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Nicolas.Balacheff, CNRS, Laboratoire d’informatique de Grenoble

EPISTEMOLOGICAL AND SOCIAL
PRINCIPLES FOR THE DESIGN OF
LEARNING SPACES
The race to 20
Setting the scene with an example
  the race to 20
Two players, one rule:
  • Add 1 or 2 to the number
  the previous player said,                                1. explanation of the rules
  • The winner is the one                                  2. one against one
  who reaches 20 first.                                    3. group against group
                                                           4. game of discovery
  • Starting number: 1 or 2


Brousseau G. (1978) Etude locale des processus d’acquisition en situations scolaires. Reproduced
in “Theory of Didactical situations” (1998) – referred to as TSD
Race to 20, lessons learned
     Strategies are used implicitly before being formulated
      so as to respond to the needs of an ongoing action
     Formulation takes place after conviction and before
      validation in order to respond to the needs of
      communicating an action
     Established statements are not immediately “stored” as
      such
           Losing stimulate commitment to search for
             conditions for success
           Proving gets its value when it has been tested as
             a tool to ensure success
           Explaining gets its value if it is technically or
             socially necessary
   Brousseau G. (1978) Etude locale des processus d’acquisition en situations scolaires. Etudes
    sur l’enseignement élémentaire, Cahier 18, 7-21. Bordeaux: IREM de Bordeaux (TSD pp.3-18)
Race to 20… convergence of meaning
                               “The aim of this sequence
                               is still the
                               communication of an
                               instruction but it has
The structure of the           slipped into an action      teacher
communication between the      phase” (TSD p.7)
teacher and students,
eliciting the place of the
situation                                 Rules of the
                                            game           message
(1) Instruction, stating the
    rules
                                           Linguistic
(2) Semantic of the rules by                 code          situation
    the first gaming
(3) Semantic of the rules by
    commenting on them         The role of playing the
                               game at the same time
                               as providing the
                                                           student
                               message is to leverage
                               the convergence of
                               meaning.
Race to 20… feedback and adaptation

 Feedback : response of the                     Rules of the                    teacher
                                                  game
 situation to a person action.
                                                 Linguistic           coding
                                                   code                         message
 Feedback provides a positive or
 negative sanction which allows
 her to adjust her action
                                                  noise                   Message as a source
                                                                          of information for
    to accept or reject a hypothesis,                                         the student

   to choose the best solution from
      among several (the one which
           improves the satisfaction                                            student
        obtained during the action)               Linguistic
                                                    code
“This feedback must be closely associated
with the learning which the teacher is trying                                  Message as
to make happen” (TSD p.8)                                                       meaning
                                                               decoding
Race to 20… situation of action/milieu
“situation of action” is where
learners form strategies and
construct a model of the situation
by experimenting an noticing                      Subject
successes and failures.


These strategies and models          constraint

are mostly implicit.
                                                  Milieu
Everything that acts on the
student or that she acts on and is
relevant to making sense of the
situation is called the “milieu”.
Race to 20… situation of formulation
The learners must
communicate about the
strategy to use, the
construction of a common
language is needed.

During this situation there
are two types of feedback:
  - immediate (discussion)
  - delayed (round played)


situation of formulation:
requirement of a common
language, specific to the
situation.
Race to 20… validity and proof
At stake is “the passage from natural
thought to a structured (logical)
thought” needed to establish the validity
of a statement .                                                  theory
                                                                   statements
This needs the construction, rejection or                             on the
use of different methods of proof:                                   strategy
rhetorical, pragmatic, semantic or
syntactic.
                                                         rounds
                                                         played


            proponent


                                            theory
                                            statements
                              opponent         on the
                                              strategy
Race to 20… validity and proof
“If one wishes to avoid having
sophistries, rhetoric and authority take
the place of consistency, logic and the
efficacy of proof, one must not let the                           theory
discussion lose touch with the situation                           statements
                                                                      on the
which reflects the students’ discourse                               strategy
and gives it meaning. Motivation must
make this double confrontation (R1 and
R2) necessary.” (TSD p.16)                 R1            rounds
                                                         played


           proponent


                       R2                   theory
                                            statements
                             opponent          on the
                                              strategy
Didactical postulates
 (P1) Meaning is not given by a text/discourse, but emerges from the
 activity which is required by this knowledge
 (P2) The specification of the knowledge stake of a didactical situation
 requires a process of transposition

The learner must                          The teacher must imagine and present
                                          learners with situations within which
 produce, formulate, prove, and
   construct                               they can live
   models, languages, concepts and         knowledge appears as the optimal
   theories                                  and discoverable solution of the
 exchanges them with other people           problem posed
 recognizes those which conform to       The teacher’s work is the opposite of the
   the culture                            knowledge producer
                                                Recontextualization
 borrows those which are useful to her         Repersonalization
   …
  (P3) “Each item of knowledge must originate from the adaptation to a
  specific situation”
The core didactical structure

