Transcript www.montanaacte.org
Making Math Work: Building Academic Skills in Context
James R. Stone III Director [email protected]
REMINDER-THE ISSUE 12 TH GRADE MATH SCORES 2005
A CAUTIONARY NOTE
94% of workers reported using math on the job, but, only 1 22% reported math “higher” than basic 19% reported using “Algebra 1” 9% reported using “Algebra 2” Among upper level white collar workers 1 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 job 2 1.
2.
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 2005 in math earning a B or better in college math) 1 who earned A or B grades in Algebra II did not meet ACT College Readiness Benchmarks (75% chance of earning a C or better; 50% chance of 25% who took
more than 3 years
did not meet Benchmarks in math of math
(NOTE: these data are only for those who took the ACT tests)
ACT, Inc. (2007)
Rigor at Risk
.
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. 2.
3.
What we did What we found 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?
Study Design 04-05 School Year
AutoTech BusEd Experimental Experimental Control Control National Research Center IT Ag P&T Health Experimental Experimental
Experimental
Control Control
Control Sample 2004-05: 69 Experimental CTE/Math teams and 80 Control CTE Teachers Total sample: 3,000 students*
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 General, grade level tests (Terra Nova, AccuPlacer, WorkKeys) Technical skill or occupational knowledge assessment 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
5 Days Professional Development 2 Days Professional Development 2 Days Professional Development Teach Lessons Teach Lessons On-going monitoring of teacher progress Teach Lessons I Day Wrap-up Celebration
WHAT WE FOUND: MAP OF MATH CONCEPTS ADDRESSED BY ENHANCED LESSONS BY SLMP Math Concept Number and Number Relations Computation and Numerical Estimation Operation Concepts Measurement Geometry and Spatial Sense Data Analysis, Statistics and Probability Patterns, Functions, Algebra Trigonometry Problem Solving and Reasoning Communication Number of Corresponding CTE Math Lessons Addressing the Math Concept Site A
8 8
0
5
0
11 7
0 0 1 Site B
4 7
0
7
1
9
1 0 1 1 Site C 0 0
4 6
1
3
0
4 3
0 Site D Site E
5
0
3
0
10 12
0 0 0 1 2 2 0 0 2
12
0
12
2
4
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 Determine pipe size and water flow rates for a water pump Problem solving involving cross-sectional area, volume, and related rates 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 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 Skill Health Standards Identification Mathematics Content Standards Michigan Content Standard
Analyze methods for the control of disease.
Prognosis and diagnosis Body planes Range of motion Pharmacy calculations (for pharmacy techs 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. Analyze changes in body systems as they relate to disease, disorder and wellness Cultures and sensitivity Lab techniques Blood 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.
2.
3.
4.
5.
6.
7.
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
OHM’S LAW IN AUTOMOTIVE CLASS
AUTO TECH – ELECTRICAL (PARTIAL)
Lesson Topic CTE Concepts Voltage, Current, Resistance and Ohm’s Law Series and Parallel Circuits Electrical Components Voltage, Current, Resistance and Ohm’s Law Series and Parallel Circuits Electrical Components Math Concepts 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 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 Solving linear equations; percents; temperature; comparing numbers; linear measurement NCTM Standards N8, N9, A2, M0, M1, P15, P16 N8, N9, A7, A8, A9, A11, P2, P15 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 keeps blowing 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 I
by itself.
by
R
, which leaves 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 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 = W 120 sq ft / 8 ft = W 15ft = 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 = RT T = D / R T = 385 / 55 mph T = 7 hours
ELEMENT 6: STUDENTS DEMONSTRATE UNDERSTANDING
Students now given opportunities to work on similar problems using this concept: Homework Team/group work Project 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 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 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.
2.
3.
4.
5.
6.
7.
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
C
Pre Test Fall Terra Nova Difference in Math Achievement Post Test Spring Terra Nova Accuplacer WorkKeys Skills Tests
X
WHAT WE FOUND: ALL CTEX VS ALL CTEC POST TEST % CORRECT CONTROLLING FOR PRE-TEST
60 50 40 30 20 10 0
p
= .03
p
= .02
p
= .08
Experimental Classes Control Classes TerraNova AccuPlacer Work Keys
MAGNITUDE OF TREATMENT EFFECT – EFFECT SIZE
the average percentile standing of the average treated (or experimental) participant relative to the average untreated (or control) participant
0 C Group 50th percentile X Group 50th 71st 67th 100th 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 Old Model PD
Math in CTE Use 1 Year Later
Total Surprise!
0.8
0.6
0.4
0.2
0 Math teacher Partners Experimental CTE Teachers Control CTE Teachers New Model PD
Affect Technical Skill Development?
NO!
DOES ENHANCING MATH IN CTE
REPLICATING THE MATH-IN-CTE MODEL:
CORE PRINCIPLES
A.
B.
C.
D.
E.
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
FINAL THOUGHTS: MATH-IN-CTE
A powerful,
evidence based strategy
improving math skills of students; for
A
way but not
THE
way to help high school students master math (other approaches – NY BOCES) Not a substitute courses for traditional math
Lab
for mastering what many students learn but don’t understand Will
not
fix all your math problems