1. Professional Development
Summer PD (5 days) – Mapping and lesson creation
Late fall PD (2-3 days) - Lesson creation
Early Spring PD (2-3 days) – Lesson creation
On-going direct and indirect math support
2. The Math Enhancement Process
(The 7 Element Pedagogic Model)
Explain that if they do not have a math teacher in their school (e.g. regional vocational center) we will provide that math support if needed
Math-in-CTE

13. Map of Math Concepts Addressed by Enhanced Lessons in each SLMP
Number of Corresponding CTE Math Lessons Addressing the Math Concept
Site A
Site B
Site C
Site D
Site E
Number and Number Relations 8 4 10 2
Computation and Numerical Estimation 7 6 12
Operation Concepts 1
Measurement 5 3
Geometry and Spatial Sense
Data Analysis, Statistics and Probability 11 9
Patterns, Functions, Algebra
Trigonometry
Problem Solving and Reasoning
Communication
Math-in-CTE

14. Time invested in Math Enhancements
Average of 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%
Math-in-CTE

15. Why
Ebbinghaus effect – refreshing or relearning previously learned material
Vocabulary effect – math as a foreign language
Spillover effect – math skills developed in one area improve performance in others
Vocabulary Instruction in Ratio and Proportion for Seventh Graders Michael B. Jackson, E. Ray Phillips Journal for Research in Mathematics Education, Vol. 14, No. 5 (Nov., 1983), pp doi: / ; Language Factors in Learning Mathematics Lewis R. Aiken, Jr. Review of Educational Research, Vol. 42, No. 3 (Summer, 1972), pp doi: /
Math-in-CTE

16. Replicating the Math-in-CTE Model: Core 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
Maximize the math in CTE curricula
CTE teachers are teachers of “math- in-CTE” NOT math teachers
Math-in-CTE

17. The Professional Development Paradigm in Practice
Old Model
A box of curriculum
Short term “training”
Little or no support after the “sage on the stage” goes away
Replicable by individual teachers (assumed)
New Model
Process not an event
Built on communities of practice
On-going support – the learning curve
Requires teams of committed teachers working together over time
Math-in-CTE

18. Power of the New Professional Development Paradigm
Old Model PD
Total Surprise!
New Model PD
Math-in-CTE

19. Math-in-CTE in Context
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
Math-in-CTE

20. Remaining Issues Class impact vs. program impact
Tipping point (how much math)
Other academic areas (e.g., science, literacy)
Pre-service options
Potential impact of other approaches (e.g., context based)
Math-in-CTE

21. Study Design 04-05 School Year
Sample : 57 Experimental CTE/Math teams and 74 Control CTE Teachers
Total sample: 3,000 students*
Math-in-CTE

22. The Experimental Treatment
The Research Design
The Experimental Treatment X X
Difference
Difference
Discuss the two group design that will ultimately yield three groups due to attrition and class changes in Spr.
The emergent 3 groups will require three levels of analysis: Group 1 will be pre and post for academic year. Group 2 and Group 1 will be pre and post for fall term. Group 3 will be post test only for Spring term. C C
On-going fidelity of treatment measures
Math-in-CTE

23. *
No difference in four sites; experimental students scored significantly higher in one site.
*p<.10
Math-in-CTE

24. What we found: All CTEx vs All CTEc Post test % correct controlling for pre-test
p=ns
Math-in-CTE

25. What we found: Magnitude of effect
Effect size (Cohen’s d)
All Classes
Terra Nova (d=.55)
Accuplacer (d=.42)
By Site
Site A –WorkKeys (d=2.8)
Site B- TerraNova (d=.69)
Site C –Accuplacer (d=.85)
Site E- Terra Nova (d=.64)
Site F – AccuPlacer (d=.39)
Percentile “Shift”
From 50th to:
71st
67th
99th
76th
81st
74th
66th
Carnegie Learning Corporation Cognitive Tutor Algebra I
d= .22
Math-in-CTE

26. Use of Method/Lessons in School Year Following Study
Math-in-CTE

27. Math-in-CTE Model Professional Development Sessions
Curriculum mapping (math/CTE nexus)
Scope & sequence (map the year)
Development of math-enhanced lessons
On-going math support
Teaching the Lessons
Math-in-CTE

