1
One Perspective on Education

• I suspect that many retarded children are
  indeed made rather than born. The process works
  like this First, a child who is not following
  usual paths or timetables of development is
  diagnosed, which is to say labeled, as being
  defective secondly, the child is treated as if
  he or she were defective all in the name of
  care, treatment, therapy thirdly, the child
  learns to think of himself as defective and
  finally, he more and more becomes what the
  experts say he was.

• Do you know the author?
• What do you think of his assessment?

2
Other than the usual path The nature of
micro-development

• Marc Schwartz
• McGill University
• Harvard-Smithsonian Center for Astrophysics
• Nov 2, 2004

3
What cognitive science can offer educators

• Microdevelopment- a model of learning
• Insights on the challenges to attend to when
  aligning curricula
• Insights on what teachers need to know about
  their subjects, themselves and their students

4
A. Microdevelopment-Problem 1 Learning about
learning

• Activity What is it?
• I will pass out an object to pairs of
  individuals.
• The first person who says, I do not know what
  this object is becomes the Researcher.
• Your goal is to figure out what the object is.
• The other person becomes the Observer.
• Your goal is to carefully record what the
  Researcher does and says as he or she attempts
  to figure out what the object is.
• Explore 3 minutes Discuss 5 minutes

5
A. Microdevelopment- Learning goes under the
microscope

• What did the Observers note?
• What do Researchers think the object is?
• How would any of you characterize your level of
  understanding about the object at this point?

6
A. Microdevelopment-History Piagets model to
Neo-Piagetian models
4 mo
Sensorimotor1 Sensorimotor 2 Sensorimotor
3 Sensorimotor 4/
12 mo
Sensorimotor
1.5 yrs
Preoperational Concrete-Operational
Representational 1 Representational
2 Representational 3 Representational 4/
Years
4 yrs
6.5 yrs
11 yrs
Abstract 1 Abstract 2 Abstract 3 Abstract 4
Formal-Operational
Fischer Bidell, 1998
7
A. Microdevelopment-Problem 1 Making sense of
our senses
What strategies did the Researcher employ to
determine what the object is?
Picked it up and smelled it
Banged it against the table

• Sm 1
• Sm 2
• Sm 3
• Sm 4/Rp1
• Rp2
• Rp3
• Rp4/ Ab1
• Ab2
• Ab3
• Ab4

Pop it into his/her mouth
Golip
Time Frame?
Gymnocladus Dioicus
SeedA --- PlantA A Kentucky Coffee
Tree
SeedA --- PlantA SeedA needs water, not heat to
germinate PlantA has leaves, not needles
8
A. Microdevelopment Increasing feats of mental
coordination

• Sm 1
• Sm 2
• Sm 3
• Sm 4/Rp1
• Rp2
• Rp3
• Rp4/ Ab1
• Ab2
• Ab3
• Ab4

PlantA
PlantA has leaves, not needles
Seed A
SeedA needs water, not heat
9
A. Microdevelopment- Summary Development vs.
Microdevelopment
The nature of liquids
The nature of flowers
The nature of seeds
The nature of trees
Seconds, Minutes or Hours
Sensorimotor1 Sensorimotor 2 Sensorimotor
3 Sensorimotor 4/
Years
Representational 1 Representational
2 Representational 3 Representational 4/
Abstract 1 Abstract 2 Abstract 3 Abstract 4
Fischer Granott, 1995 Schwartz Fischer,
2004 Yan Fischer, 2002
Fischer Bidell, 1998
10
B. The Challenge of Aligning Curricula Texas
Essential Knowledge and Skills (TEKS)
In what ways does TEKS support what we know about
learning from the perspective of microdevelopment?

• Revisiting concepts from one year to the next.
  Strength
• Providing numerous opportunities to build complex
  understandings of concepts through a variety of
  contexts. Weakness
• Providing opportunities to build concepts from
  the sensorimotor tier through the
  representational tier and into the abstract tier.
  Weakness

11
B. The Challenge of Aligning Curricula (TEKS)
Ch.112 High School Science- Integrated Physics
Chemistry 6 Concepts--
31 Knowledge Skills

• 1. Calculate speed, momentum, acceleration, work
• 2. Investigate and describe applications of
  Newton's laws
• 3. Analyze the effects caused by changing force
• 4. Investigate and Demonstrate mechanical
  advantage
• 5. Demonstrate wave types and their
  characteristics
• 6. Demonstrate wave interactions including
  interference
• 7. Identify uses of electromagnetic waves
• 8. Demonstrate the application of acoustic
  principles
• 9. Describe the law of conservation of energy
• 10. Investigate and Demonstrate the movement of
  heat through solids,
• 11. Analyze the efficiency of energy conversions
• 12. Investigate and compare economic and
  environmental impacts
• 13. Measure the thermal and electrical
  conductivity of various materials
• 14. Investigate and compare series and parallel
  circuits
• Analyze the relationship between an electric
  current and the strength of an electromagnet
• Analyze the effects of heating and cooling
  processes in systems
• 17. Investigate and Identify properties of fluids
  including density,
• 18. Research and describe the historical
  development of the atomic theory

