Using variation theory as a guiding principle of didactical design with the focus on the object of learning, its critical aspects and how they can be taught

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Using variation theory as a guiding principle of

Using variation theory as a guiding principle of

Using variation theory as a guiding principle of

Using variation theory as a guiding principle of

didactical

didactical

didactical

didactical design. W

design. W

design. With

design. W

ith

ith

ith the focus on the object of

the focus on the object of

the focus on the object of

the focus on the object of

learning, its critical aspects and how they can be

learning, its critical aspects and how they can be

learning, its critical aspects and how they can be

learning, its critical aspects and how they can be

taught.

taught.

taught.

taught.

Ulla Runesson University of Jönköping, Sweden and University of the Witwatersrand, South Africa

=25% 
=40%  =0,625=62,5% 5% of 800= 6% of 700=

Lesson 1

25% of 200=

10% of 200=

40% of 200=

75% of 200=

Different theories explain learning in different

ways

Emphasizes e.g. • intellectual maturity, • function of the brain, • activity,

• cognitive change,

• the social and linguistic dimensions,

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Variation theory (Marton & Booth, 1997; Marton,

Runesson & Tsui, 2004; Lo, 2012; Marton, in press)

When we learn, we always learn something. Learning has an object.

The object of learning

For every object of learning there must be something learned

Themes of my presentation:

• How are differences in learning outcomes explained by

variation theory?,

• Learners’ meaning making and the nature of ‘the what’,

• How can learning be designed from the point of view of

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Splitting 9 marbles into two boxes (Neuman,

1987; 2013)

The cardinal aspect is attended to

The ordinal aspect is attended to

Learning simple arithmetic…

…takes the simultaneous

discernment of

the ordinal, cardinal and

part-part-whole aspect (critical aspects)

A B

C D

What does it mean to be able to …..?

What must be discerned in order to be able to…..? What must not be taken for granted ?

Results before and after the lesson (Kullberg,

2010)

Class A N=19

Class B N=17 Are there decimal numbers between

0,97 och 0,98? Pre-test Many numbers /endless One numberl Ten numbers No numbers Other 5% (1) 21% (4) 0% (0) 42% (8) 32% (6) 24% (4) 29% (5) 0% (0) 18% (3) 29% (5) Are there decimal numbers between

0,97 och 0,98?Pre-test Many numbers /endless One numberl Ten numbers No numbers Other 21% (4) 0% (0) 47% (9) 21% (4) 11% (2) 94% (16) 0% (0) 6% (1) 0% (0) 0% (0) 11

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What aspects were the critical aspects?

• The interchangeable representation • The number as a part of a whole • The divisibility of parts

Learning from seeing examples of the same thing…..

…or by contrasting? Seeing

what is not a dog?

We learn by the experiencing of

differences rather than of similarities

=25% 
=40%  =0,625=62,5% 5% of 800= 6% of 700=

Lesson 1

25% of 200=

10% of 200=

40% of 200=

75% of 200=

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4.

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The example space

(Pillay, manuscript)

Lesson 1

Example substituting values plotting drawing the

graph

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and

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and

_{  = }

Lesson 2

Comparing pairs of

functions

Principles of variation theory

• Learning implies seeing something in a new way

• Experiencing something in a certain way takes the simultaneous discernment of certain aspects.

• For every object of learning there are certain aspect that must be discerned

• The discernment of an aspect presupposes an experienced variation of that particular aspect. (Marton, Runesson, & Tsui, 2004)

Thank you!

Further readings

• Lo, M. L. (2012). Variation theory and the improvement of teaching and learning

https://gupea.ub.gu.se/bitstream/2077/29645/5/gupea_2077_29645 _5.pdf

• Marton, F., & Booth, S. (1997). Learning and awareness. Mahawa NJ: Erlbaum.

• Kullberg, A., Runesson, U., Mårtensson, P. (2013). The same task? -different learning possibilities? In C. Margolinas (Ed.) Task Design in Mathematics Education Proceedings of ICMI Study 22, ISBN 978-2-7466-6554-5 http://hal.archives-ouvertes.fr/hal-00834054