making math work.ppt
TRANSCRIPT
Making Math Work
A Pedagogic and Professional Development
Strategy for SuccessDr Sherrie Schneider
Mary Fudge
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:
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?
Perkins IV requires . . .
Develop challenging academic and technical standards and related challenging, integrated instruction
Here is the Problem: Math Performance of American Youth
300 299 302 305 307 306 307 308 307304
150170190210230250270290310330350
NAEP Scores for 17 Year olds
Despite the fact, students are taking more math and science
Why Focus on CTE
CTE provides a math-rich context
CTE curriculum/pedagogies do not systematically emphasize math skill development
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.
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 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
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
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)
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 B Site C
Site D Site E
Number and Number Relations 8 4 4 10 2
Computation and Numerical Estimation 8 7 6 12 12Operation Concepts 0 0 1 0 0
Measurement 5 7 3 0 12Geometry 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
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%
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
Replicating the Math-in-CTE Model:Core Principles
A. Develop and sustain a community of practiceB. Begin with the CTE curriculum and not with
the math curriculum C. Understand math as essential workplace skillD. Maximize the math in CTE curriculaE. CTE teachers are teachers of “math- in-CTE”
NOT math teachers
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
Power of the New Professional Development Paradigm
0
0.2
0.4
0.6
0.8
Math teacherPartners
ExperimentalCTE Teachers
Control CTETeachers
Math in CTE Use 1 Year Later
Old Model PD
New Model
PD
Total Surprise!
Math-in-CTE in Context 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
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)
National Research Center
AutoTech BusEd IT
Experimental
Control
Experimental
Control
Experimental
Control
Ag P&T Health
Experimental
Control
Experimental
Control
Sample 2004-05: 57 Experimental CTE/Math teams and 74 Control CTE Teachers
Total sample: 3,000 students*
Study Design 04-05 School Year
The Research Design
X
C C
X
Diff
eren
ce
On-going fidelity of treatment measures
Diff
eren
ceThe Experimental
Treatment
02468
1012
Site A Site B Site C Site E Site F
Difference on Occupational Skills Post Test - Classroom
Level
No difference in four sites; experimental students scored significantly higher in one site.
What we found: All CTEx vs All CTEcPost test % correct controlling for pre-test
0
10
20
30
40
50
60
TerraNova AccuPlacer WorkKeys
Experimental Classes Control Classes
p= .02 p= .03 p=ns
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)
What we found: Magnitude of effect
Carnegie Learning Corporation Cognitive Tutor Algebra Id= .22
Percentile “Shift”From 50th to: 71st 67th
99th 76th 81st 74th 66th
Use of Method/Lessons in School Year Following Study
0
10
20
30
40
50
60
70
80
Perc
ent U
sing
Experimental Control Mathematics
Math-in-CTE ModelProfessional 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 Professional Development“Year-at-a-Glance”
July-Aug Sept-Nov Dec-Feb Mar-May June
Teach Lessons
2 Days Professional Development
5 Days Professional Development
2 Days Professional Development
Teach Lessons Teach Lessons
I Day Wrap-upCelebration
On-going monitoring of teacher progress
The Seven Elementsof a Math-Enhanced Lesson
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
Curriculum Mapping
Mary Fudge
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 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 chartsProblem 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 decimalsArea of rectangle
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
FractionsRatio & Proportion
Business/Marketing Distribution Control inventory: order, receive, count, maintain
Ratio/PercentagesGraphing/PredictionsAlgebraic ExpressionsEquations
Manufacturing Technology
Measurement Measure items for production
Number SenseFractionsDecimalsAngles
CURRICULUM MAPPING
Sample Curriculum MapAgricultural Mechanics
CurriculumMathematics Content
StandardsPASS
StandardsNCTM
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
Sample Curriculum MapHealth Standards
IdentificationHealth Skill Mathematics Content
StandardsMichigan Content
Standard
Analyze methods for the control of disease.
Prognosis and diagnosisBody planesRange of motionPharmacy calculations
(for pharmacy techs
Solve linear equations Read and interpret graphs
and chartsProblem solving involving
statistical dataRatio 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 sensitivityLab techniquesBlood 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
Curriculum MappingExercise
Curiculum Map Template.pdf
The Pedagogy
Mary Fudge
The Pedagogy
The “seven elements” provide the pedagogic framework for creating and teaching math-enhanced lessons.
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
Element 1:Introduce the CTE lesson
Explain the CTE lesson. Identify, discuss, point out, pull out the
math embedded in the CTE lesson.
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.
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.
Element 4: Work through related, contextual math-in-CTE examplesUsing 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.
Element 5: Work through traditional math examplesUsing 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.
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.
Element 7: Formal Assessment Include math questions in formal
assessments, for example:CTE unit exams CTE project assessments
Some Final Thoughts…
1 math concept 1 math concept ≠ ≠ 1 lesson 1 lesson ≠≠ 1 class period 1 class period
Lessons can address one or more concepts and/or last longer than one class period.
PEDAGOGY:The “Seven Elements” in brief
1. Introduce the CTE lesson2. Assess students’ math awareness3. Work through embedded example4. Work through related, contextual example5. Work through traditional example6. Students demonstrate understanding7. Formal assessment
Math in CTE Health Lesson
Alices Areas Health Lesson
Making It All Work:The Math-in-CTE Model
Final Thoughts
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
Contact Information
Sherrie [email protected]
Office 303-252-6390 Cell 303-489-4145 Mary Fudge [email protected] 269-668-4817Cell 269-217-4348
Questions