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Making Math Work Building Academic Skills in

Context

- James R. Stone III
- Director
- James.Stone_at_Louisville.edu

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.

1. What we did 2. What we found 3. What we

learned

Reminder-The issue12th Grade Math Scores 2005

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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

- M. J. Handel survey of 2300 employees cited in

What Kind of Math Matters Education Week, June

12 2007 - 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.

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?

Study Design Participants

- Participants
- Experimental CTE teacher
- Math teacher
- Control CTE teacher

- Primary Role
- Implement the math enhancements
- Provide support for the CTE teacher
- Teach their regular curriculum

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

Study Design 04-05 School Year

Sample 2004-05 69 Experimental CTE/Math teams

and 80 Control CTE Teachers Total sample

3,000 students

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

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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

Sample Curriculum Map

What we found Map of Math Concepts Addressed by

Enhanced Lessons by SLMP

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

Ohms Law in Automotive Class

Auto Tech Electrical (partial)

Element 1Introduce 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 keeps
- blowing out. He has 0.4 Ohms of
- resistance.

Element 2Find 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 2Find 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.
- Ohms Law E I R

Element 3Work 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 3Work 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 3Work 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 also - divided by R.
- I E / R

Element 3Work 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 4Work 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 4Work 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 4Work 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 5Work 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 W
- 120 sq ft / 8 ft W
- 15ft W

Element 5Work 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 RT
- T D / R
- T 385 / 55 mph
- T 7 hours

Element 6Students demonstrate understanding

- Students now given opportunities to work on

similar problems using this concept - Homework
- Team/group work
- Project work

Element 6Students demonstrate understanding

- A vehicle with a 12 volt system and a 100 amp

alternator has the following circuits - 30 amp a/c heater
- 30 amp power window/seat
- 15 amp exterior lighting
- 10 amp radio
- 7.5 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 7Formal Assessment

- Include math questions in formal assessments...

both embedded problems and traditional problems

that emphasize the importance of math to

automotive technology.

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

Analysis

Pre Test Fall Terra Nova

Difference in Math Achievement

X

Post Test Spring Terra Nova Accuplacer WorkKeys

Skills Tests

C

What we found All CTEx vs All CTEcPost test

correct controlling for pre-test

Magnitude of Treatment Effect Effect Size

Accuplacer

Terra Nova

the average percentile standing of the average

treated (or experimental) participant relative to

the average untreated (or control) participant

50thpercentile

X Group

C Group

71st

0

50th

100th

67th

Carnegie Learning Corporation

Cognitive Tutor Algebra I

d.22

Why

- Ebbinghaus effect refreshing or relearning

previously learned material - Spillover effect math skills developed in one

area improve performance in others - Vocabulary effect math as a foreign language

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

Old Model PD

Total Surprise!

New Model PD

Does Enhancing Math in CTE

- Affect Technical Skill Development?

NO!

Replicating the Math-in-CTE ModelCore

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

Challenges

- Professional development time
- Lack of fit flow of content among classes
- Resistance of some teachers to change
- Must be more than a few integrated

activities/lesson plans - Building communities of practice Academy (sub)

networks?

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

dont understand - Will not fix all your math problems

Technical Assistance

- Replicating the Math-in-CTE approach in your state

Technical Assistance

- Replicating the Math-in-CTE approach in your state

Necessary Ingredients for Replication

- 1. Communities of practice
- A. 10 CTE-Math Teacher teams or 20-20
- B. Specific occupational foci
- C. Invite not compel
- 2. Administrator support
- A. Professional Development (532) for at
- least one full year
- B. PD support (facilities, substitutes, etc.)
- D. Staff the structure

Staffing the Technical Assistance

www.nccte.org

- James.stone_at_nrccte.org