Philosophy of Teaching and Learning?

COL Alex Heidenberg

Ideas from Lowman, Bain, & Sousa

“Would your class have been different if there was a different group of students?”

unknown

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Why?

Student Types (Learners)R.D. Mann

Compliant Student Anxious-Dependent Student Discouraged Student Independent Heroes Sniper Attention Seeking Student Silent

Joseph Lowman, Mastering the Techniques of Teaching

Compliant Student Good student Tell them what to do – teacher dependent Learn what instructor wants (19-2) Speak to agree with instructor

Anxious Dependents Excessive concern with grades (20-1) Frazzled; complain about “trick” questions Low self-esteem

Discouraged workers Worked hard in the past, but burned out Little control of learning (19-2)

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Independent High performers High participators Make friends with the instructor (5-16)

Heroes Try to impress early, show interest and knowledge (15-6) Fail to deliver

Snipers Hostile, little hope that they will be recognized. Cynical (5-16)

Attention Seekers Social butterflies (social needs trump intellectual) (7-14) Organize group study (6-15)

Silent (8-13) Afraid instructor will not think highly of them Hard to classify

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How We LearnBain- Ch. 2

Knowledge is Constructed, not received; Questions are Crucial – help construct

knowledge; Mental Models Change Slowly;

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How We LearnA Private Universe

A Private Universe Video

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How We LearnBain- Ch. 2

Knowledge is Constructed, not Learned; Questions are Crucial – help construct

knowledge; Mental Models Change Slowly; Caring is Crucial: WGAD; What Motivates/Discourages Students?

(Jul 23rd)

Tappers vs. Listeners

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Tappers vs. Listeners

1. Happy Birthday2. The Star Spangled Banner3. We Will, We Will Rock You – Queen4. I will Survive – Gloria Gaynor5. Do-Re-Me - Sound of Music6. Amazing Grace7. It’s a Small World After All – Disney8. The Sun Will Come Out Tomorrow – Annie9. I’m a Little Tea Pot10.Hail to the Chief

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Tappers vs. Listeners

1. Happy Birthday2. The Star Spangled Banner3. We Will, We Will Rock You – Queen4. I Will Survive – Gloria Gaynor5. Do-Re-Me - Sound of Music6. Amazing Grace7. It’s a Small World After All – Disney8. The Sun Will Come Out Tomorrow – Annie9. I’m a Little Tea Pot10.Hail to the Chief

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The Curse of Knowledge

Helping Student’s Learn

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Knowledge

Comprehension

Application

Analysis

Synthesis

Eval

Remembering

Understanding

Applying

Analyzing

Evaluating

CreatingBloom’s Taxonomy

1971

RevisedBloom’s

Taxonomy

2001

Revised Bloom’s Taxonomy

Creating – Combine, Plan, Compose, Actualize

Evaluating – Rank, Assess, Conclude, Action

Analyzing – Order, Explain, Differentiate, Achieve

Applying – Classify, Experiment, Calculate, Construct

Understanding – Summarize, Interpret, Predict, Execute

Remembering – List, Describe, Tabulate, Appropriate Use

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Bloom’s Taxonomy

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If p is a polynomial, then

lim ( ) ( )x b p x p b

CreateEvaluateAnalyzeApplyUnderstandRemember

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9lim

2 3x

x

x x

CreateEvaluateAnalyzeApplyUnderstandRemember

1lim ( )x

f x

1

lim ( )x

f x

1lim ( )x

f x

5lim ( )x

f x

(5)f

CreateEvaluateAnalyzeApplyUnderstandRemember

Sketch the graph of the following function and determine and

1lim ( )x

f x 1

lim ( )xf x

2

2 - if -1

( ) if -1 1

( 1) if 1

x x

f x x x

x x

CreateEvaluateAnalyzeApplyUnderstandRemember

Sketch the graph of a function f that satisfies all

of the following conditions:

   

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1)(lim0

xfx

1)(lim0

xfx

1)2( f

0)(lim2

xfx

1)(lim2

xfx

undefined)0( f CreateEvaluateAnalyzeApplyUnderstandRemember

Students Learn Best (Critical Thinking):Bain Pg. 85-86.

Consciously raising the questions, what do we know? How do we know?;

Clearly and explicitly aware of gaps in information;

Discrimination between observation and inference;

Probing for assumptions;

Test one’s own line of reasoning for internal consistency.

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Closing Thoughts

Mathematical Problem Solving is the art of transforming representations until the solution is visible.

One of the core skills of a mathematician is to simultaneously hold different representations of a (mathematical) object in his or her mind and to choose the one that is most useful in a given context.

Bernhard Kutzler

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