28. Math-in-CTE

29. The Seven Elements of a Math-Enhanced Lesson
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
Math-in-CTE

30. Curriculum Mapping
Mary Fudge
Math-in-CTE

31. 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)
Math-in-CTE

32. CURRICULUM MAPPING CTE PROGRAM CTE UNIT CTE CONCEPTS MATH CONCEPTS
HEALTH OCCUPATIONS
Human Structure and Function
Compare cell, tissue, organ and body systems relationships
Solve linear equations
Read and interpret graphs and charts
Problem solving involving statistical data
Ratio and Proportion
CONSTRUCTION
Dry wall
Determine amount of wall board to purchase for a specific room
Multiplication and division of whole numbers and decimals
Area of rectangle

33. CURRICULUM MAPPING CTE PROGRAM CTE UNIT CTE CONCEPTS MATH CONCEPTS
CULINARY ARTS
Cooking large quantities
Increase recipes to make large quantities of a food item for a banquet
Fractions
Ratio & Proportion
Business/Marketing
Distribution
Control inventory: order, receive, count, maintain
Ratio/Percentages
Graphing/Predictions
Algebraic Expressions
Equations
Manufacturing Technology
Measurement
Measure items for production
Number Sense
Decimals
Angles

34. Agricultural Mechanics Curriculum Mathematics Content Standards
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
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
Math-in-CTE

35. Sample Curriculum Map Health Standards Identification Health Skill
Mathematics Content Standards
Michigan Content Standard
Analyze methods for the control of disease.
Prognosis and diagnosis
Body planes
Range of motion
Pharmacy calculations (for pharmacy techs
Solve linear equations
Read and interpret graphs and charts
Problem solving involving statistical data
Ratio and Proportion
1.2 Students describe the relationships among variables, predict what will happen to one variable as another variable is changed, analyze natural variation and sources of variability to compare patterns of change.
Analyze changes in body systems as they relate to disease, disorder and wellness
Cultures and sensitivity
Lab techniques
Blood sugar and user failure versus accurate sample collection
C & S of wounds, collection contamination process and outcome
Calculate time, temperature, mass measurement and compare to known standards
Interpretation of measurement results
Calculate accurate measurement in both metric and English units
2.3 Students compare attributes of two objects or of one object with a standard (unit) and analyze situations to determine what measurement(s) should be made and to what level of precision

36. Curriculum Mapping Exercise
Curiculum Map Template.pdf

37. The Pedagogy
Mary Fudge

38. The Pedagogy
The “seven elements” provide the pedagogic framework for creating and teaching math-enhanced lessons.
Math-in-CTE

39. 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
Math-in-CTE

40. Element 1: Introduce the CTE lesson
Explain the CTE lesson.
Identify, discuss, point out, pull out the math embedded in the CTE lesson.

41. Element 2: Assess students’ math awareness
Begin “bridging” between the CTE and math.
Introduce math vocabulary through the math embedded in the CTE.
Use methods and techniques to assess the whole class.

42. Element 3: Work through the math example embedded in the CTE lesson
Work through the steps or processes of the embedded math example.
Continue to bridge the CTE and math vocabulary.

43. Element 4: Work through related, contextual math-in-CTE examples
Using the same embedded math concept:
Work through similar problems in the same occupational context.
Use examples of varying levels of difficulty; order from basic to advanced.
Continue to bridge CTE and math vocabulary.
Check for understanding.

44. Element 5: Work through traditional math examples
Using the same embedded math concept:
Work from applied to abstract problems.
Work through examples as they may appear on standardized tests.
Move from basic to advanced problems.
Continue to bridge CTE-math vocabulary.
Check for understanding.

45. Element 6: Students demonstrate understanding
Provide students with opportunities to demonstrate their understanding of the math concepts embedded in the CTE.
Connect the math back to CTE context.
Conclude the lesson with CTE.

46. Element 7: Formal Assessment
Include math questions in formal assessments, for example:
CTE unit exams
CTE project assessments

47. Some Final Thoughts… 1 math concept ≠ 1 lesson ≠ 1 class period
Lessons can address one or more concepts and/or last longer than one class period.

48. PEDAGOGY: The “Seven Elements” in brief
Introduce the CTE lesson
Assess students’ math awareness
Work through embedded example
Work through related, contextual example
Work through traditional example
Students demonstrate understanding
Formal assessment

49. Math in CTE Health Lesson
Alices Areas Health Lesson

50. Making It All Work: The Math-in-CTE Model Final Thoughts

51. Final thoughts: Math-in-CTE Model
A powerful, evidence based strategy for improving math skills of students;
A way but not THE way to help high school students master math
Not a substitute for traditional math courses
Lab (experiential venue) for mastering what many students learn but don’t understand
Math-in-CTE

52. Contact Information
Sherrie Schneider
Office
Cell
Mary Fudge
Office
Cell

53. Questions