Analyzing mathematical texts with parts of
Greimas’ semiotic theory
Barbro Grevholm, University of Agder, Norway
Kudžma Ričardas, Vilnius University
Saulius Žukas, Baltos lankos publishing house
Southampton,
2014-07-31
Algirdas Julius Greimas
A. J. Greimas (1917 – 1992)
Introduction
Greimas (1970, 1979), was the master of the Paris
school of semiotics. He developed a quite general
theory, mainly consisting of the semiotic square,
and the narrative grammar, which allows the
analysis of texts of any genre. Kudžma (2005)
started to apply Greimas’ theory for analysis of
mathematical texts.
Theoretical framework
According to Greimas a text can be analyzed at
three levels: discursive, narrative and logicalsemantic.
The first two levels are called surface and the
third one – deep level. The essence of the deep
level is the so called semiotic square.
P. Ricœr (1989) called the invention of semiotic
square „the stroke of genius – and this is not too
strong...“
In our workshop we will not touch upon the
semiotics square.
Narrative grammar 1
For the narrative level all narrative grammar was
established. The narrative level has four phases:
manipulation, competence, performance and
sanction.
At the manipulation phase the addresser
formulates a problem and looks for somebody
(addressee and later on subject of action) who
wants or must solve it. The addresser presents his
system of values which very often differs from the
students’ (addressee’s) systems of value. That
might cause many didactical problems.
Narrative grammar 2
At the competence phase the subject of action
must show or achieve some competence for a
solution of the problem, reaching some object of
value. The subject of action can never solve a
problem without a helper. The competence phase
ends by selecting the helper (helpers).
At the performance phase the subject of action
must do some job, must conquer the rival.
At the sanction phase the addresser evaluates the
performance and awards the subject of action.
Example 1. Folk tale
The analysis of folk tales by Propp was at the
origin of contemporary Greimas’s semiotic theory.
There was a kingdom. A dragon lived near this
kingdom and asked to give him a girl each year.
The only one girl left is the princess. The king
asked anybody to kill the dragon. He promised to
give the princess and the half of kingdom for that.
Three brothers, two clever and the third one fool,
tried their chance. The older two (clever) failed and
the youngest (fool) succeeded to kill the dragon.
Remark. There are many different versions of this
tale.
Analysis of tale
Manipulation. Addresser - king, problem – dragon,
object of value – princess and half of the kingdom.
Competence and performance. Two brothers
failed. They did not help a fish on the shore and a
bird in the bushes and did not get competence
sufficient to kill the dragon
The third brother saved the fish and the bird. They
became the helpers and awarded the hero the
special skills which enabled him to kill the dragon.
Sanction. The youngest brother was awarded by
the king as it was promised at the beginning.
Example 2. Real life problem
Real life situation
Manipulation. 1. I go to the doctor. He says. To be
healthy I need to eat apples each day.
2. There is an opinion in the society that to eat
apples is very useful for the health. An apple a day
keeps the doctor away.
Problem - I need apples.
The addresser is the doctor (case 1) and an
episthemological addresser (case 2)
Subject of action - me, object of value – apples.
Competence, helper, rival
1. I can plant a garden and later have my own apples.
Garden – is a helper. This is a long term project.
2. If I need apples right now I can buy apples in the market. I
need money.
Money – is a helper.
Lack of money – rival.
I don‘t have cash. I have a credit card. I can get cash at ATM.
Credit card and ATM are helpers.
Performance
• 1. I plant a garden, look after it, wait for 10 years and have my
own apples.
• 2. I go to the market and buy apples. There might be
formulated many mathematical problems with money and the
amount of apples.
Sanction
1. I go back to the doctor. The addresser must appear again. He
evaluates my performance.
2. If there is no personal addresser and then there is an
epistemological addresser. I am simply happy eating two
apples per day.
Zbigniew Semadieni, 1st grade (picture)
Z.Semadeni (text)
At the forest school the owl puts 9 rabbits on one
side and 6 little rabbits on the other. She asked:
„How many rabbits are there in total?“
The rabbits have been thinking for a long time,
how many there are, 9 + 6.
Later on one little rabbit with red sash jumped
towards the big rabbits and cried out: „Now it is
easy to count, because we are 10 and 5 that means
– 15.“
Analysis of the text
This text was suggested for participants of the
workshop for analysis.
Conclusions
• Greimas’s semiotics gives the method of text analysis.
• The beginning of text, the manipulation phase, is very
important. Then the confrontation between two systems of
values appears - the addresser’s (authors’ of textbook,
teachers’) from one side and addressee’s (students’) from the
other side.
• Semiotic analysis permits one to do some objective
conclusions about the quality of the text.
• The text from the Semadeni textbook provided for analysis of
participants of the workshop is a “good” one from the point of
view of Greimas’s semiotics.
References
Greimas, A. J. (1970). Du sens, Editions du Seuil, Paris.
Greimas, A. J. (1979). Du sens II, Editions du Seuil, Paris.
Kudžma, R. (2005). Semiotics in education. In C. Bergsten & B. Grevholm (Eds.),
Conceptions of mathematics, Proceedings of norma 01, Third Nordic Conference on
Mathematics Education, (pp. 171-176). Kristianstad, June 8-12, 2001, Linkoping: SMDF.
Ricœr, P. (1989). Greimas’s narrative grammar, Paris School Semiotics I. Theory, John
Benjamin Publishing Company, Amsterdam/Philadelpia.
Semadeni, Z. (1998). Matematika 1. Punsk, “Aušra”.