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
Why?
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Student Types (Learners)
R.D. Mann
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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
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Anxious Dependents
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Good student
Tell them what to do – teacher dependent
Learn what instructor wants (19-2)
Speak to agree with instructor
Excessive concern with grades (20-1)
Frazzled; complain about “trick” questions
Low self-esteem
Discouraged workers
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Worked hard in the past, but burned out
Little control of learning (19-2)
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Independent
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Heroes
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Hostile, little hope that they will be recognized.
Cynical (5-16)
Attention Seekers
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Try to impress early, show interest and knowledge (15-6)
Fail to deliver
Snipers
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High performers
High participators
Make friends with the instructor (5-16)
Social butterflies (social needs trump intellectual) (7-14)
Organize group study (6-15)
Silent (8-13)
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Afraid instructor will not think highly of them
Hard to classify
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How We Learn
Bain- Ch. 2
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Knowledge is Constructed, not received;
Questions are Crucial – help construct knowledge;
Mental Models Change Slowly;
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How We Learn
A Private Universe
A Private Universe Video
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How We Learn
Bain- Ch. 2
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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
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10.
Happy Birthday
The Star Spangled Banner
We Will, We Will Rock You – Queen
I will Survive – Gloria Gaynor
Do-Re-Me - Sound of Music
Amazing Grace
It’s a Small World After All – Disney
The Sun Will Come Out Tomorrow – Annie
I’m a Little Tea Pot
Hail to the Chief
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Tappers vs. Listeners
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Happy Birthday
The Star Spangled Banner
We Will, We Will Rock You – Queen
I Will Survive – Gloria Gaynor
Do-Re-Me - Sound of Music
Amazing Grace
It’s a Small World After All – Disney
The Sun Will Come Out Tomorrow – Annie
I’m a Little Tea Pot
Hail to the Chief
The Curse of Knowledge
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Helping Student’s Learn
Bloom’s Taxonomy
1971
Creating
Evaluating
Analyzing
Eval
Synthesis
Analysis
Application
Comprehension
Knowledge
Applying
Understanding
Remembering
Revised
Bloom’s Taxonomy
2001
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Revised Bloom’s Taxonomy
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Creating – Combine, Plan, Compose, Actualize
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Evaluating – Rank, Assess, Conclude, Action
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Analyzing – Order, Explain, Differentiate, Achieve
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Applying – Classify, Experiment, Calculate, Construct
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Understanding – Summarize, Interpret, Predict, Execute
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Remembering – List, Describe, Tabulate, Appropriate Use
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Bloom’s Taxonomy
Bloom’s Level
Increasing Level of Difficulty
Increasing Complexity
CREATE
Rewrite the story from the point
of view of the dog.
Rewrite the story from the points of
view of the dog and of the cat.
EVALUATE
Compare the two main
characters in the story. Which
would you rather have as a
friend and why?
Compare the four main characters in
the story. Which would you rather
have as a friend and why?
What were the similarities and
differences between this story
and the one we read about the
Civil War hero?
What were the similarities and
differences between this story, the
one we read about the Civil War hero,
and the one about the Great
Depression?
APPLY
Think of another situation that
could have caused the main
character to behave that way.
Think of at least three other situations
that could have caused the main
character to behave that way.
UNDERSTAND
Write a paragraph that
describes the childhood of any
one of the main character.
Write a paragraph that describes the
childhood of each of the four main
characters.
REMEMBER
Name the major characters in
this story.
Name the major characters and the
four locations in this story.
ANALYZE
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If p is a polynomial,
then
lim xb p( x)  p(b)
Create
Evaluate
Analyze
Apply
Understand
Remember
x 9
lim 2

x 3 x  2 x  3
2
Create
Evaluate
Analyze
Apply
Understand
Remember
lim f ( x) 
x 1
lim f ( x) 
x 1
lim f ( x) 
x  1
lim f ( x) 
x 5
f (5) 
Create
Evaluate
Analyze
Apply
Understand
Remember
Sketch the graph of the following function and determine
and
lim f ( x)
x  1
2 - x

f ( x)   x
( x  1) 2
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Create
Evaluate
Analyze
Apply
Understand
Remember
lim f ( x )
if x  -1
if -1  x  1
if x  1
x 1
Sketch the graph of a function f that satisfies all
of the following conditions:
lim f ( x)  1
x 0 
lim f ( x)  0
x2
lim f ( x)  1
x0
lim f ( x)  1
x2
f (2)  1
f (0)  undefined
Create
Evaluate
Analyze
Apply
Understand
Remember
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Students Learn Best (Critical Thinking):
Bain Pg. 85-86.
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Consciously raising the questions, what do we know?
How do we know?;
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Clearly and explicitly aware of gaps in information;
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Discrimination between observation and inference;
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Probing for assumptions;
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Test one’s own line of reasoning for internal consistency.
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Closing Thoughts
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Mathematical Problem Solving is the art of transforming
representations until the solution is visible.
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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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