Telling identities - In a search of the missing link between culture and learning

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Telling identities - In a search of the missing
link between culture and learning

• Anna Sfard
• The University of Haifa Michigan State
  Univerwsity

Ålborg, 2 February 2010
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• How we came across the context in which to use
  the notion of identity just one example

From Israeli press
There are immigrant children who arrive at
the highest places in international competitions
in mathematics and physics and thanks to them,
Israel climbed from 24th to 13th place in the
1995 international championship (2.06.96).
Approximately 200 thousand children immigrated
to Israel in 11 years, most of them from the
former Soviet Union they constitute 15 of the
Israeli youth (31.08.01).
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What is it that produces widespreadsuccess (or
failure)in mathematics?

• Question

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Perhaps
highly unlikely
Genes?
Better teaching methods in the former Soviet
Union?
Sure, but there must be more
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Plan of this talk

1. Operationalizing the question explorative
   ritualized learning
2. Preparing the tools defining identity
3. Answering the question from sociocultural
   context to learning - via identity

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Part 1 Operationalizing the question

• explorative vs. ritualized learning

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Taking a look at the success in makingThe study
Theme Cultural embeddedness of mathematics
learning
Researchers Anna Prusak Anna Sfard
Question What are the differences, if any, in
the ways of learning mathematics by students
coming from different cultural backgrounds?
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Background The study
1 year-long ethnographical participant-observati
on of the process of learning in 11th grade
high-level mathematics classroom with

• 10 native Israelis (OldTimers, OTs)

• 9 new immigrants from the former Soviet Union
  (NewComers, NCs)

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we looked at the students

• problem-solving activities
• use of mathematical language
• collaboration with others
• becoming skillful in procedures
• use of symbols and of visual means
• independent work preparations to exams
• reactions to grades
• expectations from math teacher
• use of textbooks
• and many more

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Activity under study Learning alone from a
textbook

• Step 1 Homework
• Learn new topic, Cosine Law and its
  applications, from the textbook.

Step 2 Unannounced test Formulate and prove the
law (with a new drawing)
Step 3 Task Describe the way you learned
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Homework
OldTimers
NewComers

• 10 students written answers to the teachers
  questions

• 1 student full written answer
• 3 students written partial answers

All the students claimed that they understood
everything
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Test Students reaction
From the teachers journal Everybody was quiet
during the first few minutes of the test. But
then, several OldTimers started complaining We
learned at home with the letters A, B, C and we
got used to them. The Newcomers did not show
any sign of surprise. All of them, even Boris
usually the slowest finished quickly.
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Test The results
OT
NC

• Full proof, textbook version

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1

• Full proof, modified version

-
2

• Partial, erroneous proof

1
-

• No proof

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1
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What did they say about the way they learned?
An OT wrote
An NC wrote

• I read the chapter in the book and tired to
  understand
• When I felt I understood, I copied the proof to
  the notebook

• I read the text a number of times, trying to
  remember and making notes on a separate page.
• I reproduced the proof without writing
• I wrote the proof from memory with the book
  closed.
• I compared the proof to the one in the book.
• I then read and tried to understand the examples
  of application in the book

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Close-up on the difference in the way of learning
OldTimers
NewComers

• Performed the actions required by the teacher,
  and for the teacher

• Made their own decisions what to do, did not
  address it at the teacher

• Tried to have a dialogue with the book and to
  turn it into a dialogue with themselves

• Just read the book, as required by the teacher

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• Two types of learning

Explorative learning Learning that aims at
turning mathematics into a discourse-for-oneself
Ritualizedlearning Learning of the student
who practices math only as discourse-for-others
Discourse-for-oneself discourse one turns to on
her own accord, to solve self-posed problems
Discourse-for-others discourse into which one
engages only when requested to do so by others,
to whom it makes sense
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Summary and conclusion