“Between the moment the student accepts the problem as if it were
her own and the moment when she produces her answer, the
teacher refrains from interfering and suggesting the knowledge
that she wants to see appear” (TSD p.30)



                   adidactical situation


                 actual teaching situation
    devolution                               institutionalization

                    didactical situation
The core didactical structure

        “Each item of knowledge can be characterized by a (or some)
        adidactical situation(s) which preserve(s) meaning ; we shall call
        this a fundamental situation” (TSD p.30)

             fundamental situation                 Knowledge analysis
              restriction
             deformation
                                adidactical situation


                              actual teaching situation
             devolution                                         institutionalization

                                  didactical situation

“[The teacher] is involved in a game with the system of interaction of the student with the
problem she gives her […] This game, or broader situation, is the didactical situation” (TSD
p.31)
Didactical design of a learning space
LoE didactical problem
 The problem
   Medical students (2nd year) are reluctant to learn theoretical
    statistics, they don’t catch its practical relevance
   Hypothesis: this difficulty can be overcome by situating
    learning in a way demonstrating its professional value
   Take a concrete case: design a decision tool for
    hospitals, based on a risk factor analysis of a 'nosocomial'
    disease.
      Role: a team of physicians working for a health committee
      Learning goals:
        Some statistics
        Epidemiological methodology
        Critical reading of medical papers
      Tasks
        To collect data at the (virtual) hospital
        To design a method to analyze data
        To present results at a (simulated) conference
LoE didactical problem

                               Critical reading
Statistics
                                 of scientific
 Survey
                                   articles
             Healthcare   •
              decision
              making          Nosocomial
                              Risk


 Hospital
The core didactical structure

  fundamental situation             Knowledge analysis


   restriction
  deformation
                  adidactical situation


                 actual teaching situation
  devolution                                  institutionalization

                   didactical situation
LoE didactical structure (1)




 Appropriation of the      Design and            Writing of the
 problem, bibliograph      validation of the     procedure and
 y                         statistical           of its
 (medical, statistical),   procedure, complian   justification, pu
 first approach on the     ce with the medical   blic
 field, field              procedures, (public   communication
 investigation             health)               (congress)
LoE phase 1
1.    Design the main steps of the protocol in
      order to study the disease status in each
      department and the risks factors
2.    Validate the protocol by submitting it
      verbally to the heads of departments
3.    Collect data by interviewing patients and
      staff of the departments
                                    Analysis situation / knowledge


      Appropriation of the
      problem, bibliograph
      y
      (medical, statistical),
      first approach on the
      field, field
      investigation
                                                Critical point: clinical
                                                practice Vs public health
                                                (status of the disease
                                                and the patient)
LoE phase 2
1.    Submit to the technical platform a request for
      the necessary medical analysis
2.    Process and interpret all data, design and
      validate a procedure
3.    Formulate actions and decisions to be taken to
      decrease the nosocomial risks or impacts
                                    Analysis situation / knowledge



     Design and
     validation of the
     statistical
     procedure, complian
     ce with the medical
     procedures, (public
     health)
LoE phase 3
1.    Submit a paper to the conference (only
      half of the papers are accepted)
2.    Present the paper at the conference
      and discuss the different solutions
      proposed (esp. for the same hospital)
                              Analysis situation / knowledge



      Writing of the
      procedure and
      of its
      justification, pu
      blic
      communication
      (congress)
Interactional immersion

Phases                  Student                       proactive
                                                                      System
                                                                                        Relation feedback / knowledge


          Ask for authorization to interview
                                                                  An argued answer
          patients at the hospital


Phase 1                                                           Validation by the
          Send protocol to Ethics Committee
                                                                  experts
                                                                  • Question/response
               • Interview patients at the hospital
                                                                  • News about a
                        • See a patient on request                patient

Phase 2   Request data from the hospital                          A Table of data

                                                                  Review by the
Phase 3   Submit the article to the congress                      scientific
                                                                  committee
Interaction diagram for protocol validation
                             Roles
                                            Heads of
         Student                            departments            Experts
                   Doctors                                                                 Tutor
                                                                   (commission)

                       Record voice message
   Loop                (describe protocol)
                                                             Signal new message
                                                          Post reply (approve: yes/no)

                        Send SMS (yes/no)


                              Send mail (written protocol)
                                                                          Signal message

                                                                              Post reply
                                                                              (comments)
                              Send mail (protocol comments)

time
Interaction, the learning space/time

             Phone call
                                          SMS       Head of the Hospital
 Doctor                                                Department



              Email
             Message
                                                 Ethical Research Committee
                                        Email
                                                 Public Health Commission
                                       Message
 Doctor
                                                     Medical Congress



              Web site

                                        Video
 Doctor                                                   Patient

Students                  Technology               Tutoring agents
Interaction, the virtual space
 Public Health
 Commission




