UNIVERSITY OF ALASKA ANCHORAGE
ALASKA DEPARTMENT OF EDUCATION & EARLY DEVELOPMENT
Naked Math Gets a CTE Cover-up
UAADr. Sally Spieker
[email protected] 907-786-6498
EEDMarcia Olson
[email protected] 907-465-8704
Research by National Research Center for Career & Technical Education
Questions to think about . . .
Do math and CTE teachers collaborate at your school or district?
Do math teachers know what math concepts kids need in CTE courses?
Do CTE teachers use the same math vocabulary and algorithms that are used in math class?
Let’s Look at Some Trends
1.7 Math
Credits
3.6 math
credits
3.8 math credits3.4
math credits
Source: NAEP Trends in Academic Progress
How Can We Increase Math Achievement?
One way – not THE ONLY way – to help increase math achievement
A model of curriculum integration and pedagogy to increase CTE students’ math achievement while maintaining technical skill attainment.
Students showed significantly higher math achievement on Terra Nova and Accuplacer
For complete research results, see NRCCTE
Core Principles of the Model
Community of practice is criticalBegin with the CTE curriculum –
NOT the math curriculumMath is an essential workplace skillMaximize the math in the CTE curriculumCTE teachers are teachers of math-in-CTE
– they are not math teachers
What is the Model?
1 CTE Teacher + 1 Math Teacher = 1 TeamEach team
Maps the CTE curriculum Identifies embedded math concepts Creates math-enhanced lessons
CTE teacher delivers the lessonsCTE teacher and math teacher continue to
collaborate before and after each math-enhanced lesson is delivered
What is a “Math-Enhanced CTE Lesson” ?
Introduce the CTE lessonAssess students’ math awarenessWork through the math example embedded in
CTE lesson – using standard math vocabularyWork through related, contextual
math-in-CTE examplesWork through “naked math” examplesFormative assessment Summative assessment includes math
questions
Sample Curriculum Map – Healthcare
CTE Course or Unit
CTE Concepts or Applications
Embedded Math Concepts
Diseases Work-place safety, body
mechanics and disease prevention practices
Basic human anatomy and physiology, growth, development, wellness and disease.
Relationship between diseases /disorders to the environmental or genetic causes.
Statistics Whole numbers Interpreting data Temperature Charts and graphs Percentages Graphing Probability
Growth and Develop-ment
Basic human anatomy and physiology, growth, development, wellness and disease.
Proportion Charts and graphs Estimation Weights Percents Reading interpreting
data Whole numbers
Health Careers
Potential health science careers required education, and opportunities.
Measure and perform calculations.
U.S health care system and the interdependence of careers and professionals.
Statistics Cost/benefit ratio Computation Ratios Decimals Conversion Trends Charts/ graphs
CTE Course or Unit
CTE Concepts or Applications
Embedded Math Concepts
Body Structures
Basic human anatomy and physiology, growth, development, wellness and disease.
Basic anatomy and physiology of body systems and topographic terms.
Quadrants Planes Measuring Ratios
Skeletal System
Basic anatomy and physiology of the skeletal system.
Measurements Angles Formulas Positive and
negative numbers
EstimationIntegu-mentary System
Body surface area Wound Area
Percent Surface area Area
Respiratory System
Major structures of the respiratory system
Managing the airway.
Volume Estimation Dilation
Sample Curriculum Map – Construction
CTE Course or
Unit
CTE Concepts
or Applicatio
ns
Embedded Math Concepts
Construction
Floor systems
• Area perimeter• Measurement• Estimation• Ratio• Whole numbers• Interpret tables• Two dimensional drawings• Scaling
Construction
Scaling/ conversions
• Ratios/ proportions• Fractions & Decimals• Measurement• Factors• Inverse fractions• Two and three dimensional drawings• Point of reference• Linear equations• Quadratic equations• Area
Construction
Electricity • Units• Direct variation• Indirect variation• Solve equations• Schematics• Formulas• Percent• Average
CTE Course or Unit
CTE Concepts or Applications Embedded Math Concepts
Construction Doors and windows • Ratios• Tolerances• Formulas• Whole numbers & Fractions• Measurement
Construction Squaring • Pythagorean theorem• Congruence• Measurement• Whole numbers & Fractions
Construction Measurement • Linear measurement• Area• Angle measurement• Fractions• Ratios/ proportions
Construction Walls • Measurement- linear• Area• Whole number operations• Fractions & Decimals• Pythagorean theorem
Construction Roofing • Slopes• Trig• Area• Conversion• Fractions• Pythagorean theorem• Linear equations
The Model does NOT . . .
