Classroom Applications of Cognitive Psychology
The recently-developed science of
human learning reveals and confirms many principles concerning how people
acquire learning initially, how we recall learning, how learners apply
knowledge to new situations, and the role of attention in every aspect of
learning. This site is dedicated to helping teachers become even more
effective. Many of us started teaching before cognitive psychology
emerged (early 1980's). Many more teachers endured relatively
useless "educational psychology" courses as part of pre-service
training and in-service workshops. Those who have learned how to survive
the hard way will wonder why the information in this web site
wasn't available when they started teaching. Never mind -- onward.
This web site is also dedicated to what can
be accomplished with the power to share.
As knowledge
in general is power, mathematics knowledge is more power than other knowledge,
in our day. Mathematics education has more effect on a person’s lifetime income
than knowledge in any other discipline, per the U.S. Bureau of Labor
Statistics. In mathematics education lies ability and confidence to create in
any field, from engineering to visual and performing arts.
·
Sharing this power has gone the way of sharing any
other real power. True, we’ve learned to share money, and call it welfare. We
have tried to compensate for errors of history (for example, Jim Crow laws) by
equal-employment opportunities. But opportunities to earn one’s own money via
efficient, effective education have not been shared, and have been deliberately
suppressed by some.
·
The strength to share genuine opportunity -- not
monetary or employment handouts -- is a spiritual strength. The spiritual power
to share genuine economic and political power is behind this web site.
Site Outline
I. Psychology of Learning A Introduction to Cognitive
Psychology
a. Principles
of Learning (brief)
b. Attention
c. Learning
Principles from Cognitive Psychology Textbooks
II. Psychology
of Learning B: Verbal and Visuospatial Sense Development
a.
Origami
2. Origami,
Spatial Relations, and Gender
6. Crane
c. Abstract
of Research: Effects of Origami and Ambiguous Drawing on Visuospatial Sense
Development
III. Psychology of Learning C: Initial Learning
c. Contexts
for Multiplication of Algebra Variables
e. Information
Processing Summary
IV. Psychology of Learning D: Recall
a.
Association
1. Associative
Networks and Saxon’s Practice Structure
2. How
students recall -- and what is NOT involved
b. Review
2. Thorndike
Support for Correct Practice Structure
4. A
Great Teacher’s Further Development
c.
Stress (benevolent)
V. Psychology of Learning E: Applications
a.
Problem-Solving
3. Chapter 2 Domain Knowledge
c) Strategy:
The Harmonic Mean in Problem-Solving
d) Strategy:
The Cantor Heuristic
e) Strategy:
Assume an Ideal Case
f) Strategy:
Look for a Hidden Assumption
5, Chapter
4 Miscellaneous Problem Lists
a)
Aha
Insight and Catch Questions
b) More
Quotes
c) GAMES
Genres and Captain Pi
d) The
Seven or Eight Bridges of Konigsberg
e) Catch
Questions from Mathematical Nuts
f) Examples
from Puzzles-dot-com
6. Chapter
5 Verification and Linkages
b) Horseman
g) Induction
Logic Details
for Classic Problems (A)
h) Induction
Logic Details
for Classic Problems (B)
i) Induction
Logic Details
for Classic Problems (C) Subsets
l) Proof
by Exhaustion: Knights Moves
m) Chain
Links Payments - - Minimal Weights - - Old Timer
n) Constraints
and Balancing Act
q) Recursion
Inventory of Problems and Issues
7. Z Appendices
a) References
b)
b.
Adventures in Mathematics
VI. Psychology of Learning F: Associative Networks
a. Connections
1.
Awesome
Initiatives Elementary
a) Numeration: Writing Numbers in Columns of 25
b) Numeration: Reading & Writing Whole Numbers & Decimal Fractions
CC. K2 Roman Numerals chart organization
d) Numeration: Significant Digits
e) Fraction: Common Fraction Reducing Stages
f) Fraction: Making the Fraction Concept Digestible
g) Operations: Addition concept and implications
h) Operations: Four Operations Development
i) Geometry: Classification/Relationship (Geom Only)
j) ii. Classification/relationship geometry definitions
k) Geometry: Distance/Area/Volume combined best
l) Geometry: Dist area vol gearshift plus sectorArea arcLength (JrHi)
m) Geometry: Metric Units
n) Geometry: Clarifying Area and Volume concepts (teachers only?)
mm. Geometry: Generalization/Discrimination Basic Shapes
o) Applications: Arithmetic Word Problems Resolved by TAPS
p) Applications: Algebraic Thinking From Arithmetic
q) Applications: Sample Spaces
r) Applications: Tree Diagrams: When to + or × probability?
2.
