Assessment, learning and identity: sociocultural perspectives on learning mathematics

1. Assessment, learning and identity: sociocultural perspectives on learning mathematics Dylan Wiliam Institute of Education, University of London

2. 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

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

4. Key ideas • Structure and agency • Attunement to constraints and affordances • Desire, belonging and identity

5. Three cases • National testing in primary schools • Ability-grouping in secondary schools • Options in upper secondary education

6. National testing (1) I: So what are the SATs for? Jackie: To see if the teachers have taught us anything. Terry: If we don’t know nothing then the teacher will get all the blame. Jackie: Yeah. It’s the teacher’s 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 haven’t been teaching you properly

7. National testing (2) I: So are they important, SATs? Lily: Depends Tunde: 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 I’m gonna be a road sweeper.

8. National testing (3) I: You mean, you think that if you do badly in SATs then you won’t be able to do well or get good jobs? Jackie: Yeah, ’cause that’s what David [the class’s teacher] is saying. I: What is he saying? Jackie: He’s saying if we don’t 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 ain’t gonna be nothing like that if we don’t 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.

9. National testing (4) Sharon: I think I’ll get a two, only Stuart will get a six. I: So if Stuart gets a six what will that say about him? Sharon: He’s heading for a good job and a good life and it shows he’s 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.

10. National testing (5) Hannah: I’m really scared about the SATs. Ms. O'Brien [a teacher at the school] came and talked to us about our spelling and I’m no good at spelling and David [the class teacher] is giving us times tables tests every morning and I’m hopeless at times tables so I’m frightened I’ll do the SATs and I’ll be a nothing. I: I don’t understand Hannah. You can’t be a nothing. Hannah: Yes, you can ’cause you have to get a level like a level 4 or a level 5 and if you’re no good at spellings and times tables you don’t get those levels and so you’re a nothing. I: I’m sure that’s not right. Hannah: Yes it is ‘cause that’s what Ms. O'Brien was saying.

11. 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 you’re trying to concentrate you’re thinking, no, maths is hard, I don’t want to do it. I: So where do you think that comes from? Fathima: I don’t know, people all around. People —you don’t see mathematicians being a normal person— they have to be really big and brainy (Fathima, set 1, Cedar School)

12. 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 clever…I 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 by—those kind of people, I find that they’ll 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 can’t do it like that. That’s why I bring in old work because I won’t be able to answer the question like how they do it. So I’ll 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: It’s like…imagine we’re doing an equation or something and we’re trying to find a solution to it, they’ll say “Here’s 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 I’ll do that and then I’ll get an answer like that. (Tania, set 1, Willow School)

13. Options (1) T: There’s definitely a certain type of person who’s better at math. Generally, if you’re better at English they seem to be more social. And the math people. I don’t know, they’re just as social, but in a different way. They express themselves differently, they like to see things in black and white. They don’t see the colors and greys between. With English people they like things that don’t necessarily have an answer. They like to explore that. (Tom, Lemon school)

14. Options (2) JB: Why wouldn’t 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 isn’t 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)

15. 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)

16. 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.