• NewComers strove toward explorative learning

• constant backtracking self-examination

• preference for individual work

we saw it everywhere in their

• care for the mathematical appropriateness

OldTimers satisfied themselves with ritualized
learning
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Findings and further questions
QUESTION How can we account for these
differences?
FINDINGS The OTs and NCs learned differently
(and with different results)
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How do we account for the difference in learning?
conjectureNewComers former learning? (were
taught how to learn?)
Sure, but how to explain the students
willingness to use these techniques?
conjectureTheir immigrant status amplified
their willingness to learn?
Yes, but why mathematics?
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Seems that we need to consider a wider cultural
context
We need better understanding of the relationship
between the quality of students mathematics
learning and the context in which their learning
occurs Wang Lin (2005). Comparative studies
on US and Chinese mathematics learning.
Educational Researcher
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Seems that we need to consider a wider cultural
context
If so, we also need a conceptual tool for
explaining how the cultural (the collective) may
enterindividual learning And the tool we chose
is.. identity
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• Why
• identity
• and not
• personality
• nature or
• character?

Because all the latter imply natural givens,
but to deal with cultural shaping we need an
entity that can be understood as man-made
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Part 2Preparing the tools

• Defining identity

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What is identity?
Those who define, do it in terms of who we are
or what kind of person we are (e.g. Gee, 2001
Holland et al.)
Most writers who use the word do do not
define (e.g. Lave Wenger, 1991 Wanger, 1998)
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Lack of operationality

• How does one answer the question
• Who are you?

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How operational is it?

• Dr. B So, Dave, tell us about
  yourself. Who are you?
• Dave Well, I am an executive assistant in a
  major pet product company.
• Dr. B Interrupts Dave, I dont want you to
  tell us what you do, I want you to tell us who
  you are.
• Dave Oh, all right, ah I am a pretty good guy,
  I, I like playing tennis on occasions, I
• Dr. B Interrupts Also, not your hobbies,
  Dave. Just the simple task Who you are.
• Dave Im just nice easy going manIm being a
  little bit indecisive at times, I 
• Dr. B Interrupts Dave, youre describing your
  personality. I want to know who you are.

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It may be easier to answer the questionWhat is
theactivity of identifying?
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The activity of identifying is eveywhere. It is
about how we talk.
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• Identifying turning sentences about DOING
  into sentences about BEING (or HAVING)

BEING (HAVING)
DOING
A is an able student (has a gift)
In the majority of school tests and activities A
attained above average scores
B investigates mathematical problems and teaches
mathematics in the university
B is a mathema-tician
I am a bad driver
I caused minor road accidents many times.
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We identify, among others, with

• Grades
• Diagnoses (e.g. IQ, LD)
• Certificates
• Diplomas
• Ranks

• Titles (prof, officer)
• Licenses
• Awards, prizes
• Red tickets

• Personal websites
• Self-presentations

we believe all these merely describe reality,
but is this so?
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If it was so, there would be no reason for the
American literary critic Richard Gilaman to say

• I dont think about myself as critic or
  teacher.., but simply as someone who teaches,
  writes

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Identifying

• means translating actions, which do not last,
  into properties of a person, which are lasting
• it means making our social relations appear as if
  they were permanenet (although they are not!)

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Why do we identify?

• Because the identity talk allows us to overcome
  the constant change

make sense of what we see now in terms of our
past experience
as well as plan for the future.
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Definition

• Identity of A stories about A that

• reify As actions

use the verb be and have rather than do, and
avoid past tense
the author believes they apply to A

• are endorsed by their author

They have an impact on how the author feels
about A

• are significant to their author

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If so,

• We can speak of different identities of A,
  depending on who is telling the story to whom.
  Thus, identity is the triple
• BAC
• A the identified B the author C the
  recipient

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The identity of A

• AAA

(the story one tells about oneself to oneself)
- has the greatest impact on what one does

• is a collective creation stories give rise to
  new stories

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The object of study in our research
Yes
No
Identifying (activity)
Identity (agentless, atemporal)
More specifically, the interplay between the
activity of identifying and other human
activities (e.g. learning)
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Data analysis
Sample 2 (from Learning Disability
Study) Mira 5 and 6 is 11. Ah.. 4 and 9 is
., hold on.. 4 and 9 makes 13. 13, just a
second, .............................. 8000.
Oh, I forgot. Interv. You said 5 and 6 makes 11,
right? Then you found 4 and 9. Its
13. Interv. Would you like to write it
down? Mira Thats it. I cant. It boggles my
mind. mumbling . My brain is so slow.
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Part 3 Answering the question

• From sociocultural context to learning via
  identity

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Identifying is not just describing it is
making things happen!
How does it work?
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Current designated identities
Current IDis an identity told in present tense
and formulated as a factual statement

• Designated IDis an identity told in future tense
  or with the help of words like should, must, have
  to, can, cannot
• I will be a doctor, I have to be a better
  person

Designated identities are all important because
they influence how the person - feels about
herself - acts (stories as self-fulfilling
prophecy)
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Toward a narrative theory of identity

• Where does As designated identity of the type
  AAA come from?

