Analyzing mathematical texts with parts of Greimas

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Analyzing mathematical texts with parts of
Greimas semiotic theory

• Barbro Grevholm, University of Agder, Norway
• Kudžma Ricardas, Vilnius University
• Saulius Žukas, Baltos lankos publishing house

Southampton, 2014-07-31
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Algirdas Julius Greimas
A. J. Greimas (1917 1992)
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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.

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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.

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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 (addressees) systems of
  value. That might cause many didactical
  problems.

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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.

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Example 1. Folk tale

• The analysis of folk tales by Propp was at the
  origin of contemporary Greimass 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.

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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.

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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.

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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 dont have cash. I have a credit card. I
  can get cash at ATM.
• Credit card and ATM are helpers.

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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.

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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.

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Zbigniew Semadieni, 1st grade (picture)

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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.

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Analysis of the text

• This text was suggested for participants of the
  workshop for analysis.

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Conclusions

• Greimass 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 addressers
  (authors of textbook, teachers) from one side
  and addressees (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 Greimass
  semiotics.

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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). Greimass narrative grammar,
  Paris School Semiotics I. Theory, John Benjamin
  Publishing Company, Amsterdam/Philadelpia.
• Semadeni, Z. (1998). Matematika 1. Punsk,
  Aušra.
•