Moving between discourses: from learning-as-acquisition to learning-as-participation

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Moving between discourses from
learning-as-acquisition to learning-as-participat
ion
AAPT PERC bridging session
Anna Sfard The University of Haifa The
Michigan State University

• Ann Arbor, 29 September 2008

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Answer This is the Dove of Peace
Question What is this?
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Question What is happening here?
Question What is this?
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Answer People are moving according to certain
rules
Question What is happening here?
Question What is it?
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conclusion

• It changes what we see

How we talk about things matters

• and may thus change what we do

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Meta-question on learning
How to talk about learning mathematic (physics)?
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Basic assumptions

• How we talk about learning matters

• We need more than one way of talking

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Meta-question on learning - refined
How should I
How to talk about learning mathematic (physics)?
so as to answer my questions?
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an example of the questions I ask
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Learning mathematics in schoolThe case of
negative numbers Study with Sharon Avgil and her
7th grade students
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Learning mathematics in schoolThe case of
negative numbers Study with Sharon Avgil and her
7th grade students
Whenever I say mathematics, you think physics, ok?
and when I say negative number, you think force,
ok?
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Some facts about the study

• The teacher opted for re-invention with concrete
  models

• Expected difficulty the rule for minus times
  minus

• The students re-invented adding and subtracting
  signed numbers

• First difficulty the rule for plus times
  minus

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When asked about 2 ? (-5)

• Adva it is like 2 times -5, so it is -5 plus
  -5. It gives -10

Roi 2 times -5 is -10 because 5 is the bigger
number
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And the class followed Roi
The teacher asked about 6 ? (-2) Vladis Me too
Plus 12 because 6 is bigger. Teacher Why
this rule? Yoash Because this is what Roi
said. Teacher But Roi did not explain
Leah The bigger is the one that decides.
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and Roi concluded

• Roi I am more charismatic I
  managed to influence them all.

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And when the teacher presented her argument

• The children openly disbelieved

• Especially when the teacher tried to explain the
  rule minus times minus is plus

• And they kept being skeptical all along the way

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example of Questionabout learning I am asking
in my research
What went wrong in this classroom?
What could/should be done differently?
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Plan of this talk

• Two ways of talking about learningacquisitionist
  participationist
• B. Commognition as a special case of
  participationist approach School learning as
  developing discourses
• C. Applying commognitive discourse back to th
  question on learning negatives

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If learning means change, what is it that
changes when a person learns mathematics
(physics)?
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Acquisitionist answer
What is it that changes when one learns?
Ones knowledge / concepts / mental schemas which
one acquires/ constructs
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Acquisitionist answer
Participationist answer
What is it that changes when one learns?
Ones participation in an activity, form of life,
practice
Ones knowledge / concepts / mental schemas which
one acquires/ constructs
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Examples of historically established human
activities cooking, dressing, talking, drawing,
making/using tools
uniquely human learning
individualization of patterned, historically
established ways of doing things
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Individualization development of ones agency as
a participant in a given form of doing
uniquely human learning
individualization of patterned, historically
established ways of doing things
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Just to remind If learning means change, what is
it that changes?

• ACQUISITIONIST answer
• Students conceptions

• PARTICIPATIONIST answer
• Form of activity
• (way of performing some well defined tasks)

There is much space in learning for contingency
and for human agency
individual learning is a matter of human
biological makeup and external constraints
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Acquisitionism vs. participationism a number
of remarks

• Whats the relation between them? They are
  incommensurable, not incompatible
• Why both are useful? Each has its relative
  advantages and weaknesses
• Which to choose? Depends on the nature of ones
  enterprise

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My choice participation metaphor
and as Ill try to show, this helps to answer
my questions

• Why? Because it leaves more space for human
  agency

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Plan of this talk

• Two ways of talking about learningacquisitionist
  participationist
• B. Commognition as a special case of
  participationist approach School learning as
  developing discourses
• C. Applying commognitive discourse back to th
  question on learning negatives

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Fotnote 1 Sources of ideas
not just Vygotsky
but also Wittgenstein
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This approach shows family resemblance to that of
Rom Harré (discursive psychology) and
Michael Halliday(functional linguistics)
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Question 1
School learning means a change in thinking.
But what is thinking?
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Question which collective activity is the best
candidate for the precursor of thinking?
Taking participationism one step further
Communication!

• participationists uniquely human skills and
  abilities develop by individualization of
  historically established collective activities

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Taking participationism one step further
Commognition communication cognition

• participationists uniquely human skills and
  abilities develop by individualization of
  historically established collective activities

conclusion Human thinking is an
individualized form of inter-personal
communication
Communication does not have to be verbal
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Question 2
What is mathematics (physics)?
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So, what is mathematics (or history, or physics,
or..)?
physics

• mathematics

• way of thinking

mathematics
a discourse
physics
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What makes discourses of mathematics (physics)
distinct?
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Discourses of mathematics are made distinct by

• keywords and their use

• Three function
• derivative triangle

?
endorsed narratives

• 224, (x2) 2x
• In triangle, equal sides face equal angles.

