Making Math Work: Building Academic Skills in Context James R. Stone III Director [email protected].

Making Math Work: Building Academic Skills in Context

James R. Stone IIIDirector [email protected]

REMINDER-THE ISSUE12TH GRADE MATH SCORES 2005

A CAUTIONARY NOTE

94% of workers reported using math on the job, but, only1

22% reported math “higher” than basic 19% reported using “Algebra 1” 9% reported using “Algebra 2”

Among upper level white collar workers1

30% reported using math up to Algebra 1 14% reported using math up to Algebra 2

Less than 5% of workers make extensive use of Algebra 2, Trigonometry, Calculus, or Geometry on the job2

1. M. J. Handel survey of 2300 employees cited in “What Kind of Math Matters” Education Week, June 12 2007

2. Carnevale & Desrochers cited in “What Kind of Math Matters” Education Week, June 12 2007

TAKING MORE MATH IS NO GUARANTEE

43% of ACT-tested Class of 20051 who earned A or B grades in Algebra II did not meet ACT College Readiness Benchmarks in math (75% chance of earning a C or better; 50% chance of earning a B or better in college math)

25% who took more than 3 years of math did not meet Benchmarks in math

(NOTE: these data are only for those who took the ACT tests)

ACT, Inc. (2007) Rigor at Risk.

MATH-IN-CTEA 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.

1. What we did

2. What we found

3. What we learned

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

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?

National Research Center

AutoTech

Experimental

Control

BusEd

Experimental

Control

IT

Experimental

Control

Ag P&T

Experimental

Control

Health

Experimental

Control

Sample 2004-05: 69 Experimental CTE/Math teams and 80 Control CTE Teachers

Total sample: 3,000 students*

Study Design 04-05 School Year

STUDY DESIGN: PARTICIPANTS

Participants

Experimental CTE teacher

Math teacher

Control CTE teacher

Liaison

Primary Role

Implement the math enhancements

Provide support for the CTE teacher

Teach their regular curriculum

Administer surveys and tests

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) Focus of the experimental intervention

was naturally occurring math (embedded in curriculum)

A model of Curriculum Integration Monitoring 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

THE EXPERIMENTAL TREATMENT

Professional Development The Pedagogy

PROFESSIONAL DEVELOPMENT

CTE-Math Teacher Teams; occupational focus

Curriculum mapping Scope and Sequence On going collaboration CTE and

math teachers

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

WHAT WE FOUND: MAP OF MATH CONCEPTS ADDRESSED BY ENHANCED LESSONS BY SLMP

Math Concept

Number of Corresponding CTE Math Lessons Addressing the Math Concept

Site A Site B Site

CSite 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

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

DEVELOPING THE PEDAGOGY: CURRICULUM MAPS

Begin with CTE Content Look for places where math is part

of the CTE content Create “map” for the school year Align map with planned curriculum

for the year (scope & sequence)

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

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 Identification

Health Skill Mathematics Content Standards

Michigan Content Standard

Analyze methods for the control of disease.

Prognosis and diagnosis

Body 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

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

OHM’S LAW IN AUTOMOTIVE CLASS

AUTO TECH – ELECTRICAL (PARTIAL)

Lesson Topic CTE Concepts Math Concepts NCTM Standards

Voltage, Current, Resistance and Ohm’s Law

Voltage, Current, Resistance and Ohm’s Law

Whole numbers; decimals and fractions (adding, subtracting, multiplying and dividing); solving linear equations; ratio proportion; system of equations; metric to metric conversions; metric prefixes; reading and writing percents

N8, N9, A2, M0, M1, P15, P16

Series and Parallel Circuits

Series and Parallel Circuits

Decimals and fractions (adding, subtracting, multiplying and dividing); solving linear equations; ratio proportion; system of equations; metric to metric conversions; substituting data into formulas; working with reciprocals

N8, N9, A7, A8, A9, A11, P2, P15

Electrical Components

Electrical Components

Solving linear equations; percents; temperature; comparing numbers; linear measurement

N8, N9, A2, M0, M1, P2, P15

ELEMENT 1:

INTRODUCE THE AUTOMOTIVE LESSON

A student brought this problem to class:

He has installed super driving lights on a 12 volt system. His 15 amp fuse keepsblowing out. He has 0.4 Ohms of resistance.

ELEMENT 2:

FIND OUT WHAT STUDENTS KNOW: Discuss what they know about voltage,

amperes, and resistance.

Volt is a unit of electromotive force (E)Ampere is a unit of electrical current (I)Ohm is the unit of electrical resistance (R)

ELEMENT 2:

FIND OUT WHAT STUDENTS KNOW: What is an Ohm? Where did the name come from? Georg Ohm was a German physicist.

