504 Moving into Third Space — High School Students’ Funds of Knowledge in the Mathematics Classroom Steve Thornton University of Canberra steve.thornton@canberra.edu.au Students enter Australian high schools with a wide variety of knowledge, background experiences, attitudes to school and discourses, their “funds of knowledge”. Much of this comes from their “first space” — what they bring from the home and community. Some of it comes from their “second space” — what they bring from prior school experiences and what they experience in the current school environment. This second space is profoundly shaped by the experience of formal, textbook-oriented approaches to high school mathematics. This theoretical paper looks at the experience of students entering their first year of high school mathematics in terms of first and second space, and casts forward to the creation of a “third space” — one which values and builds on students’ funds of knowledge. 23 May 2002, 9.40am: Royal Avenue High School 1 Lucy, a student teacher, is teaching a year 7 maths class. There are fifteen students in the class, mostly boys, clearly from a variety of cultural backgrounds. According to the teacher, Mr C, there are five students missing from today’s lesson. Four of the students here today were absent yesterday. As they wait outside the class some students push each other so that they can get into the room quickly and have first choice of seat; one tells his friend about the fight at home the previous night; some talk loudly about how much being at school “sucks”. When they enter the room many of the students race towards the single heater at the far side of the room, pushing over chairs or desks on their way. Lucy writes a few simple addition questions on the blackboard, and one or two of the students start to write some answers on paper. Another student yells that he doesn’t have a pencil, others just sit there, others do not even seem to notice that there is anything written on the board. After a few minutes Lucy tries to talk to the class to check their answers, but no one seems to listen. Mr C seems powerless to help. The lesson proceeds, with Lucy handing out a blackline master with a mixture of addition and subtraction questions. It is all she can do to prevent the students from physically harming each other, vandalising the room, not climbing out of the windows, and not running out of the room and disturbing other classes. 23 May 2002, 11.30am: McWilliam College Melinda, a student teacher, is teaching a year 7 maths class. There are twenty-six students in the class, about two thirds are girls, all dressed neatly in school uniforms. Ms L, their normal teacher arrives with Melinda to allow the students into the classroom. The room is arranged in a U-shape, and when they enter the room each student makes their way to their chair, puts their schoolbag on the floor, and takes out a pen, a textbook and an exercise book. Melinda writes some algebraic simplification questions on the board, and the 1 The names of the schools, teachers and student teachers in these vignettes have been changed. When I made these observations of the classes my focus was on the teaching skills of my student teachers, rather than the school students or the classroom environment. Hence the vignettes were written in hindsight. They are written as impressions, rather than as an attempt to record accurate details.