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Making math work An evidence-based approach to

improving math skills of high school students

- James R. Stone III
- Director

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

Background What do we know about CTE?

- CTE does not necessarily limit postsecondary

education (NAVE, 2004 Stone Aliaga, 2004 but

see Deluca et al., forthcoming) - There is evidence that math and science course

taking by CTE students is increasing amount and

complexity (NAVE, 2004 Stone Aliaga, 2004) - CTE as a function of the HS experience reduces

the probability of dropping out of school (Plank,

2001, 2005 Castellano et al 2006) - CTE is an economic value to the individual and

the community (ROI) (Bishop Mane, 2004 NAVE,

2004Hollenbeck, 2001) - It is possible to major in CTE and Academics

(NAVE, 2004)

What else do we know? CTE enrolls many students

who are the focus of closing the achievement

gap

Levesque, K. (2003). Public High School Graduates

Who Participated in Vocational/Technical Education

Major Issues of HS Reform

- Engagement attending school and completing

(graduating) high school - Achievement academic (and technical) course

taking grades, test scores - Transition to postsecondary education without

the need for remediation and to the workplace

National Graduation Rates 1998 and 2001 The

problem of engagement

of 9th Graders who complete High School

68

Source One-Third of a Nation (ETS, 2005)

Carnegie Grows!

CTE and School Engagement

Source Plank, 2001

CTE and Drop Out Reduction The Debate Continues

- NAVE, 2004 No effect (NELS88 - Class of 1992

data) - Plank, 2001 Significant effect, especially for

low ability youth (NELS 88 - Class of 1992 data)

Plank, forthcoming. NLSY97 Transcript

data

When do they leave?

9th grade 10th grade

11th grade 12th grade 5th year

From Plank, forthcoming

Graduation School and CTE Effects

From Castellano, Stringfield Stone, Forthcoming

CTE Structures and Pedagogies and Dropping Out

- Students in or Career Majors are 16 more likely

to graduate from high school. - Students in Tech Prep are 30 more likely to

complete high school. - Students who participated in specific STW

activities are 18 more likely to complete high

school.

Stone Aliaga, in press

Do CTSOs Add Value to CTE?

Comparisons

General Student Population Class (same school)

CTE Class with CTSO

General Student Population Class (same school)

CTE Class-No CTSO

Preliminary Findings (NRCCTE, forthcoming)

- Compared to the general population of students
- No direct effect of CTSO on grades (student

self-report) - Being in a CTSO positively affects academic

motivation and engagement - General student population and CTSO students have

different educational aspirations (4-year vs.

2-year) more realistic?

- Within CTSOs
- Experience of SCANs type skills in the classroom

positively affects career self-efficacy and

grades - Degree of participation in the CTSO positively

affects grades, aspirations, career

self-efficacy, academic engagement, self-esteem,

and civic engagement the more participation,

the better - Effect is strongest for competitive events

Academic Achievement of Youth in CTE Articulated

Programs

Development of Skills

Transition to college The Challenge

31 Leave with 0 Credits

68 Graduate HS in 4 Years

18 GraduateCollege in 4 Years

100 Start 9th Grade

40 Start College

27 Start Sophomore Year

31

Source Education Weekly March 2005

College for All The Reality

Percentages by Race and Ethnicity

- By age 29
- 34 of white
- 18 of African Americans
- 10 of Hispanic
- Have bachelors degrees

Hoffman, N. (2003)

Venezia, A., M. W. Kirst, et al. (2003)

College Degree At What Cost?

According to the Public Interest Research Group's

Higher Education Project, 39 percent of new

graduates with loans carry an "unmanageable debt,"

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 An evidenced based approach to

improving academic performance of CTE students

The Problem Math PerformanceOf American Youth

NAEP Scores for 17 Year olds

More ProblemsScience Performance 17 Year Olds

A Nation At Risk

The number of 17-year-old students taking

advanced math classes has also increased -- with

17 percent studying calculus and 53 percent

studying second-year algebra -- it is unclear

why that trend has not resulted in higher average

math scores over all.

http//nces.ed.gov/nationsreportcard/ltt/results20

04/

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 found 2. What we learned

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 Key Features

- Random assignment of teachers to experimental or

control condition - CTE teachers were the teachers of math in study
- 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

Math-in-CTE Experimental Treatment What we

tested

- Professional Development
- Curriculum mapping
- Development of math-enhanced lessons
- Scope Sequence
- On-going math support

What we tested The Seven Elements

- 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

What we found Map of Math Concepts Addressed by

Enhanced Lessons in each SLMP

What we found (results) All CTEx vs All

CTEcPost test correct controlling for pre-test

p.08

p.03

p.02

Results follow one year of implementation in one

CTE class

What we found Site level analyses

Only Significant effects shown

Magnitude of Treatment Effect Effect Size

Measure

Effect Size Cohens d .80

the average percentile standing of the average

treated (or experimental) participant relative to

the average untreated (or control) participant

50thpercentile

X Group

C Group

79thpercentile

0

50th

100th

Example of an effect size of .80

What we found Magnitude of effect

Effect size (Cohens d) All Classes Terra

Nova (d.34) Accuplacer

(d.17) By Site Site A WorkKeys

(d2.8) 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
- 62nd
- 56th
- 99th
- 76th
- 81st
- 74th
- 66th

Comparison Carnegie Learning Corporation

Cognitive Tutor

Algebra I d.22

Does Enhancing Math in CTE

- Affect Technical Skill Development?

No difference in four sites experimental

students scored significantly higher in one site

plt.10

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 in one

CTE class

What we learned

- When We Began (assumptions)
- A box of curriculum
- Individual teacher training
- Replicable by individual teachers

- After the Study, we know
- A curriculum development is a process
- Replicable by teams of committed teachers working

together over time - Core Principles

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

What we are and are not A contextual continuum

- 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

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 - Not a substitute for traditional math courses
- Lab for mastering what many students learn but

dont understand

For more information

- James R. Stone III
- stone003_at_umn.edu

The University of Minnesota 612-624-1795