Force extra math into the CTE programCreate a mentoring or coaching relationship –
the teachers are partnersInclude developing or re-designing
curriculumUse “team-teaching”, i.e., math teacher does
not teach in the CTE classAbove all, it does NOT make the CTE
class into a math class
Statewide Participants in Math-in-CTE
2010-2011 Anchorage Denali Fairbanks Ketchikan Mat-Su
Bering Strait
Craig Fairbanks Kenai
Ketchikan
Mat-Su Unalaska Valdez UAA
2011-2012
* 5 Construction Teams* 5 Health Careers Teams* 1 Transportation Team
* 8 Construction Teams* 4 Health Careers Teams
Alaska Team Reactions
CTE teachers: Now I know why my construction students can’t
subtract ¼” from 15” in their heads! Now I know the correct math vocabulary for the
3-4-5 stair riser lesson. You mean a ratio is not the same as a proportion?
Math teachers: I had no idea there was so much math in the CTE
class. I see that my students need practice in
performing ‘mental math’ for use in real life. Now I know why we really do teach this stuff!
A Sample Math-Enhanced Lesson
SCALINGDRAWINGS
Developed by Dave Oberg and Jen Nelson, Service High School, Anchorage School District, 2010
What would you need to know before you begin your drawing?
1. Dimensions of the building.
2. Size of the paper you are going to print the plans on.
What are standard paper sizes? A: 8.5” X 11”B: 11” X 17”
C: 18” X 24”D: 24” X 36”
What is the relationship between the size of the building and the size of
the paper?
How many times larger is the building
footprint than the paper it must fit on?
What units would be used on the drawing? The building?
What does the term “scale” mean?The fraction used to represent the ratio making the drawing and building proportional.
A ratio is a comparison of two things expressed as a fraction. In drafting, the drawing measure is
always given first, followed by the measurement of the actual
building.
So, what is meant by “ratio”?
A proportion is an equation showing that 2 ratios are
equivalent.
Then, what is a proportion?
Let’s say we have a building whose floor plan footprint is 120’ X 40’. What size paper would we need to use if our
drawing is to be done at a scale of ¼” = 1’?
¼” = 1’;therefore the ratio is 1/4.
Set up a proportion for each dimension:
Inches 1 = L and 1 = W Feet 4 120 4 40
Cross multiply to create an equation
4L = 120 and 4W = 404 4 4 4 Divide by 4 to solve.
L = 30 inches and W = 10 inches Therefore, we would need to use D-size (36” X 24”) paper.
Your client wants you to design a warehouse that is 40’ x 200’. What size paper should be used, and what scale should be used, for the
blueprints of the building?
Trying the ratio of ¼ first:1 = W and 1 = L 4 40 4 200
Cross multiply to create an equation,4W = 40 and 4L= 2004 4 4 4 Divide by 4 to solve.
W = 10 inches and L = 50 inches The width at this scale is too large for D-size paper.
Trying the ratio of 1/8:1 = W and 1 = L 8 40 8 200Cross multiply to create an equation,8W = 40 and 8L = 200 8 8 8 8 Divide by 8 to solve.
W = 5 inches and L = 25 inches
At this scale the size would fit on D-size
paper, but would not fit on C-size paper.
Therefore, the drawing must be at 1/8” = 1’ on
D-size paper.
Each day, the seals at an aquarium are each fed 1 pound of food for every 10 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day?
One pound of food per 10 pounds of body weight is equivalent to a ratio of 1/10. Set up a proportion using food to body weight.
Pounds of food 1 = _x_ Body weight of seal 10 280
Cross Multiply to get the equation: 10x = 280
10 10 Divide by 10 to solve.
x = 28 pounds of food per day
“Naked Math” Problems
In teams of 2-3 students, use a tape measure to find the dimensions of this classroom (wall to wall).
Determine the appropriate scales to use for each common paper size (if possible).
Questions?
UAADr. Sally Spieker
[email protected] 907-786-6498
EEDMarcia Olson
[email protected] 907-465-8704
Research by National Research Center for Career & Technical Education