In 1827 he defined the fundamental relationship between voltage, current, and resistance.

Ohm’s Law: E = I R

ELEMENT 3:

WORK THROUGH THE EMBEDDED PROBLEM: The student has installed super

driving lights on a 12 volt system. His 15 amp fuse keeps blowing. He has 0.4 Ohms of resistance.

ELEMENT 3:

WORK THROUGH THE EMBEDDED PROBLEM: Continue bridging the automotive

and math vocabulary. The basic formula is:

E = I R

We know E (volts) and R (resistance).We need to find I (amps).

ELEMENT 3:

WORK THROUGH THE EMBEDDED PROBLEM: We need to isolate the variable. We do that by dividing IR by R, which

leaves I by itself. What you do to one side of the

equation you must do to the other...therefore E is alsodivided by R.

I = E / R

ELEMENT 3:

WORK THROUGH THE EMBEDDED PROBLEM:

I = E / R

I = 12 / 0.4

I = 30 amps

The student needs a 30 amp fuse to handle the lights.

ELEMENT 4:

WORK THROUGH RELATED, CONTEXTUAL EXAMPLES A 1998 Ford F-150 needs 180

starting amps to crank the engine. What is the resistance if the voltage is 12v?

R = E / I

R = 12 / 180

R = .066... Ohms

ELEMENT 4:

WORK THROUGH RELATED, CONTEXTUAL EXAMPLES If the resistance in the rear tail light

is 1.8 Ohms and the voltage equals 12v, what is the amperage?

I = E / R

I = 12 / 1.8

I = 6.66 amps

ELEMENT 4:

WORK THROUGH RELATED, CONTEXTUAL EXAMPLES

A 100-amp alternator has 0.12 Ohms of resistance. What must the voltage equal?

E = I R

E = 100(0.12)

E = 12 volts

ELEMENT 5:

WORK THROUGH TRADITIONAL MATH EXAMPLES The formula for area of a rectangle is A = LW

where A is the area, L is the length and W is the width.

Find the area of a rectangle that has a length of 8 ft. and an area of 120 sq. ft.

A / L = W120 sq ft / 8 ft = W15ft = W

ELEMENT 5:

WORK THROUGH TRADITIONAL MATH EXAMPLES The formula for distance is D = RT where D is the

distance, R is the rate of speed in mph and T is the time in hours.

If a car is traveling at an average speed of 55 mph and you travel 385 miles, how long did the trip take?

D = RTT = D / RT = 385 / 55 mphT = 7 hours

ELEMENT 6:

STUDENTS DEMONSTRATE UNDERSTANDING

Students now given opportunities to work on similar problems using this concept:

HomeworkTeam/group workProject work

ELEMENT 6:

STUDENTS DEMONSTRATE UNDERSTANDING

A vehicle with a 12 volt system and a 100 amp alternator has the following circuits:

30 amp a/c heater30 amp power window/seat15 amp exterior lighting10 amp radio7.5 amp interior lighting

1. Find the total resistance of the entire electrical system based on the above information.

2. Find the unused amperage if all of the above circuits are active.

ELEMENT 7:

FORMAL ASSESSMENT

Include math questions in formal assessments... both embedded problems and traditional problems that emphasize the importance of math to automotive technology.

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

ANALYSIS

C XPost Test Spring

Terra Nova Accuplacer WorkKeys Skills Tests

Difference in Math Achievement

Pre Test Fall

Terra Nova

WHAT WE FOUND: ALL CTEX VS ALL CTECPOST TEST % CORRECT CONTROLLING FOR PRE-TEST

0

10

20

30

40

50

60

ExperimentalClasses

ControlClasses

TerraNova

AccuPlacer

Work Keysp=

.03

p=

.02

p=

.08

50thpercentil

e

71st

C Group

0 50th 100th

X Group

MAGNITUDE OF TREATMENT EFFECT – EFFECT SIZE

Ter

ra N

ova

the average percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant

Acc

upl

acer

67th

Carnegie Learning Corporation Cognitive Tutor Algebra I d=.22

WHAT WE FOUND: 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%

POWER OF THE NEW PROFESSIONAL DEVELOPMENT MODEL

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 Surpris

e!

DOES ENHANCING MATH IN CTE

Affect Technical Skill Development?

NO!

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 curriculaE. CTE teachers are teachers of “math-in-

CTE” NOT math teachers

FINAL THOUGHTS: MATH-IN-CTE

A powerful, evidence based strategy for improving math skills of students;

A way but not THE way to help high school students master math

(other approaches – NY BOCES) Not a substitute for traditional math

courses Lab for mastering what many

students learn but don’t understand Will not fix all your math problems

[email protected]