Awesome
Initiatives Secondary
a) Algebra: Clarifying the Varied Roles of Variables
b) Algebra: “Where Did That ONE Come From?”
c) Algebra: Addends -- Products -- Powers
e) Algebra: Arithmetic Catalysts for Algebra Word Problems
f) Algebra: Customary Function Language
g) Algebra: Quadratic Formula Development and Graph Connection
h) Algebra: Parent Functions I II III IV
i) Algebra: Transformations on Parent Functions with examples
j) Algebra: Odd and Even Functions Extravaganza
k) Algebra: Function Inverse Extravaganza Activity
l) Algebra: Solving Extravaganza with Logarithm Equations
m) Algebra: Rational Functions Extravaganza
n) Geometry: Per area vol gearshifting enhanced: sector area & arc length
o) Geometry: Pythagorean Triples per Sierpinski
p) Geometry: Angle Measures in Circles
q) Geometry: Ratios in Similar Solids
r) Geometry: Dilbert Head -- Prism Surface Area & Volume
rr. Dilbert Grandson hexagon base
s) Geometry: Deductive Structure
t) Geometry: Form and Number Definitions Chart
u) Geometry: Proof Strategies “from the board”
v) Geometry: Cevians and CLRS best Jan 2010
w) Geometry: Statement Classification and Truth Tables
x) Geometry: Representation of Means
y) Trig: Reciprocal Function vs. Inverse Function
z) Analytic Geometry: Conics Constructed by Manipulation
3.
Essential
Defenses Elementary
a)
Numeration: Whole Number Operations; Terminology;
Meanings
b)
Numeration:
GCF and LCM Organized
c)
Operations: Division Practice Basic to Complexity Parts 1 and 2
d)
Fractions:
Ruler for Mandy -- Inch Ruler and Equivalent Fractions
e)
Fractions:
Equivalent proportions dial
f)
Fractions:
Four Operations Chart
g)
Geometry:
Circle Attributes Schema
h)
Geometry:
Polygon Congruence Distinction/Discrimination (JrHi)
i)
General:
Permutation and Combination Concept Development
j)
General:
Set Relationships DICES and Core Concepts
k)
General:
Core Concepts in Mathematics
4.
Essential
Defenses Secondary
a) Numeration: Numbers Outlined
b) NumerationAlgebra But It Looks Easy operations with ONE and ZERO
c) Algebra: Distributivity and NON Distributivity (and Mutations)
d) Algebra: Exchanging Greater-Than with Less-Than
e) Algebra: Rational Expressions vs. Rational Equations
f) Algebra: When Do Solutions Disappear in Algebra?
g) Algebra: Three Key Ideas for Understanding Radicals
h) Algebra: Six Connections for Systems of Equations
i) Algebra: Two Takes on Completing Square
k) Algebra: GCF LCM all methods
l) Algebra: GCF LCM poster with blanks secondary
m) Algebra: Parabola Extravaganza
n) Algebra: Domain and Domain Issues
o) Algebra: Consecutive Integers Reminders
p) Geometry: Regular Polygons and Tessellations
q) Geometry: Surface Area and Volume
r) Geometry: Principles of Negation
s) Analytic Geometry: Slope/Equation/Chart/Graph/Definition Extravaganza
t) Analytic Geometry: Conics Connections
u) Trig: Function Values for Nice Angles
v) Trig: Development of Identity Cluster
w) Calculus: Derivatives and Integrals List
x) General: Distinctions Between Probability Situations
y) General: Properties of Operations and Relations
5.
Inspiring
Rainbows Starscapes Elementary
a) Classification/Relationship: Numbers, Statements, Sets, Operations
b) Early Similarity, Proportion, Slope, Trig
c) Concept of Denominator/Denomination
d) Fractal Forms From Platonic Solids
e) Reasoning -- Induction and Deduction
6.
Inspiring
Rainbows Starscapes Secondary
a) The Concept of Order in Mathematics
e) Concept Nodes in Arithmetic and Algebra
f) Definition Chain from Abstract Algebra
7.
Connections to Other Disciplines
a) Art: Alternation of Attention Impossible E Triangle Cage
b) Soccer: Shootout and Probability
c) Science: What science students need to know about fractions
d) Citizenship: Simpsons Paradox
e) Theology: Amazing Grace and Cantor’s Definition of Infinity
f) Psychology: Wallas & Poincare, Problem-solving per Cognition Principles
g) Application Ratio-Prop-PerCent Problems w Connecting Strategy
h) Elementary experience of math: sine curve
b.
A
Tapestry of Geometry Objectives
VII. Psychology of Learning G Generalization and Discrimination
VIII. Psychology of Learning H Affective Outcomes
IX. DARES
a.
Grade 1
b. Grade 2
c.
Grade 3
d.
Grade 4
e.
Grade 5
f.
Grade 6
g.
Grade 7
h.
Grade 8
1. Days
1-25
2. Days 26-50
3. Days
51-100
4. Days 111-154
i. Carencro DARES instructions
k. Science DARES
Examples (early grades)
l. Science
DARES Fifth Grade - - one week’s examples
X. Incremental Geometry
XI. Teacher Resources
a.
Reading Questions: Blue Pelican Java
b. Slot
Outlines
XII. The
War for Learning: Social and Political Implications
a. A
Storming of Our Pythagorean Aristocracy
b. Declaration
of Non-Dependence
c. Social
and Political Implications of Mathematics Education
d. Changes
Recommended: Elementary Grades
e. Changes
Recommended: Secondary Grades
f. Professor
Hardknocks Speaks: What My Methods Courses Never Told
Me
i. A
Christian Calling in Public Education
j. On
Numerical vs Criteria Regulation of Math Literacy
l. What
Most of Us Need re: Learning
XIII. Humor
a. Invitation: Return to Pig Run Island