Ethical Research Committee        Medical Congress   Library
Back to theory and design
  Principle: knowledge as a baseline for design,
  social interactions and situations as tools


Modeling a learning situation means
producing a game specific to the target
knowledge which should appear as
• the means of understanding the rules and
  strategies
• the means of elaborating winning
  strategies
“Game” the key modeling tool
G1: situations in which decisions and actions are
    determined by pleasure derived] from
    accomplishing them, or from their effect
G2: organization of this activity within a system of
    rules defining success and failure, gain or loss
G3: whatever is used for playing, the instruments
    of the game
G4: the way in which one plays
G5: the set of possible positions from among which
    the player can choose in a given state of the
    [G2-game]
                                            (pp.48-49)
“Game” the key modeling tool
                                stake, function of reference
Game1: situations
  determined by /                        information

  associated to                         observed state         Milieu
                       Player                                  (Game3 )
  pleasure                              action, decision       (Game5)
Game2: organization                        (Game4)
  of the activity
  within a system of
  rules
Game3: instruments                        (Game2)
  of the game
Game4: the way in
  which one plays                        Formal rules

Game5: the set of
  possible positions
                                            (Game1)
Game for learning, some issues
 “Is knowing this property the only way of shifting from a
given strategy to another one?

 “why should the student look for a way of replacing this
strategy with that one?

 “what cognitive motivation leads to the production of
such-and-such a formulation of a property or to such-and-
such a mathematical proof?

 “Is the given reason for producing this knowledge
better, more correct, more accessible or more effective
than any other reason?”
                                                   (pp. 47-48)
From the model to a method
The study of the adequacy of a situation for a piece of
knowledge K has the aim…

    To show that the optimum strategy can be brought about by
     K with a clear advantage
    To state hypotheses about the variables of the situation and
     their influence on strategies and changes of strategies

The meaning of a student decision can be modeled with

    a) the set of choices he/she considers and rejects
    b) the set of possible strategies considered and excluded,
                                 and some light on their rational
    c) the conditions of the game that determine the choices
Adidactical situations
     Two distinct types of games:
      a) the student’s games with
       the adidactical milieu (games
       specific to each piece of
       knowledge)
      b) the teacher’s games as
       organizers of these student’s
       game. These games concern at
       least :
           the teacher,
           the student,
           the student’s immediate
            environment                                      “The milieu is the system
           the cultural milieu                              opposing the taught system
         They include the game of devolution                 or, rather, the previously-taught
         and of institutionalization.                        system”. (p.57)

“As the student's progress gradually continues, this cultural and didactical representation of the milieu
will be assumed to approach “reality”, and the subject's relationships with this milieu will have to become
free of didactical intentions.” (p.57)
Interaction – knowing - situation
                   The relationships between a student and the milieu
                                  can be classified into three major categories
        [1] Action → actions and decisions that act directly
        [2] Formulation → exchange of info coded into a language
        [3] Validation → exchange of judgment
                       They correspond to different forms of knowledge
        [3] the forms of knowledge which allow the explicit “control” of the
         subject's interactions in relation to the validity of her statements. It is
         composed of…
             a description or model expressed in a certain “language”
             a judgment about the adequacy of this description
        [2] the formulation of the descriptions and models
        [1] the models for action governing decisions


“The fact that different types of interaction with the milieu and different forms
of knowledge are justified a priori and independently allows us to discuss the
particularities of the milieu which are necessary for them.” (p.65)
Interaction – knowing – situation
                         By pragmatic questions like
                               Why would the student do or say this rather than that?
                               What must happen if she does it or doesn’t do it?
                               What meaning would the answer have if she had been given it?
                         it is possible to elicit the conditions which the typologies impose on the milieu.
Design and engineering




                            [3] Does the milieu include an opponent (or a proponent ) with whom the
                             subject must be confronted in order to attain the fixed goal in an exchange of
                             opinions?
                            [2] Does the milieu include a receiver of messages that the student must
                             send in order to attain the target goal?
                            [1] Does the milieu include a feedback function adapted to the need for
                             adjustment of the interaction to the targeted knowledge?

                         The answer to these two questions determines the layout of the milieu and the
                         rules of the games, which are totally different. (Brousseau 1998, p.65)
First possible end…
The didactical contract
The teacher must arrange not the communication of knowledge, but the
devolution of a good problem

“The didactical contract is the rule of the game and the
strategy of the didactical situation” (p.31)