• 2nd 3rd person identities BAA BAC
• other peoples identities told by significant
  narrators

• How does designated identity influence As
  learning?

• Explorative learning is closing a critical gap
  between As current designated identities

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Toward a narrative theory of identity

• Where does ones designated identity come from?

• From what other people (parents, teachers) say
  bout her or him

• Where does As designated identity of the type
  AAA come from?

• 2nd 3rd person identities BAA BAC
• other peoples identities told by significant
  narrators

• How does designated identity influence As
  learning?

• Explorative learning is closing a critical gap
  between As current designated identities

• How does designated identity influence ones
  learning?

• If one has mathematical competence in her DI, she
  will learn exploratively

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Lets take a look at NewComers and OldTimers
self-told designated identities
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Sources of data on NewComers OldTimers
designated identities

• Stories told by the students to the teacher
  AAthe teacher
• What the students said about others ABteacher
• Other teachers and parents stories other
  teachersAthe teacher, parentsAthe teacher

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This is what I want to be
OTs
NCs

• What I want changes, because I change
• For me, the only important thing is to be happy,
  and I dont have any particular profession in
  mind.

• In Russia I knew all the time that Ill follow in
  my brothers footsteps and learn computers
• From the earliest childhood I dreamt to be a
  medical doctor, like my mother.

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The place of mathematics Why learn it?
OTs
NCs

• I want to have a matriculation certificate
• It is obligatory
• I have to pass matriculation examination if I
  want to achieve anything in life.

• I need it because I need knowledge and good
  education, and I love learning
• I need to be a full-fledged human being if I
  want to feel I did something in life

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OldTimers and NewComers had different
expectations from the teacher
OTs said the teacher should
NCs said the teacher should

• have the necessary math pedagogical expertise
• be able to interest students
• be able to explain math clearly
• be just
• be inventive

• be a human being
• refrain from pushing
• adjust herself to students
• be always ready to help students
• be close to the students
• be lenient with students

should be a human being
should be professional
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Summary of designated identities
OTs
NCs

• Future plans and their source

unspecified (to be happy)
to be a professional

• The reason for learning math

math is a gatekeeper
maths is a desirable activity

• Expectation from the math teacher

should be a human being
should be a professional
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From the difference in designated identities to
the difference in learning mathematics
NCs
OTs

• Role of math fluency in designated ID

significant
insigni- ficant

• Type of learning

explorative
ritualized
therefore ?

• Relation between ID and learning

learning math closing the identity gap
no math-related identity gap
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Last questionWhere do students designated
identities come from?
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A. Who were NCs and OTssignificant narrators?
Where students designated identities come from?
NCs
OTs

• From the earliest childhood I dreamt to be a
  medial doctor, like my mother.
• My parents know best whats good for me.
• For me, my grandma is the greatest authority.

• My parents want me to be happy, so it is not so
  important for them what Im going to do.
• They want for me to be what I want.

Many references to parents
Very few refs to parents
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SummaryComparison of NCs and OTs designated
identities
NCs
OTs

• Significant narrators

parents
mainly peers

• Flexibility

stable, continuing
fluid, ever new

• Openness

determined, closed
undefined, open

• Math fluency

a critical element
not a critical element
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These finding corroborate the claim that

• sociocultural context
• shapes the learning of mathematics
• via designated identities

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Having said all this, how do we improve the
learning of mathematics?
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This question is tantamount to this one
How can we help young people in forming
designated identities that would include
mathematical fluency as a critical element?
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As parents teachers we should remember

• success and failure in mathematics are collective
  creations. We are all responsible.

• What we say to children about themselves is
  important it may perpetuate success or failure

• Making math a critical element of ones
  designated identity promotes explorative
  learning, but it may also backfire!

