UNIVERSITY OF ALASKA ANCHORAGE ALASKA DEPARTMENT OF EDUCATION & EARLY DEVELOPMENT Naked Math Gets a CTE Cover-up UAA Dr. Sally Spieker [email protected]

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


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


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


Body Structures


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


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


EEDMarcia Olson


Research by National Research Center for Career & Technical Education

Documents

UNIVERSITY OF ALASKA ANCHORAGE ALASKA DEPARTMENT OF EDUCATION & EARLY DEVELOPMENT Naked Math Gets a CTE Cover-up UAA Dr. Sally Spieker [email protected]