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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


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.

5/16/2016

5


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


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



Both are deemed important for

mathematics.



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.



Commutative Property of Multiplication

o o o o o

o o o o o

o o o o o

=

o o o

o o o

o o o

o o o

o o o

3 groups of 5 = 5 groups of 3

3 x 5 = 5 x 3

15 = 15



richard skemp (1971) - wordpress.com · richard skemp (1971) the major pioneer in mathematics...

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