• 19. Identify constituents of various materials or
  objects such as metal salts,
• 20. Relate the behavior of an element to its
  placement on the periodic table
• 21. Classify samples of matter from everyday life
  as elements, compounds,
• 22. Distinguish between physical and chemical
  changes in matter
• 23. Analyze energy changes.. to Classify them as
  endergonic or exergonic
• 24. Investigate and Identify the law of
  conservation of mass
• 25. Describe types of nuclear reactions such as
  fission and fusion
• 26. Research and describe the environmental and
  economic impact of the
• 27. Relate the structure of water to its function
  as the universal solvent
• 28. Relate the concentration of ions to chemical
  properties such as pH,
• 29. Simulate the effects of acid rain on soil,
  buildings, statues,
• Demonstrate how various factors influence
  solubility
• Demonstrate how factors such as particle size,
  influence the rate of dissolving.

12
B. The Challenge of Aligning Curricula TEKS for
Integrated Physics Chemistry From the
perspective of Blooms Taxonomy of Ed.
Objectives

• 1. Calculate (Comprehension)
• 2. Investigate and describe (Comprehension)
• 3. Analyze (Comprehension)
• 4. Investigate (Comprehension)
• 5. Demonstrate (Application)
• 6. Demonstrate (Application)
• 7. Identify (Knowledge)
• 8. Demonstrate (Application)
• 9. Describe (Comprehension) the law of
  conservation of energy
• 10. Investigate (Comprehension)
• 11. Analyze (Analysis)
• 12. Investigate and compare (Analysis)
• 13. Measure (Application)
• 14. Investigate and compare (Comprehension)
• 15. Analyze the relationship (Analysis)

• 16. Analyze (Comprehension)
• 17. Investigate and Identify (Knowledge)
• 18. Research and describe (Comprehension)
• 19. Identify (Application)
• 20. Relate (Comprehension)
• 21. Classify (Comprehension)
• 22. Distinguish (Application)
• 23. Analyze (Comprehension)
• 24. Investigate and Identify (Knowledge)
• 25. Describe (Knowledge)
• 26. Research and describe (Knowledge)
• 27. Relate (Comprehension)
• 28. Relate (Comprehension)
• 29. Simulate (Application)
• Demonstrate (Application)
• Demonstrate (Application)

Bloom, 1956
13
B. The Challenge of Aligning Curricula Blooms
Taxonomy/Hierarchy vs. Microdevelopment

• Blooms Hierarchy

• Microdevelopment

Abstract 4 Abstract 3 Abstract 2 Abstract 1
Evaluation
Synthesis
Representational 4/ Representational
3 Representational 2 Representational 1
Analysis
Application
Comprehension
Sensorimotor4/ Sensorimotor 3 Sensorimotor
2 Sensorimotor 1
Knowledge
14
B. The Challenge of Aligning Curricula
Distribution of skills for Integrated Physics
Chemistry according to Blooms Taxonomy/Hierarchy
of Objectives
15
B. The Challenge of Aligning Curricula Can
microdevelopment occur in Integrated Physics and
Chemistry?
Science concept (5 of 6) The student knows
relationships exist between properties of matter
and its components. Total of skills 5

• Sm 1
• Sm 2
• Sm 3
• Sm 4/Rp1
• Rp2
• Rp3
• Rp4/ Ab1
• Ab2
• Ab3
• Ab4

17. Investigate and identify properties of
fluids including density, viscosity, and
buoyancy
18. Research and describe the historical
development of the atomic theory
20. Relate the chemical behavior of an element
including bonding, to its placement on the
periodic table
Seconds, minutes or hours maybe never
21. Classify samples of matter from everyday
life as being elements, compounds, or mixtures.
19. Identify constituents of various materials
or objects such as metal salts, light sources,
fireworks displays, and stars using
spectral-analysis techniques
?
16
C. What teachers need to know about their
subjects, themselves, as well as students.
Problem 2 Investigating Density
TEKS 17. Investigate and Identify properties of
fluids including density

• What is the density of water?
• A) 0 gms/cc B) 1 gm/cc C) 5 gms/cc
• 2. If an objects density is 2 gm/cc, will it
  float?
• A) Yes B) No C) Can not tell from this
  information
• 3. If an object has a mass of 2 grams and a
  volume of 4 cc, what is its density?
• A) 8 gms/cc B) 2 gms/cc C) .5 gms/cc
• key gms grams cc cubic centimeters

17
C. What teachers need to knowProblem 2 The
usual path towards understanding floating and
sinking

• Collecting data on the four original questions
• 1. What is the density of water?
• 2. If an objects density is 2gm/cc, will it
  float?
• 3. If an object has a mass of 2 grams and a
  volume of 4 cc, what is its density?