?
routines
how to look, how to convince, how to inscribe,
how to prove, etc.
?
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Discourses of mathematics are made distinct by
physics
Force Big Bang quark energy work

• keywords and their use

• Three function
• derivative triangle

?
endorsed narratives

• 224, (x2) 2x
• In triangle, equal sides face equal angles.

• Emc2 Fma
• the loss in weight of an object immersed in a
  fluid

?
routines
how to look, how to convince, how to inscribe,
how to prove, etc.
?
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But can discourse be all there is to mathematic?
For example, what is the number (negative or
otherwise)?
Number is a discursive construct people created
to communicate about the world. It is to be found
in the discourse, not in the world
Is it any different for force?
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Question 3
And what does it mean to learn mathematics
(physics)?
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What does it mean to learn mathematics
(physics)?
Important!
Were in the business of defining here, not of
finding the truth about the world!
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criteria for assessing the quality of the
definitions

• coherence
• consistency with other elements of the system
• adequacygood fit with the informal use of the
  word
• operationalitycommunicational effectiveness
• usefulnesscapability to bring abut new insights
  re-/dis-/solve old quandaries

?
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Plan of this talk

• Two ways of talking about learningacquisitionist
  participationist
• B. Commognition as a special case of
  participationist approach School learning as
  developing discourses
• C. Applying commognitive discourse back to th
  question on learning negatives

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Questionabout learning
What went wrong in this classroom?
What could/should be done differently?
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Alternatively
What was the nature of the expected learning?
Was it possible for this learning to happen by
re-invention?
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Two levels of learning
Example one already knows what function is and
now learns about properties of different types
of functions

• object level
• Adding endorsed narratives about existing objects
  or narratives, built according to existing
  meta-rules

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Two levels of learning
Example transition from the discourse on
unsigned numbers to the one on signed numbers
Example transition from Aristotelian to
Newtonian discourse on force and motion

• meta level
• adding new objects
• changing meta-rules
• changing use of words

• object level
• Adding endorsed narratives about existing objects
  or narratives, built according to existing
  meta-rules

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From unsigned to signed numbers What changes in
the discourse?
Meta-level learning results in discourse incommens
urable with the previous one
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What was the nature of the expected learning?
Was it possible for this learning to happen by
re-invention?
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Just to remind, in our study

• the teacher tried to honor the principle of
  inventive learning

The learners should have as much agency over
their learning as possible
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Is there room for inventive learning?
object-level learning can happen by
(re-)invention
meta-level learning Not that simple!
The nature of discourse change logically
necessary
The nature of the required meta-discursive
change contingent
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Circularities of meta-level learning
Meta-rules changeTo modify a meta-rule you
need to understand the usefulness of such change
but the only way to become aware of the
usefulness of meta-rule is to enact it
meta-discursive rules are contingent, not
necessary (are historically established
conventions).
Object construction To participate in a
discourse on an object you need to have already
constructed this object but the only way to
construct an object is to participate in the
discourse about it
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Meta-level learning what is possible?
spontaneous immersion in the new discourse

• reflective imitation of a historically
  established discourse
• object-level imitation
• meta-level (re-)invention

an ongoing attempt to discover the meta-rules of
this new discourse, along with their rationale
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Condition for inventive imitation the new
discourse must be explicitly present
an expert participant of the new discourse must
actually practice this discourse so that the
learners can observe and join
but this is likely to create a commognitive
conflict incoherence stemming from different
participants disparate use of the same words
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Needed Learing-teaching (L-T) agreement - a
tacit agreement between participants about

1. which interlocutors discourse should be given
   the lead in the case of conflict

1. what are interlocutors respective
   responsibilities (division of labor) in the
   process of closing the discursive gap

1. what would be a reasonable course and pace of the
   discursive change

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In sum, here are two condition for inventive
meta-level learning

• the new discourse (e.g. on negatives) must be
  explicitly present

and in our case.

• there must be learning-teaching agreement between
  interlocutors

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in our case, both conditions were violated

• the new discourse must be explicitly present

• There must be learning-teaching agreement between
  interlocutors

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In the view of this theory it is thus not really
surprising that

• The students invented and agreed on a
  non-canonical meta-rule

• Learning-teaching agreement seemed to have been
  lost and difficult to regain

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Plan of this talk
And to close the circle, lets go back to the
meta-question
How should we talk about learning mathematic
(physics) so as to answer our questions?

• Two ways of talking about learningacquisitionist
  participationist
• B. Commognition as a special case of
  participationist approach School learning as
  developing discourses
• C. Applying commognitive discourse back to th
  question on learning negatives

• I hope to have shown that
• theories are but optional
• ways of talking/thinking
• about the world
• we can do without the
• dichotomy of thought communication

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Still confused?
Want to know more?

• You may able to find what you are looking for in

Sfard, A (2008, January) Thinking as
communicating Human development, the growth of
discourses, mathematizing. Cambridge University
Press