Different Learners General Learning Processes in Learning Math

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Different Learners General Learning Processes
in Learning Math?
Applied in general math teaching
Applied in teaching the different learner
Consequences for practice
Theoretical basis
Gunvor Sønnesyn, Pedverket Kompetanse
gunvors_at_online.no
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Luria (1973) Three Functional Units of the Brain
1. The unit for regulating tone and waking and
mental states.
2. The unit for receiving, analyzing and storing
information.
3. The unit for programming, regulation and
verification of activity
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Knowledge, Conceptual Systems
Skills
Illustration of different structures concerning
knowledge and skills with reference to Nyborg,
Das, and McNamara
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NUMBERS
Knowledge, Conceptual Systems
Changes in numbers
Relations between numbers
Increase in number
Decrease in number
Similarity in number
Large/ small number related to
Skills
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Two concepts from Vygotsky

• Zone of proximal development (ZPD), the
  discrepancy between a childs actual mental age
  and the level he reaches in solving problems with
  assistance.
• Vygotsky 1962, p. 103

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• Word function from nominative to significative
• We distinguish a words nominative from its
  significative function.
• In the beginning only the nominative function
  exists and semantically, only the objective
  reference signification independent of naming,
  and meaning independent of reference appear later.

Vygotsky 1962, p. 130
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Raising the questions How to create zones of
proximal development in ways that facilitate
processes towards zones of actual
development? How to create a context for language
learning in terms of words becoming signifiers
rather than just names?
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Concept learning
M E D IATION
Skill learning

• Cognition PhaseLearning about the skill
  

1. Learning Association Categories connected to
verbal expression
2. Imitation Trial and error
2. Learning Difference Differences within and
between categories
3. Exercise, training towards automation
3. Verbalizing Partial Similarities they are
similar in...
ANALYTIC CODING/MULTIPLE CLASSIFICATION/ABSTRACTIO
N
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Example The task is to find similarities and
differences between the two boxes in each row.
This enforces processes of analytic coding, and
verbal consciousness about these similarities and
differences.
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8
10
7 10
0,3
7 10
0,7
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CASE. Tanja has general learning problems
Difficulties in -processes of
analysis-detecting partial similarities
She requires a different progression, but the
same learning processes as other children.

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It is a ten, because there are ten tassels
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I put ten beads on the pipe cleaner, and make a
ten.
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It is a ten, because there are ten flags
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ten treklossar
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They are similar in that they are tens
How are they similar ?
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Multiplication in terms of repeated addition
When each set contains an identical number, we
can multiply.
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Multiplication 2
Point to the row where we can find the number by
multiplication
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Multiplication 3
Find the number of round shapes Find the number
of four sided shapes. How are these two tasks
similar?
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multiplication 4
Count in nines
Kjetil puts 9 marbles in each bag. How many
marbles are there in
bags
marbles
bags
marbles
bags
marbles
bags
marbles
bags
marbles
bags
marbles
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Mattis og Mattea 1 Mattis og Mattea 1, Resource
book Mattis og Mattea 2A Mattis og Mattea
2B Mattis og Mattea 2, Resource book
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Directing attention
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Number
Figures
Digits
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Look at the two groups in each row.In what
respect are they similar?In what respect are
they different?

• To verbalize

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To learn concepts of ...symbols
The red colour of the milk carton is a symbol,
because it has a meaning
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.......... are symbols, because they mean
something
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Which pink colour is a symbol?
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Which red colour is a symbol?
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Which is a symbol, the figure or the number of
three round shapes?
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Look at the pink colour of the milk pack and the
red colour at the traffic light. In what respect
are they similar?
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2
The Ringo-logo and the figure 2, in what respect
are they similar?
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• To practise

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• Math learning, different or general?

Math learning, general and different Knowledge
of the general processes provides tools to with
which to meet each different learner.
General learning processes Different learners
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Who has the figure with a triangular shape and
the colour green?
Who has the figure with the straight line shape,
the number two, vertical position and the colour
blue?
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Concepts of numbersThe number three
Count, and find the number of dinosaurs.
Make a group with the number of three pigs.
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Point to the groups which have the number three.
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How are these groups similar?