“[There is a] system of obligations which resembles a contract”
(p.31) but “[which] is not exactly a contract
              it cannot be made completely explicit
 […] The teacher must however accept responsibility
 […] similarly, the student must accept responsibility
              clauses concerning the breaking and the stake of
             the contract cannot be written in advance” (p.32)
Paradox raised by the TSD
1.       Paradox of the devolution of situations (p.41) result from
         the tensions between the necessary student autonomy and
         the teacher responsibility to teach which is known from
         both. The teacher must refrain from teaching even if the
         student asks for it.
2.       Paradox of the adaptation of situation (p.42) the
         knowledge appropriated by adaptation may be…
          Maladjusted to correctness
          Maladjusted to a later adaptation
3.       Paradox of learning by adaptation (p.44-45)
          Negation of knowledge: knowledge deems to be trivial
          Destruction of the cause of knowledge: lost of motivation
4.       Paradox of the actor (p.46) “[the knowledge] whose text
         already exists is no longer a direct production of the
         teacher, it is a cultural object, quoted and re-quoted”
Didactical phenomena
The didactical phenomena witness the complexity of didactical
processes, there elicitation frames the objectives of research in
didactique.
1.  Topaze effect (p.25) obtaining a behavior at the cost of the
    meaning of the knowledge at stake
2. Jourdain effect (p.25) acknowledgement of a piece of knowledge
    based on a surface characteristics of behaviors
3. Metacognitive shift (p.26) the teaching method or means
    becomes the object of teaching
4. Improper use of analogy (p.27) pointing similarities to facilitate
    which are not relevant in themselves
5. Ageing of teaching situations (p.27) feeling of the need to change
    lessons organizations, discourse, behaviours -- teacher does
    repeat a text (see also the Actor paradox)
6. Dienes effect (p.35) freeing the teacher from his or her
    responsibility towards learning
Second possible end…
“Game” the key modeling tool
                                                                         Stake, function of reference

                                                                                information
                                                                                                             milieu
(A) formalisation of the game                               player
                                                                               predicted state
                                                                                                              game
                                                                              action, decision          (meaning 3 and 5)
1.   X set of distinct “positions”, J set of players                         game (meaning 4)



2. rules of the game [Γ : X → P(X)]
                                                       player's rules;                                         constraints of
3. initial state I and final states F                  strategies,
                                                       knowledge
                                                                                     game
                                                                                  (meaning 2)
                                                                                                               the milieu


4. turn taking [θ : JxX→ J]
                                                                                 formal rules
5. gain, stake, preference [F      A X f: A → R]                                    game
                                                                                 (meaning 1)




Round : a finite sequence of states (from I to F).
Strategy : any mapping X→X that determines choices from permissible states
Tactic : strategy defined on a subset A of X
Player 's state of knowing : mapping of X →Γ(X) such that [ x C(x) Γ(X)]
Determining knowledge reduces the player’s choice to a single state
Acquisition of knowledge is a modification of the state of knowing
Fundamental patterns (1)                                         action
                                                                                        Stake, function of reference
Check list for a game based situation of action
                                                                                               information
    Can the situation be perceived as devoid of didactical                                   predicted state               milieu
     intentions?                                                          player                                             game
                                                                                             action, decision          (meaning 3 and 5)
    Must students effectively chose a state from among several                             game (meaning 4)

     ones? Do they know which states they can select from?
    Can students lose? Do they know that they can? Do they
     know the final states in advance (including the winning         player's rules;                                          constraints of
                                                                     strategies,
     ones)?                                                          knowledge
                                                                                                    game                      the milieu
                                                                                                 (meaning 2)
    Do they know the rules without knowing a winning strategy?
     Can they be taught the rules without being given a solution?
                                                                                                formal rules
    Is the target knowledge necessary?
                                                                                                   game
    Can students start again? Does the game “gratify”                                          (meaning 1)
     anticipation?
    Have students any chance of finding out the sought strategy
     for themselves if they borrow it (from other students)?
                                                                                                                           student
    Are feedback to the students choices relevant to the                                                         S
                                                                                                                  E

     construction of the knowledge?
                                                                              teacher
                                                                                           T
                                                                                           S
    Is the control of decisions possible?
    Is a reflective attitude useful necessary for progress in the                                               M         milieu
     solution?
Fundamental patterns (2)                                       formulation
                                                                  stake about the milieu
A milieu for communication
include a receiver/sender and                                              information
a receiver/sender/executor                  player A
                                                                                                  milieu for action
   1. insufficient means of action:     sender and receiver
                                                                          actions
      A must describe to B the
      action which she had to carry




                                                                                                                          milieu for communication
      out and often a part of the
      milieu as well so that the
      message is intelligible,                                             messages        information          actions
   2. insufficient information for A
      but sufficient means of action:
      B must describe the milieu           A's repertoire               stake
      and A must decode the                                                of
                                                                            transmission
      description and direct the                  repertoire of
      observation                                   messages
                                                                                                         player B
   3. means of action and                              B's repertoire                             receiver, sender,
      information insufficient for A.                                                                 executor




 “The messages exchanged are under the control of linguistic, formal or
 graphical codes and therefore make them function” (p.68)
Fundamental patterns (2)                                validation
                                                                      A's stake
Only valid knowing can be
recognized within the teaching
                                                                     information
situation, it makes situation of       player A                                         action
validation an ultimate objective   proposer, opposer
                                                                                        milieu         messages

of the didactical process.                                           actions




Proponent and opponent must                                      statements
have a symmetric position                                        proofs




