110_Making Math Work

Study Design Random assignment of teachers to experimental or control condition  Five simultaneous study replications  Three measures of math skills applied, traditional, college plac

Making Math Work

A Pedagogic and Professional

Development Strategy for Success

Dr 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

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

Key Questions of the Study

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

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

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 12

Operation Concepts 0 0 1 0 0

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

Problem Solving and Reasoning 0 1 0 3 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%

 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 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

The P rofessional Development

P aradigm in P ractice

Old Model

 A box of curriculum

 Short term “training”

 Little or no support after

the “sage on the stage”

 On-going support – the learning curve

 Requires teams of committed teachers working together over time

Power of the New Professional

Development Paradigm Old Model

PD

New Model PD Total

Surprise!

 Occupation is the context for delivery of

traditional academics (Related or applied math)

 Academics emerge from occupational content

Remaining Issues

 Other academic areas (e.g., science, literacy)

 Pre-service options

 Potential impact of other approaches (e.g., context based)

National Research Center

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

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

What we found: All CTEx vs All CTEc

Post test % correct controlling for pre-test

0 10 20 30 40 50 60

TerraNova AccuPlacer WorkKeys

Experimental Classes Control Classes

Effect size (Cohen’s d)

Use of Method/Lessons in School Year Following Study

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

The Seven Elements

of a Math-Enhanced Lesson

Curriculum Mapping

Mary Fudge

Curriculum Maps

 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 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

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

inventory: order, receive, count, maintain

Ratio/Percentages Graphing/Predictions Algebraic

Expressions Equations

Manufacturing

Measure items for production Number SenseFractions

Decimals Angles

CURRICULUM MAPPING

Sample Curriculum Map

Agricultural Mechanics

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 Map

Health Standards

Analyze methods for

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

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 Mapping

Exercise

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

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

the CTE.

 Use methods and techniques to assess the whole class.

Element 3: Work through 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,

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.

Element 5: Work through

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.

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.

Element 7: Formal

example:

CTE unit exams

CTE project assessments

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.

The “Seven Elements” in brief

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

Questions