1. Nicolas.Balacheff, CNRS, Laboratoire d’informatique de Grenoble
EPISTEMOLOGICAL AND SOCIAL
PRINCIPLES FOR THE DESIGN OF
LEARNING SPACES

2. The race to 20

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)

34. First possible end…

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

38. Second possible end…

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.