Given the distribution of answers, how would you
characterize your understanding or the level of
understanding of density in this class?
18
C. What teachers need to knowProblem 2 An
un-usual but demanding path towards
understanding floating and sinking

• 1. You come across a canoe in a swimming pool.
  You notice a large anvil sitting in the canoe.
  You wonder if the level of water in the swimming
  pool will change if you take out the anvil and
  throw it in the water. First you closely mark
  the level of water in the swimming pool and then
  throw the anvil in the water. What happens to
  the water level?
• A) It goes up B) It goes down C) It remains
  unchanged

19
C. What teachers need to knowProblem 2 The
Challenge of Understanding
Fishing weights are hard, heavy, grey.

• Sm1
• Sm2
• Sm3
• Sm4/Rp1
• Rp2
• Rp3
• Rp4/Ab1
• Ab2
• Ab3
• Ab4

Canoes float, are narrow, low to the water
Water is clear, wet, it flows
Putting weights in the pool will raise the water
level
seconds, minutes or hours
A fishing weight has both volume weight
canoes float fishing weights do not
The anvil weighs more than the same volume of
water
A quantity of water equal to the weight of the
anvil would far exceed the volume of the anvil
The volume of water displaced by the canoe weighs
less than the water displaced
Under water the fishing weight displaces an
amount of water equal to its volume
Archimedes Principle

• An object that floats displaces a volume of water
  equal to the objects weight
• An object that sinks displaces a volume of
  liquid equal to the objects volume.

20
Summary What I have learned

• Microdevelopment
• All learning is a recapitalization of normal
  development.
• All learning is a hierarchical process that is
  sensitive to new contexts.
• All meaningful representations come from our
  experiences in the world
• Abstract principles are difficult cognitive
  structures to maintain.
• Aligning Curricula
• Learning new concepts requires time, support,and
  repeated opportunities in various contexts to
  coordinate representations into abstractions.
  -- True for new teachers as well as
  students--
• Without time, support, opportunities and context,
  concepts are reduced to lower level
  representations (memorizing the density equation
  is easier than understanding Archimedes
  Principle).
• Working with models and principles is not
  historically the kind of work we have asked from
  students or teachers and it is easy to settle
  for lower level skills (as described in Blooms
  taxonomy or in the microdevelopmental model) as
  the standards for measuring understanding.
• Preparing Teachers
• A new paradigm for education is necessary-
  BUILDING VS BORROWING
• My answer can not replace the active process
  necessary for students to construct their
  understanding of models or principles (e.g.,
  Archimedes).
• Learning to teach well is an abstract skill,
  which requires support, time and numerous
  contexts to master.

21
References

• Bloom, B. (Ed.) (1956). Taxonomy of educational
  objectives The classification of educational
  goals. Handbook 1 The cognitive domain. David
  McKay Co New York
• Fischer, K., W. and T. R. Bidell (1998). Dynamic
  development of psychological structures in action
  and thought. Handbook of child psychology
  Theoretical models of human development. W.
  Damon. New York, Wiley. 5 467-561
• Fischer, K. W. and N. Granott (1995). "Beyond
  one-dimensional change Parallel, concurrent,
  socially distributed process in learning and
  development." Human Development 38 302-314.
• Schwartz, M. S. and K. Fischer, W. (2004).
  Building general knowledge skill. Emergence and
  transformation in the mind Modeling and
  measuring cognitive change. A. Demetriou and A.
  Raftopoulos. Cambridge, UK, Cambridge University
  Press.
• Yan, Z. and K. Fischer, W. (2002). "Always under
  construction Dynamic variations in adult
  cognitive development." Human Development 45
  141-160.

22
C. What teachers need to knowProblem 2 The
usual path towards understanding floating and
sinking --- Harvard August 2004---

• Collecting data on the four original questions
• 1. What is the density of water?
• 2. If an objects density is 2gm/cc, will it
  float?
• 3. If an object has a mass of 2 grams and a
  volume of 4 cc, what is its density?

Given the distribution of answers, how would you
characterize your understanding or the level of
understanding of density in this class?
23
Two Foundational Points

• Science is hard
• Abstract principles are difficult cognitive
  structures to maintain.
• They remain counter-intuitive because less
  complex cognitive structures can offer more
  compelling solutions to the problems we face in
  science.
• Curriculum development may be easier
• Although the capacity of abstract reasoning is
  present in adults, this skill can only emerge
  when we capture and coordinate the appropriate
  sensorimotor and representational understandings.