Assessment, learning and identity: sociocultural perspectives on learning mathematics

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Assessment, learning and identity sociocultural
perspectives on learning mathematics

• Dylan Wiliam
• Institute of Education, University of London

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Assessment in education

• There is no such thing as assessment degree
  zero
• Assessments are objects of history
  (Cherryholmes, 1989)
• Concerns for reliability change the construct
• Assessments reify the constructs they purport to
  assess

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Three approaches

• Community of practice (Lave Wenger)
• Figured worlds (Holland et al.)
• Activity theory (e.g., Engeström)

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Key ideas

• Structure and agency
• Attunement to constraints and affordances
• Desire, belonging and identity

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Three cases

• National testing in primary schools
• Ability-grouping in secondary schools
• Options in upper secondary education

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National testing (1)
I So what are the SATs for? Jackie To see if
the teachers have taught us anything. Terry If
we dont know nothing then the teacher will get
all the blame. Jackie Yeah. Its the teachers
fault. Tunde Yeah. They get blamed.
... Mary SATs are about how good the teachers
have been teaching you and if everybody gets
really low marks they think the teachers havent
been teaching you properly
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National testing (2)
I So are they important, SATs? Lily Depends Tund
e Yes Terry No, definitely not. Lewis It does
affect your life Ayse Yeah, it does affect your
life Terry No, as if it means you know I do
badly then that means Im gonna be a road
sweeper.
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National testing (3)
I You mean, you think that if you do badly in
SATs then you wont be able to do well or get
good jobs? Jackie Yeah, cause thats what David
the classs teacher is saying. I What is he
saying? Jackie Hes saying if we dont like, get
good things in our SATs, when we grow up we are
not gonna get good jobs and Terry Be plumbers
and road-sweepers Tunde But what if you wanted
to do that? I Instead of what? Terry Footballers
, singers, vets, archaeologists. We aint gonna
be nothing like that if we dont get high
levels. I And does that worry you about your
future? Jackie Yeah. Lewis Yeah. Ayse Yeah it
worries me a lot Terry No, because he
referring to the teacher is telling fibs.
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National testing (4)
Sharon I think Ill get a two, only Stuart will
get a six. I So if Stuart gets a six what will
that say about him? Sharon Hes heading for a
good job and a good life and it shows hes not
gonna be living on the streets and stuff like
that. I And if you get a level two what will
that say about you? Sharon Um, I might not have
a good life in front of me and I might grow up
and do something naughty or something like that.
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National testing (5)
Hannah Im really scared about the SATs. Ms.
O'Brien a teacher at the school came and talked
to us about our spelling and Im no good at
spelling and David the class teacher is giving
us times tables tests every morning and Im
hopeless at times tables so Im frightened Ill
do the SATs and Ill be a nothing. I I dont
understand Hannah. You cant be a
nothing. Hannah Yes, you can cause you have to
get a level like a level 4 or a level 5 and if
youre no good at spellings and times tables you
dont get those levels and so youre a
nothing. I Im sure thats not
right. Hannah Yes it is cause thats what Ms.
O'Brien was saying.
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Ability grouping (1)
Fathima Also people find maths very hard. There
is always a psychological thing in your mind that
maths is hard. No matter what, everyone thinks
maths is hard. So when youre trying to
concentrate youre thinking, no, maths is hard, I
dont want to do it. I So where do you think
that comes from? Fathima I dont know, people
all around. People you dont see mathematicians
being a normal person they have to be really big
and brainy (Fathima, set 1, Cedar School)
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Ability grouping (2)
Tania There were a couple of lessons where it
really sort of hit me as like I was really
working hard and I really changed my attitude in
maths. I found that the people I thought were so
cleverI was getting better marks than them and I
was more ahead of them in class, while they were
just like chatting. So well I thought, you
know Tania I think that with some people,
like the people in my class the ones people feel
threatened bythose kind of people, I find that
theyll just stick to it like this is it, this is
how you have to do it and you always have to do
it like this. Whereas me, I cant do it like
that. Thats why I bring in old work because I
wont be able to answer the question like how
they do it. So Ill try and bring in everything I
know and try and find an answer. I So, what
do you think it is that they do? Tania Its
likeimagine were doing an equation or something
and were trying to find a solution to it,
theyll say Heres the formula, this is what you
do. Where I would probably go If I look back at
this topic, I can use that to solve this bit and
then Ill do that and then Ill get an answer
like that. (Tania, set 1, Willow School)
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Options (1)
T Theres definitely a certain type of person
whos better at math. Generally, if youre better
at English they seem to be more social. And the
math people. I dont know, theyre just as
social, but in a different way. They express
themselves differently, they like to see things
in black and white. They dont see the colors and
greys between. With English people they like
things that dont necessarily have an answer.
They like to explore that. (Tom, Lemon school)
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Options (2)
JB Why wouldnt you major in math? C I think
I'm a more creative person, I can do it and I can
understand it but it's not something I could do
for the rest of my life and I think if I had a
job I'd like one that let me be a little more
creative. JB Math isnt creative? C No.
(Cathy, Lemon school) I think women, being that
they're more emotional, are more emotionally
involved and math is more like concrete, it's so
"it's that and that's it." Women are more, they
want to explore stuff and that's life kind of
like and I think that's why I like English and
science, I'm more interested in like phenomena
and nature and animals and I'm just not
interested in just you give me a formula, I'm
supposed to memorize the answer, apply it and
that's it. (Kristina, Apple school)
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Options (3)
JB Do you like math? V No, I hate it. JB Why
do you hate it? V It's just too, I'm into the
history, English () It's like too logical for
me, it always has to be one answer, you can't get
anything else BUT that answer. (Vicky, Lime
school) B I used to love math, but now I
think, it's like I'm going to make sure that I
don't major in math or anything because it's
starting to be like too much competition, it's so
weird. When it came to calculus and precalculus,
I just kind of lost interest. It's like I'm going
to do this for the points, I don't really care. I
care more about science and English, stuff that
makes sense to me where I think I'm learning
morals and lessons from this, where I can apply
it to something.(Betsy, Apple school)
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References
Boaler, J., Wiliam, D., Zevenbergen, R. (2000).
The construction of identity in secondary
mathematics education. In J. F. Matos M. Santos
(Eds.), Mathematics Education and Society (pp.
192-202). Montechoro, Portugal Centro de
Investigacao em Educacao da Faculdade de Ciencias
Universidade de Lisboa. Engeström, Y., Miettinen,
R., Punamäki, R.-L. (Eds.). (1999).
Perspectives on activity theory. Cambridge, UK
Cambridge University Press. Holland, D.,
Lachicotte Jr, W., Skinner, D., Cain, C.
(1998). Identity and agency in cultural worlds.
Cambridge, MA Harvard University Press. Wenger,
E. (1998). Communities of practice learning,
meaning, and identity. Cambridge, UK Cambridge
University Press. Wiliam, D., Bartholomew, H.,
Reay, D. (2004). Assessment, learning and
identity. In R. Zevenbergen P. Valero (Eds.),
Researching the socio-political dimensions of
mathematics education issues of power in theory
and methodology (Vol. 35, pp. 43-61). Dordrecht,
Netherlands Kluwer Academic Publishers.