# Analyzing mathematical texts with parts of Greimas’ semiotic theory

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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,

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 logical-semantic. 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
I can plant a garden and later have my own apples. Garden – is a helper. This is a long term project. 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 I go back to the doctor. The addresser must appear again. He evaluates my performance. If there is no personal addresser and then there is an epistemological addresser. I am simply happy eating two apples per day.

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, 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.“

This text was suggested for participants of the workshop for analysis.
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 ). 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”.