Any Excuse for Math!Learning Math in a T&I Context

toAbstract Math Learning

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f(x) = x² − 14 x + 49Series1

Polynomial (Series1)

Run the Show and Click Here for Math Resources

Mathematics Testing•T&I concentrators performed lowest on standardized mathematics tests.•This happens before students enroll in T&I.•DPI wants all T&I teachers to help strengthen mathematics skills of its students.

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Research•To improve math performance of CTE students•The National Research Center in CTE•Treatment group versus control group•2000 students and 131 teachers•1 year treatment•Treatment group significantly outperformed control group on standardized (Accuplacer) testing•No difference in CTE related achievement

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Transfer of Learning•When you learn something in one setting or context, can you apply that concept or construct in another, unrelated context?•Adults can sometimes transfer learning after years of incidental practice.•Students don’t automatically transfer their learning.•They need to be taught how to do this.

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Research on Transfer•Transfer might be context dependent.•If I learn a math construct that helps me in carpentry, I might use it again in a similar carpentry situation.•I’m not likely to naturally apply it to shopping for groceries.•Grocery shopping lacks the contextual prompt that causes me to realize the applicability.

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Concrete to Abstract•Standardized math tests are more abstract than using math in an applied situation like you would find happening in T&I labs.•T&I teachers will need to teach in context•AND then teach toward the abstract.

That is,teach away from the contextual prompt.

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Mathematics TargetsBecause most T&I students have survived some math upon arriving at your labs:•Algebra I (review and skill strengthening)•Geometry (may currently be enrolled)and•Any math courses in which you know your students are enrolled.

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Curriculum Integration•Team teaching (not practical)

•Close coordination (somewhat more practical)

•Loose coordination (probably best for this situation)

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The Hardest Part•Identifying grade-level math applicable to T&I

•T&I Blueprints and Course Outlines show the math currently, naturally being taught in T&I.

•That math is inherently necessary to succeed in the particular trade or technical area.

•But it’s not Algebra or higher.

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Any Excuse for Math

In addition to teaching necessary math in T&I:

•Teach math that COULD be taught but isn’t being taught.

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MotivationIt won’t just provide more practice.It will provide motivation.

Why do we have to know this?

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Simple ExampleThe 3-4-5 rule in carpentry helps the carpenter make sure that a corner of a structure is square.

In addition, teach the Pythagorean Theorem.

A2 + B2 = C2

And solve for an unknown.

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Seven-Step Model1. Introduce the T&I lesson.2. Assess students’ math awareness of T&I lesson.3. Demonstrate the math as applied to T&I lesson.4. Demonstrate a few more applied examples.5. Demonstrate non-applied math examples

(traditional math).6. Have students apply the math to the T&I task at

hand AND have them work the math traditionally.7. Formal assessment.

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Seven-Step ModelThe National Center’s report will be posted on

the CTE conference website.Pages 12 & 13 present the model in detail.

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Get Help1. Look over math blueprint for target skills.2. Match those skills to what you need to teach

in T&I.3. It’s not the math that is being taught in T&I.

It’s what could be taught in T&I.4. Get the math teacher (or an engineer T&I

teacher) to help you with your own math.5. Look over the Resource CD that will be

posted on the conference website.

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Assessment• For the T&I application, it’s the usual

assessment.• For math, by the end assessment should

focus on:1. Students showing the process for working

the math, and2. Correct answers.3. See the math teacher for extra problems to

work.

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Key to SuccessWithout slowing your own blueprint progress:• High frequency of engagement in math.• Start out teaching the math in context.

• By the end of the lesson, students are also working traditional math problems.

Math Resources CD

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Seven StepsTaken directly from the National Center report.1. Introduce the CTE lesson.• Explain the CTE lesson.• Identify, discuss, point out, or pull out the math embedded in the CTE lesson.2. Assess students’ math awareness as it relates to the CTE lesson.• As you assess, introduce math vocabulary through the math example embedded in the CTE.• Employ a variety of methods and techniques for assessing awareness of all students, e.g., questioning, worksheets, group learning activities, etc.

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Seven Steps, cont.3. Work through the math example embedded in the CTE lesson.• Work through the steps/processes of the embedded math example.• Bridge the CTE and math language. The transition from CTE to math vocabulary should be gradual throughout the lesson. 4. Work through related, contextual math-in-CTE examples. Using the same math concept embedded in the CTE lesson:• Work through similar problems/examples in the same occupational context.• Use examples with varying levels of difficulty; order examples from basic to advanced.• Continue to bridge CTE and math vocabulary.• Check for understanding.

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Seven Steps, cont.5. Work through traditional math examples.Using the same math concept as in the embedded and related, contextual examples:• Work through traditional math examples as they may appear on tests.• Move from basic to advanced examples.• Continue to bridge CTE and math vocabulary.• Check for understanding.

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Seven Steps, cont.6. Students demonstrate their understanding.• Provide students opportunities for demonstrating their understanding of the math concepts embedded in the CTE lesson.• Conclude the math examples back to the CTE content; conclude the lesson on the topic of CTE.7. Formal assessment.• Incorporate math questions into formal assessments at the end of the CTE unit/course.

Math Resources CD

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