                                                                                                                  B's stake
                                                                 refutations       information          actions
 “it should not be possible for
   one of the players to obtain                               stake
   the agreement of the other      statements, theories           constraints
   by “illegitimate” means such    allowed by A                      of
                                                                        debate
   as authority, seduction,
   force, etc.” (p.70)                                                                           player B
                                              statements, theories                       opposer, proposer,
 Knowledge should be the                     allowed by B                                   executor
   only legitimate reference for
   decision making
“Game” the key modeling tool
       (A) formalisation of the game                                        Model for action: every strategy
       1.   X set of distinct “positions”, J set of players
                                                                            or calculation procedure giving
                                                                            rise to a strategy or a tactic
       2. rules of the game [Γ : X → P(X)]                                  Winning strategy : round with
       3. initial state I and final states F                                positive payoff. It comes with…
                                                                                - a cost
       4. turn taking [θ : JxX→ J]                                              - a gain
       5. gain, stake, preference [F            A X f: A → R]
                                                                            A non-systematically-winning
                                                                            strategy can be better in terms
      Round : a finite sequence of states…                                  of the risk of loss that it
      Strategy : any mapping X→X that…                                      entails, the gains that it allows
      Tactic : strategy defined on a subset A of X…                         one to hope for, etc.
      Player 's state of knowing : mapping of X …
      Determining knowledge reduces …                Game theory allows the study of
      Acquisition of knowledge is a modification of… the dilemmas that arise.
An acknowledged reference today is : Fudenberg D., Levine D. K. (1998) The theory of learning in games. The MIT Press. The
limitation Brousseau makes in his choice of a game type is the same in that classical book.

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About learning games and the design of learning spaces

