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RICHARD SKEMP
(1971)
The major pioneer in Mathematics Education who first integrated
the disciplines of mathematics, education and psychology
5/16/2016
1 Dr. Priya Mathew St. Joseph's College of Education Mysore
• The main 'thrust' of his argument is that
learners construct schemata to link what
they already know with new learning.
• Mathematics involves an extensive
hierarchy of concepts - we cannot form any
particular concept until we have formed all
the subsidiary ones upon which it is
depends.
• Also suggested that emotions play a
dominant part in the way in which we learn.
Skemp’s Theory……..
5/16/2016 2 Dr. Priya Mathew St. Joseph's
College of Education Mysore
Two kinds/ways of learning in
mathematics:
• Instrumental understanding
• Relational Understanding
Understanding:
“To understand something means to assimilate it into an appropriate schema.” (schema: a conceptual structure) 5/16/2016 3 Dr. Priya Mathew St. Joseph's
College of Education Mysore
Instrumental understanding
It is a mechanical, rote learning
It is a kind of learning the rule/ method/
algorithm
which gives quicker results for the teacher in the
short term
e.g. writing 10 would be understood as "This is how
we write 10" in instrumental terms.
5/16/2016
4
Dr. Priya Mathew St. Joseph's College of Education Mysore
Instrumental understanding…
• It is a shallower form of understanding.
For example, we might develop an instrumental
understanding of how to add, subtract, multiply and
divide using a set procedure or algorithm by memorising
the steps required.
we might not understand how the procedure worked or
why the various steps in the procedure are needed.
One of the difficulties with this level of understanding is
that if our memory of the procedure failed, we would be
unable to continue.
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5
Dr. Priya Mathew St. Joseph's College of Education Mysore
Relational understanding
Knowing both what to do and why
we understand how and why the procedures work.
It is more meaningful learning in which the learner is able to understand the links and relationships which give mathematics its structure.
which is more beneficial in the long term and aids motivation
e.g. writing 10 would be understood as "This is why we write 10 like
this (in terms of place value)" in relational terms.
5/16/2016
6
Dr. Priya Mathew St. Joseph's College of Education Mysore
Example of Instrumental &
Relational Understanding
• Instrumental Understanding: Justification by
(a + b)2 = (a + b)(a + b) = a2 +2ab + b2
• Relational Understanding: Picture ‘proof’
a
b
a b
a2
b2 ab
ab
5/16/2016 7 Dr. Priya Mathew St. Joseph's
College of Education Mysore
Both are deemed important for
mathematics.
5/16/2016 8 Dr. Priya Mathew St. Joseph's
College of Education Mysore
Implications of Skemp's theory for
the teaching of mathematics
• Mechanical learning must not take superiority
over understanding. Merely learning 'a
method which works' is a poor kind of
learning which leads to a weak understanding
of the nature of mathematics.
• Attitudes to mathematics affect learning of the
subject.
• Motivation is important in promoting
achievement.
5/16/2016 9 Dr. Priya Mathew St. Joseph's
College of Education Mysore
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