Philosophy of Teaching and Learning? COL Alex Heidenberg Ideas from Lowman, Bain, & Sousa
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Transcript of Philosophy of Teaching and Learning? COL Alex Heidenberg Ideas from Lowman, Bain, & Sousa
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Philosophy of Teaching and Learning?
COL Alex Heidenberg
Ideas from Lowman, Bain, & Sousa
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“Would your class have been different if there was a different group of students?”
unknown
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Why?
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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
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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)
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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
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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
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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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2
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9lim
2 3x
x
x x
CreateEvaluateAnalyzeApplyUnderstandRemember
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1lim ( )x
f x
1
lim ( )x
f x
1lim ( )x
f x
5lim ( )x
f x
(5)f
CreateEvaluateAnalyzeApplyUnderstandRemember
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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
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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
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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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