  • 1. Nicolas.Balacheff, CNRS, Laboratoire d’informatique de Grenoble EPISTEMOLOGICAL AND SOCIAL PRINCIPLES FOR THE DESIGN OF LEARNING SPACES
  • 3. Setting the scene with an example the race to 20 Two players, one rule: • Add 1 or 2 to the number the previous player said, 1. explanation of the rules • The winner is the one 2. one against one who reaches 20 first. 3. group against group 4. game of discovery • Starting number: 1 or 2 Brousseau G. (1978) Etude locale des processus d’acquisition en situations scolaires. Reproduced in “Theory of Didactical situations” (1998) – referred to as TSD
  • 4. Race to 20, lessons learned  Strategies are used implicitly before being formulated so as to respond to the needs of an ongoing action  Formulation takes place after conviction and before validation in order to respond to the needs of communicating an action  Established statements are not immediately “stored” as such  Losing stimulate commitment to search for conditions for success  Proving gets its value when it has been tested as a tool to ensure success  Explaining gets its value if it is technically or socially necessary  Brousseau G. (1978) Etude locale des processus d’acquisition en situations scolaires. Etudes sur l’enseignement élémentaire, Cahier 18, 7-21. Bordeaux: IREM de Bordeaux (TSD pp.3-18)
  • 5. Race to 20… convergence of meaning “The aim of this sequence is still the communication of an instruction but it has The structure of the slipped into an action teacher communication between the phase” (TSD p.7) teacher and students, eliciting the place of the situation Rules of the game message (1) Instruction, stating the rules Linguistic (2) Semantic of the rules by code situation the first gaming (3) Semantic of the rules by commenting on them The role of playing the game at the same time as providing the student message is to leverage the convergence of meaning.
  • 6. Race to 20… feedback and adaptation Feedback : response of the Rules of the teacher game situation to a person action. Linguistic coding code message Feedback provides a positive or negative sanction which allows her to adjust her action noise Message as a source of information for to accept or reject a hypothesis, the student to choose the best solution from among several (the one which improves the satisfaction student obtained during the action) Linguistic code “This feedback must be closely associated with the learning which the teacher is trying Message as to make happen” (TSD p.8) meaning decoding
  • 7. Race to 20… situation of action/milieu “situation of action” is where learners form strategies and construct a model of the situation by experimenting an noticing Subject successes and failures. These strategies and models constraint are mostly implicit. Milieu Everything that acts on the student or that she acts on and is relevant to making sense of the situation is called the “milieu”.
  • 8. Race to 20… situation of formulation The learners must communicate about the strategy to use, the construction of a common language is needed. During this situation there are two types of feedback: - immediate (discussion) - delayed (round played) situation of formulation: requirement of a common language, specific to the situation.
  • 9. Race to 20… validity and proof At stake is “the passage from natural thought to a structured (logical) thought” needed to establish the validity of a statement . theory statements This needs the construction, rejection or on the use of different methods of proof: strategy rhetorical, pragmatic, semantic or syntactic. rounds played proponent theory statements opponent on the strategy
  • 10. Race to 20… validity and proof “If one wishes to avoid having sophistries, rhetoric and authority take the place of consistency, logic and the efficacy of proof, one must not let the theory discussion lose touch with the situation statements on the which reflects the students’ discourse strategy and gives it meaning. Motivation must make this double confrontation (R1 and R2) necessary.” (TSD p.16) R1 rounds played proponent R2 theory statements opponent on the strategy
  • 11. Didactical postulates (P1) Meaning is not given by a text/discourse, but emerges from the activity which is required by this knowledge (P2) The specification of the knowledge stake of a didactical situation requires a process of transposition The learner must The teacher must imagine and present learners with situations within which  produce, formulate, prove, and construct  they can live models, languages, concepts and  knowledge appears as the optimal theories and discoverable solution of the  exchanges them with other people problem posed  recognizes those which conform to The teacher’s work is the opposite of the the culture knowledge producer  Recontextualization  borrows those which are useful to her  Repersonalization … (P3) “Each item of knowledge must originate from the adaptation to a specific situation”
  • 12. The core didactical structure “Between the moment the student accepts the problem as if it were her own and the moment when she produces her answer, the teacher refrains from interfering and suggesting the knowledge that she wants to see appear” (TSD p.30) adidactical situation actual teaching situation devolution institutionalization didactical situation
  • 13. The core didactical structure “Each item of knowledge can be characterized by a (or some) adidactical situation(s) which preserve(s) meaning ; we shall call this a fundamental situation” (TSD p.30) fundamental situation Knowledge analysis restriction deformation adidactical situation actual teaching situation devolution institutionalization didactical situation “[The teacher] is involved in a game with the system of interaction of the student with the problem she gives her […] This game, or broader situation, is the didactical situation” (TSD p.31)
  • 14. Didactical design of a learning space
  • 15. LoE didactical problem  The problem  Medical students (2nd year) are reluctant to learn theoretical statistics, they don’t catch its practical relevance  Hypothesis: this difficulty can be overcome by situating learning in a way demonstrating its professional value  Take a concrete case: design a decision tool for hospitals, based on a risk factor analysis of a 'nosocomial' disease.  Role: a team of physicians working for a health committee  Learning goals:  Some statistics  Epidemiological methodology  Critical reading of medical papers  Tasks  To collect data at the (virtual) hospital  To design a method to analyze data  To present results at a (simulated) conference
  • 16. LoE didactical problem Critical reading Statistics of scientific Survey articles Healthcare • decision making Nosocomial Risk Hospital
  • 17. The core didactical structure fundamental situation Knowledge analysis restriction deformation adidactical situation actual teaching situation devolution institutionalization didactical situation
  • 18. LoE didactical structure (1) Appropriation of the Design and Writing of the problem, bibliograph validation of the procedure and y statistical of its (medical, statistical), procedure, complian justification, pu first approach on the ce with the medical blic field, field procedures, (public communication investigation health) (congress)
