W.KI

1
About understanding

• W.KI

2
Parts and Whole, the invisible links
3

• "When presented with the same material, what you
  see is the same as what the students see." (naive
  truism)
• How much do you agree / disagree ?
• In a chemistry lesson, a beaker of water is
  boiled on top of a Bunsen burner.
• Teacher Do you see the water boiling?
• Student Yes, I do.
• Teacher Do you see that the water changes from
  liquid to gas?
• Student ...
• Teacher So now you can see that with the heat
  energy received, the water molecules are now
  escaping to the air ?
• Student ...

4
Cognitive psychologists emphasize the role of
internal / mental representations
The person is actively perceiving the
environment,encoding, interpreting the
environment, to construct their own internal /
mental representation of the environment, with
certain elaboration / omission /
transformation,depending on the prior knowledge
in the person's long term memoryand the way
that the information is presented
5

• Studies on peoples perception indicate that
  there is a natural tendency for human to
• look for a way which can bring the parts into
  a meaningful whole (Gestalt)
• "Aha, I  understand now!
• This feeling comes when all the parts can be
  linked to form a holistic picture
• Meaning' lies in the connection.

6
The teacher shows a short program of three
steps 1. Copy the value of cell B to cell A 2.
Copy the value of cell C to cell B 3. Copy the
value of cell A to cell C T lets dry run the
program and see the result Following is a dry
run table
T so now you understand it is a program to
exchange the content of the values of the cells B
C
7
T So with the highlighting on the flow of data,
The conclusion will still be true for
other initial values of B C
8

• Or we start first by bring out the X
• T Try the following steps.
• Copy the content of Cell A to Cell B
• Copy the content of Cell B to Cell A
• Do you think you can swap the contents of the
  cell A and B with these steps?

9
T So we have a difficulty here. Now think
about an analogical scenario. You have a glass of
orange juice and a glass of lemon juice, How
can you swap the content between the two glass?
Can we make use of another spare glass? What is
the method? Analogical models are often useful
in teaching about software / algorithm which are
designed by human
10
Cognitivists approach to instruction emphasize
providing learners with effective mental models
/ advanced organizers for the comprehension of
the information received (get an organizing
concept ready before receiving the details)
11
Try the following task "The ice cream truck is
running down the street. Mary ran home to get
some money." What sort of inference would you
make? How do you arrive at such inference?
Try the second task What logical inference can
you make from the following 2 statements? 1.
Some of the beekeepers are artist 2. None of the
chemist are beekeepers Can you tell me how you
do the reasoning?
Reasoning through Heuristic generation of model,
tentative conclusion, destructive test, and
Variation
12

• The use of Enactive Mental model.
• "If the organism carries
• a small-scale model of external reality
• and of its possible actions within its head,
• it is able to try out various alternatives,
• conclude and react to future situations before
  they arise..."
• (Kennth Craik 1943)

13
J.S.Bruners theory of Enactive, iconic,
symbolic representations of knowledge
This is an algorithm for sorting FOR I 1 to
4 FOR J 1 to 4-I If AJgtAJ1 then
swap the content of
AJ and AJ1 NEXT J NEXTI
What is the mode of representation? Can it be
presented first in an enactive way? Example 1
think about an enactive way to present the idea
of a binary search on a ordered list /array
14
Richard E Mayors research

• The use of mental model
• Helps program comprehension ( correct
  understanding about semantics of the programming
  language)
• Helps program production( trying out possible
  actions in the mind )
• Provides a language for the learner to verbalize
  their plans or to paraphrase others plans(
  e.g. move this to the 2nd box and then that to
  the 1st box etc, here the learner describe his
  plan in terms of boxes, the objects in the
  model)

15

• Try to do these procedures
• 1. Turn the number cards (1,2,3,4,5) face
  downward
• A student compare the first two cards,
• swap them if necessaryso that the left one
  is small and the right one is large
• A new student works on the cards in the 2nd 3rd
  positions
• Then a new student proceed to work the 3rd and
  4th positions
• Another new student proceed to the 4th and 5th
  positions
• Open the last card after all these procedures
• Randomize the cards and try the procedure again.
• Do you get the same result? Explain why?

16
T Now instead of randomizing the cards after you
finish, You try to do a second round. S
There is in fact no need to compare the last two
cards! T OK, do one less then. TWhat would you
expect to get in the end?
T Can you then think of a systematic method
for sorting all the five cards?
T will the method guarantee correct result for
different possible cases? (concept of algorithm)
T Can you write down you method in some form?
17
iconic
Symbolic (pseudo code)
18
Progressing through different representations
Loop Card1 to 4
Nested Loop
Loop Card 1 to 3
Loop Card 1 to 2
Loop Card 1 to 1
? Relating / flexible switching between
representations ?
19
up to here. What is an advanced organizer? Why do
we need an advanced organizer? What is a mental
model? What is the benefit of having a mental
model? What are the basic elements of an enactive
mental model? What makes a model good? What
process is important in making the model
work? (See Bruner,J.S. (1960).The process of
Education. For more about the different mode of
knowledge representation. Vygotsky,L.S. (1987).
Mind in Society the development of higher
psychological processes. For a thorough
discussion about the creation of symbolic
representations.
20
Summaryto provide an effective mental model
/organizer

• Conceptual analysis
• Advanced (comes in advance) organizer
• Main ideas before details
• Analogy/designers model (e.g. flip book ?
  animation program)
• The pre-X that engender X
• Enactive mental model
• Enactive? iconic? symbolic representation

21
What counts for a good model?

• Objects,
• with constraints allowable actions,
• Simplicity, comprehensible feedback
• Correspondence isomorphic to the target
  domains critical features
• One poor example which spoils the whole point of
  match-box computer
• One good example which illustrate procedure calls
  and recursion (The method of the lazy magic
  monkey)
• The translation from enactive to symbolic
  representation is non-trival!

22
What can be the Advanced organiser?
Cold water on Hot water on
Flow?
Too high
Too low
More Flow
Less Flow
OK
Temp?
More Cold Less Hot
Too high
Too low
More Hot Less Cold
OK
shower
23
Pre-X

• Think about advanced organisers or models that
  would help the understanding of
• Branching
• Loop
• (c.f. intersection of line ? intersection of
  circle)
• Recursion

24
Thinking about enactive / analogical models
/examples /advanced organizers that help
understanding the ideas of

• The idea of program (cf instruction)
• The idea of procedures (c.f. program).
• The idea of parameters (c.f. procedures with no
  parameters)
• The idea of local variables (c.f. global
  variables)
• The idea of syntactic structure of a Pascal
  program, eg. the use of ""
• The working principle of PowerPoint (c.f. Word)
• The working principle of Flash (c.f. PowerPoint)
• The working principle of a database search (vs
  human search of records)
• The working principle with which 2 FoxPro files
  are linked
• The functions of the different registers in the
  CPU, such as PC MAR, MDR,etc.
• The working principle behind the 2's complement
  representation
• The working principle of the OSI model of
  communications

25
Related topicclues to predict usability /
difficulties in using a software
Dornald Norman, The Psychology of Everyday
thingsAffordance, feedback, conceptual model,
visibility, mapping