Cognitive Theory: Powerful Tools for
Educators?
HAL Online
Mar 2, 2010
Goals for Topic 8: Understanding
Children’s Thinking
1. To better understand relationships and differences among
cognitive science, brain science and sociocultural theory;
to be able to discuss these views in terms of tools they
provide for educators.
2. To use ideas from cognitive science to analyze the problem
solving of learners and to better understand and improve
your own problem solving.
3. To understand and be able to discuss some important
relationships between problem solving and learning.
4. To enhance your awareness of how it feels to be a naive
learner; to be able to take a learner's perspective and
empathize with a learner's struggle to understand.
Goals for Topic 8: Understanding
Children’s Thinking
1. To better understand relationships and differences among
cognitive science, brain science and sociocultural theory;
to be able to discuss these views in terms of tools they
provide for educators.
Course Perspectives
 Social (Sociocultural)
 Lecture, instructional method
 Brain Science
 Blakemore & Firth Text
 Cognitive
 Halpern Text
Cognitive Theory
Long Term Memory
Prior Knowledge: Ideas,
Beliefs,Skills . . .
Constructs
Knowledge
Cognitive
Working
Effort
Memory
Focuses Attention
Senses
Eyes
Ears
Etc.
Information . . . Information . . . Information . . . Information . . .
Example Cognitive Theory: Piaget
 Active prior knowledge (schemas):
Interprets incoming experience
 If experience consistent with known:
 Assimilation
 If experience challenges known:
 cognitive dissonance
 reflection
 accommodation (old schemas change)
Cognitive Theory:
What Controls Learning?
 Learning Environment
 Teacher, instructional design features, etc.
 Other Stuff
 Intelligences, habits of mind, cultural background,
situational variables, opportunities to learn
 Learner
 Metacognitive “self-regulation”
 Strategies for self-motivation, memory, etc.
 Reflection
Cognitive Science Metaphors
 Information Processing
 Mind like computer
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Active knowledge construction
Effortful meaning making
Successful learning is schematic, organized
Abstract knowledge transfers to life
 Justification for most school disciplines
Misconceptions About Cognitive
Science
 Myth: Advocates direct Instruction (versus)
active learning environments
 Truth: ALL learning effortful, active; may
(or may not) occur during lecture or handson activity
Sociocultural + Cognitive
Prior Knowledge
Ideas, Beliefs
Skills . . .
Construct
Knowledge
Focuses
Attention
Effort
After
Meaning
Senses
Eyes
Ears
Etc.
Social Learning Environment:
Discourse . . . Tasks . . . Activities . . . Illustrations. . .Learning Tools . . .
Guidance . . . Norms
HAL Online
 How does this course try to model a
blended socio-cultural, cognitive and
brain-based approach?
The Towers Problem
You have two colors of stacking cubes available with which to
build towers. Your task is to make as many different looking
towers as is possible, each exactly four cubes high. A tower
always points up, with the little knob on top. Solve the problem
inductively with your group, then:
1. Convince yourself and others that you have found all possible
towers four cubes high and that you have no duplicates.
2. Represent your solution to share with the class.
3. Devise a formula that would enable you to solve the problem
for towers of 2 colors and any height (advanced: with any
number of colors and any height)
After Exercise
 Any member of your group should be able to:
 Explain an inductive strategy for solving the 2color/4 tall towers problem and be able to convince
others the solution is correct.
 Explain a general formula for the 2-color towers
problem that works for towers of any height
 Using your work on the towers problem, explain
the relationship between deductive and inductive
reasoning.
Things to consider
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Expert blind spots
Inductive versus deductive reasoning
Math anxiety
Should peer mentors provide answers?