  • 19. LoE phase 1 1. Design the main steps of the protocol in order to study the disease status in each department and the risks factors 2. Validate the protocol by submitting it verbally to the heads of departments 3. Collect data by interviewing patients and staff of the departments Analysis situation / knowledge Appropriation of the problem, bibliograph y (medical, statistical), first approach on the field, field investigation Critical point: clinical practice Vs public health (status of the disease and the patient)
  • 20. LoE phase 2 1. Submit to the technical platform a request for the necessary medical analysis 2. Process and interpret all data, design and validate a procedure 3. Formulate actions and decisions to be taken to decrease the nosocomial risks or impacts Analysis situation / knowledge Design and validation of the statistical procedure, complian ce with the medical procedures, (public health)
  • 21. LoE phase 3 1. Submit a paper to the conference (only half of the papers are accepted) 2. Present the paper at the conference and discuss the different solutions proposed (esp. for the same hospital) Analysis situation / knowledge Writing of the procedure and of its justification, pu blic communication (congress)
  • 22. Interactional immersion Phases Student proactive System Relation feedback / knowledge Ask for authorization to interview An argued answer patients at the hospital Phase 1 Validation by the Send protocol to Ethics Committee experts • Question/response • Interview patients at the hospital • News about a • See a patient on request patient Phase 2 Request data from the hospital A Table of data Review by the Phase 3 Submit the article to the congress scientific committee
  • 23. Interaction diagram for protocol validation Roles Heads of Student departments Experts Doctors Tutor (commission) Record voice message Loop (describe protocol) Signal new message Post reply (approve: yes/no) Send SMS (yes/no) Send mail (written protocol) Signal message Post reply (comments) Send mail (protocol comments) time
  • 24. Interaction, the learning space/time Phone call SMS Head of the Hospital Doctor Department Email Message Ethical Research Committee Email Public Health Commission Message Doctor Medical Congress Web site Video Doctor Patient Students Technology Tutoring agents
  • 25. Interaction, the virtual space Public Health Commission Ethical Research Committee Medical Congress Library
  • 26. Back to theory and design Principle: knowledge as a baseline for design, social interactions and situations as tools Modeling a learning situation means producing a game specific to the target knowledge which should appear as • the means of understanding the rules and strategies • the means of elaborating winning strategies
  • 27. “Game” the key modeling tool G1: situations in which decisions and actions are determined by pleasure derived] from accomplishing them, or from their effect G2: organization of this activity within a system of rules defining success and failure, gain or loss G3: whatever is used for playing, the instruments of the game G4: the way in which one plays G5: the set of possible positions from among which the player can choose in a given state of the [G2-game] (pp.48-49)
  • 28. “Game” the key modeling tool stake, function of reference Game1: situations determined by / information associated to observed state Milieu Player (Game3 ) pleasure action, decision (Game5) Game2: organization (Game4) of the activity within a system of rules Game3: instruments (Game2) of the game Game4: the way in which one plays Formal rules Game5: the set of possible positions (Game1)
  • 29. Game for learning, some issues  “Is knowing this property the only way of shifting from a given strategy to another one?  “why should the student look for a way of replacing this strategy with that one?  “what cognitive motivation leads to the production of such-and-such a formulation of a property or to such-and- such a mathematical proof?  “Is the given reason for producing this knowledge better, more correct, more accessible or more effective than any other reason?” (pp. 47-48)
  • 30. From the model to a method The study of the adequacy of a situation for a piece of knowledge K has the aim…  To show that the optimum strategy can be brought about by K with a clear advantage  To state hypotheses about the variables of the situation and their influence on strategies and changes of strategies The meaning of a student decision can be modeled with  a) the set of choices he/she considers and rejects  b) the set of possible strategies considered and excluded, and some light on their rational  c) the conditions of the game that determine the choices
  • 31. Adidactical situations Two distinct types of games:  a) the student’s games with the adidactical milieu (games specific to each piece of knowledge)  b) the teacher’s games as organizers of these student’s game. These games concern at least :  the teacher,  the student,  the student’s immediate environment “The milieu is the system  the cultural milieu opposing the taught system They include the game of devolution or, rather, the previously-taught and of institutionalization. system”. (p.57) “As the student's progress gradually continues, this cultural and didactical representation of the milieu will be assumed to approach “reality”, and the subject's relationships with this milieu will have to become free of didactical intentions.” (p.57)
  • 32. Interaction – knowing - situation  The relationships between a student and the milieu can be classified into three major categories  [1] Action → actions and decisions that act directly  [2] Formulation → exchange of info coded into a language  [3] Validation → exchange of judgment  They correspond to different forms of knowledge  [3] the forms of knowledge which allow the explicit “control” of the subject's interactions in relation to the validity of her statements. It is composed of…  a description or model expressed in a certain “language”  a judgment about the adequacy of this description  [2] the formulation of the descriptions and models  [1] the models for action governing decisions “The fact that different types of interaction with the milieu and different forms of knowledge are justified a priori and independently allows us to discuss the particularities of the milieu which are necessary for them.” (p.65)
  • 33. Interaction – knowing – situation By pragmatic questions like  Why would the student do or say this rather than that?  What must happen if she does it or doesn’t do it?  What meaning would the answer have if she had been given it? it is possible to elicit the conditions which the typologies impose on the milieu. Design and engineering  [3] Does the milieu include an opponent (or a proponent ) with whom the subject must be confronted in order to attain the fixed goal in an exchange of opinions?  [2] Does the milieu include a receiver of messages that the student must send in order to attain the target goal?  [1] Does the milieu include a feedback function adapted to the need for adjustment of the interaction to the targeted knowledge? The answer to these two questions determines the layout of the milieu and the rules of the games, which are totally different. (Brousseau 1998, p.65)