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However, not all is in our hands! The general
cultural climate does not seem quite friendly
about mathematics learning If I had only one
day left to live, I would live it in my math
class it would seem so much longer.
this is what they say on the web
about mathematics Philosophy is a game with
objectives and no rules. Mathematics is a game
with rules and no objectives.
about mathematics teacher she is a person who
talks in someone else's sleep.
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One change we certainly should consider
Putting an end to the practice of using
mathematics as a gatekeeper
Some others incorporate lack of math fluency as a
critical element into their designated identities
Some students fail to incorporate it as a
critical element (OldTimers)

• After all, this use of mathematics is the
  reason why

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Any other ideas?

• Over to you now

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(No Transcript)
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What did we gain from thus defined notion of
identity?
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Advantages of identity-as-story

• It disobjectifies identity
• Identity has a human author.
• It is culture-sensitive.

• As a research concept, it is operative
• All studies on identity could be retold as
  reports on stories told by people about people,
  and about consequences of these stories

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One can build thery of indentity on the basis of
what is known about the dynamics of narratives
that is, how stories interact (bi-directionally)
with

• each other (e.g. which are critical elements? Who
  are significant storytellers?)
• with extra-discursive world
• with other human activities (e.g. learning)

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But what is identity?
James Gee, 2001 Discourses can give us one way
to define what I called earlier a persons core
identity. Each person has had a unique
trajectory though Discursive space. This
trajectory and the persons own narrativization
of it are what constitute his or her . core
identity. (p. 111).
A few pages earlier the author said Any
combination that can get recognized as a certain
kind of person (e.g. a certain kind of African
American, radical feminist, doctor, patient,
skinhead) is what I call a Discourse with a
capital d Discourses are ways of being
certain kinds of people p.110
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But first, did we lose anything?
Those who claim otherwise may be confusing
identity the discursive construct with
factors that shape identity (and this is like
confusing the portrait of Mona Lisa with Mona
Lisa, the person)

• Did we?
• Wenger, 1998
• Identity is not, in its essence, discursive or
  reflective words are important, no doubt, but
  they are not the full, lived experience of
  engagement in practice.

• Well, not really!
• It is true that we experience identities (as we
  experience velocity).
• However, identity is a concept (of oneself,
  of another person), that is, a discursive
  construct (just like velocity).
• Identity the discursive construct comes first,
  and the experience later.

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• Necessary condition for communicational
  effectiveness of research

operationalisation of the research vocabulary
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• What is operational concept? Blumers answer
  (1964)

A satisfactory concept in empirical science must
meet three simple requests
1. It must point clearly to the individual
instances of the class of empirical objects to
which it refers
2. It must distinguish clearly this class of
objects from other related classes of objects
3. It must enable the development of cumulative
knowledge of the class of objects to which it
refers
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Not sufficiently operational

• attitude is empirically ambiguous

According to Herbert Blumer (1964)
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• You may object

After all, we use most our concepts without
defining
Yes, but this is possible only because we use
the mechanism of metaphor
and in research, unlike in poetry, metaphors may
be counterproductive
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For example, objectifying metaphor

• makes us use keywords of this latter discourse
  as if they referred to mind-independent,
  extra-discursive entities

that
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Objectifying metaphorexamples
In science and mathematics

• Force, energy
• Number, function, set
• Ego, superego, id

In educational research

• Knowledge, concept, meaning
• Belief, attitude, value
• Personality, character, identity
• Ability, disability, gift

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Objectifying metaphorits message on the
referent

• transcendence the object exists in the world,
  not in the discourse
• disembodiment it does not have an author - is
  given, not man-made
• reification it is a possession (property) of an
  actor, not of the action

All this goes right against all we want to
achieve with the concept of identity!
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Here is, indeed, how the talk about identity (who
one is) leads to objectification (and to the
very trap that particiaptionist want to avoid!)

• J.M. Coetzee
• Who is to say that at each moment while the pen
  moves he is truly himself? At one moment he might
  be truly himself, at another he might be simply
  be making things up. How can he know for sure?  
• Coetzee, J.M. (2002). Youth Scenes from
  provincial life II. (p. 10)
• London Penguin Books.