  • 35. The didactical contract The teacher must arrange not the communication of knowledge, but the devolution of a good problem “The didactical contract is the rule of the game and the strategy of the didactical situation” (p.31) “[There is a] system of obligations which resembles a contract” (p.31) but “[which] is not exactly a contract  it cannot be made completely explicit  […] The teacher must however accept responsibility  […] similarly, the student must accept responsibility  clauses concerning the breaking and the stake of the contract cannot be written in advance” (p.32)
  • 36. Paradox raised by the TSD 1. Paradox of the devolution of situations (p.41) result from the tensions between the necessary student autonomy and the teacher responsibility to teach which is known from both. The teacher must refrain from teaching even if the student asks for it. 2. Paradox of the adaptation of situation (p.42) the knowledge appropriated by adaptation may be…  Maladjusted to correctness  Maladjusted to a later adaptation 3. Paradox of learning by adaptation (p.44-45)  Negation of knowledge: knowledge deems to be trivial  Destruction of the cause of knowledge: lost of motivation 4. Paradox of the actor (p.46) “[the knowledge] whose text already exists is no longer a direct production of the teacher, it is a cultural object, quoted and re-quoted”
  • 37. Didactical phenomena The didactical phenomena witness the complexity of didactical processes, there elicitation frames the objectives of research in didactique. 1. Topaze effect (p.25) obtaining a behavior at the cost of the meaning of the knowledge at stake 2. Jourdain effect (p.25) acknowledgement of a piece of knowledge based on a surface characteristics of behaviors 3. Metacognitive shift (p.26) the teaching method or means becomes the object of teaching 4. Improper use of analogy (p.27) pointing similarities to facilitate which are not relevant in themselves 5. Ageing of teaching situations (p.27) feeling of the need to change lessons organizations, discourse, behaviours -- teacher does repeat a text (see also the Actor paradox) 6. Dienes effect (p.35) freeing the teacher from his or her responsibility towards learning
  • 39. “Game” the key modeling tool Stake, function of reference information milieu (A) formalisation of the game player predicted state game action, decision (meaning 3 and 5) 1. X set of distinct “positions”, J set of players game (meaning 4) 2. rules of the game [Γ : X → P(X)] player's rules; constraints of 3. initial state I and final states F strategies, knowledge game (meaning 2) the milieu 4. turn taking [θ : JxX→ J] formal rules 5. gain, stake, preference [F A X f: A → R] game (meaning 1) Round : a finite sequence of states (from I to F). Strategy : any mapping X→X that determines choices from permissible states Tactic : strategy defined on a subset A of X Player 's state of knowing : mapping of X →Γ(X) such that [ x C(x) Γ(X)] Determining knowledge reduces the player’s choice to a single state Acquisition of knowledge is a modification of the state of knowing
  • 40. Fundamental patterns (1) action Stake, function of reference Check list for a game based situation of action information  Can the situation be perceived as devoid of didactical predicted state milieu intentions? player game action, decision (meaning 3 and 5)  Must students effectively chose a state from among several game (meaning 4) ones? Do they know which states they can select from?  Can students lose? Do they know that they can? Do they know the final states in advance (including the winning player's rules; constraints of strategies, ones)? knowledge game the milieu (meaning 2)  Do they know the rules without knowing a winning strategy? Can they be taught the rules without being given a solution? formal rules  Is the target knowledge necessary? game  Can students start again? Does the game “gratify” (meaning 1) anticipation?  Have students any chance of finding out the sought strategy for themselves if they borrow it (from other students)? student  Are feedback to the students choices relevant to the S E construction of the knowledge? teacher T S  Is the control of decisions possible?  Is a reflective attitude useful necessary for progress in the M milieu solution?
  • 41. Fundamental patterns (2) formulation stake about the milieu A milieu for communication include a receiver/sender and information a receiver/sender/executor player A milieu for action 1. insufficient means of action: sender and receiver actions A must describe to B the action which she had to carry milieu for communication out and often a part of the milieu as well so that the message is intelligible, messages information actions 2. insufficient information for A but sufficient means of action: B must describe the milieu A's repertoire stake and A must decode the of transmission description and direct the repertoire of observation messages player B 3. means of action and B's repertoire receiver, sender, information insufficient for A. executor “The messages exchanged are under the control of linguistic, formal or graphical codes and therefore make them function” (p.68)
  • 42. Fundamental patterns (2) validation A's stake Only valid knowing can be recognized within the teaching information situation, it makes situation of player A action validation an ultimate objective proposer, opposer milieu messages of the didactical process. actions Proponent and opponent must statements have a symmetric position proofs B's stake refutations information actions  “it should not be possible for one of the players to obtain stake the agreement of the other statements, theories constraints by “illegitimate” means such allowed by A of debate as authority, seduction, force, etc.” (p.70) player B statements, theories opposer, proposer,  Knowledge should be the allowed by B executor only legitimate reference for decision making
  • 43. “Game” the key modeling tool (A) formalisation of the game Model for action: every strategy 1. X set of distinct “positions”, J set of players or calculation procedure giving rise to a strategy or a tactic 2. rules of the game [Γ : X → P(X)] Winning strategy : round with 3. initial state I and final states F positive payoff. It comes with… - a cost 4. turn taking [θ : JxX→ J] - a gain 5. gain, stake, preference [F A X f: A → R] A non-systematically-winning strategy can be better in terms Round : a finite sequence of states… of the risk of loss that it Strategy : any mapping X→X that… entails, the gains that it allows Tactic : strategy defined on a subset A of X… one to hope for, etc. Player 's state of knowing : mapping of X … Determining knowledge reduces … Game theory allows the study of Acquisition of knowledge is a modification of… the dilemmas that arise. An acknowledged reference today is : Fudenberg D., Levine D. K. (1998) The theory of learning in games. The MIT Press. The limitation Brousseau makes in his choice of a game type is the same in that classical book.