Learner identity

1
Learner identity conditioned/influenced by
mathematical tasks in textbooks?

• Birgit Pepin
• University of Manchester
• School of Education
• Manchester M13 9PL
• birgit.pepin_at_manchester.ac.uk

2
Background

• Importance of textbooks and mathematical tasks in
  textbooks
• Learner identity
• Previous projects
• Learning mathematics with understanding
• Connectivity

3
Importance of mathematical tasks in textbooks

• Textbooks are one of the main sources for
  mathematical content covered and the pedagogical
  styles used in classrooms (Valverde et al, 2002)
• Importance of the nature of the learning task
  (Hiebert et al 1997)
• Students need frequent opportunities to engage
  in dynamic mathematical activity that is grounded
  in rich, worthwhile mathematical tasks
  (Henningsen Stein, 1997)
• Using the mathematical task as an analytical tool
  for examining subject matter as a classroom
  process (rather than simply as a context variable
  in the study of learning) (Doyle, 1988)

4
Learner identity

• Identity construction is situated in specific
  cultural (and national and local) contexts
  where interacting factors help or impede the
  construction of an identity as and for
  mathematical learning
• Social identity helps to consider learners as
  constructed in terms of the groups/classes of
  which they are members (or not)
• What does it mean to be a learner of mathematics
  in England, France and Germany?- interest in the
  idea that schools and classrooms help to produce
  social identities which are available to
  individual students (Osborn et al, 2003)

5
Previous projects

• Mathematics teachers pedagogies in England,
  France and Germany (Pepin, 1997, 1999, 2002)
• Mathematics textbooks and their use by teachers
  in England, France and Germany (Pepin Haggarty,
  2001, Haggarty Pepin, 2002)

6
Learning mathematics with understanding

• the tasks in which students engage provide the
  contexts in which they learn to think about
  subject matter, and different tasks may place
  different cognitive demands on students . Thus,
  the nature of tasks can potentially influence and
  structure the way students think and can serve to
  limit or to broaden their views of their subject
  matter with which they are engaged. Students
  develop their sense of what it means to do
  mathematics from their actual experiences with
  mathematics, and their primary opportunities to
  experience mathematics as a discipline are seated
  in the classroom activities in which they engage
  (p.525) (Henningsen Stein, 1997)
• Hiebert et al (1997) similarly argue that
  students also form their perceptions of what a
  subject is all about from the kinds of tasks they
  do. Students perceptions of the subject are
  built from the kind of work they do, not from the
  exhortations of the teacher. The tasks are
  critical. (p.17/18).

7
Connections and connectivity

• the way information is represented and
  structured. A mathematical idea or fact is
  understood if its mental representation is part
  of a network of representations. The degree of
  understanding is determined by the number and
  strength of the connections. (p67) (Hiebert
  Carpenter, 1992). Hiebert and Carpenter (ibid)
  further point out that if mathematical tasks are
  overly restrictive, students internal
  representations are severely constrained, and the
  networks they build are bounded by these
  constraints. Further, the likelihood of transfer
  across settings becomes even more problematic
  (p79).

8
Connections and connectors

• Research conducted at Kings College in the United
  Kingdom (Askew et al, 1997) revealed that highly
  effective primary teachers of numeracy paid
  attention to
• Connections between different aspects of
  mathematics for example, addition and
  subtraction or fractions, decimals and
  percentages
• Connections between different representations of
  mathematics moving between symbols, words,
  diagrams and objects
• Connections with childrens methods valuing
  these and being interested in childrens thinking
  but also sharing their methods. (Askew, 2001,
  p.114)

9
Aim

• In this seminar I would like to investigate
  different mathematical tasks in terms of
  connectivity and explore how this might relate
  to learner identity in the three countries.
• This might enable us to consider the different
  identities available, and further to what extent
  available identities may be different or similar
  in the three countries.

10
Questions

• What are the connections made in mathematical
  tasks in selected textbooks in England, France
  and Germany?
• How is this likely to shape pupil identity as
  learners of mathematics?
• What are the differences, in terms of
  mathematical tasks, and perhaps proposed
  learner identity, in the three countries
  textbook tasks that we can identify?

11
Contextual factors

• England whole school ethos teachers feel they
  have to attend to the needs of the individual
  child setting in mathematics with different
  mathematics taught to different groups.
• France class as a unit identity of mathematics
  as a selection (and difficult) subject mixed
  ability teaching (egalitarian ideas) and
  entitlement to the same curriculum .
• Germany class as a unit, but within tri-partite
  system different streams had different
  identities reflected in a different curriculum,
  teachers and school organisation different
  approaches to the academic and affective in
  different streams.

12
Making connections and seeking links

• Individual tasks are analysed with respect to
• context embeddedness, familiar situations- tasks
  which make connections with what students already
  know, real life (for example, in introductory
  tasks/activities)
• cognitive demand/formal statements/generalisations
  - tasks which emphasise relational rather than
  procedural understanding, tasks which make
  connections with the underlying concepts being
  learnt
• mathematical representations- tasks which make
  connections within mathematics and across other
  subjects, tasks which connect different
  representations.

13
Learning and learning identity- harmony of forces?

• Pollard Filer (1996) argue that effective
  learners are produced when their strategies and
  presentation of identities become well-adapted to
  the social understandings in the learning
  context. We can describe these as educational
  cultures, and the conditioning that is
  happening is likely to be dependent on classroom
  and mathematics cultures (which in turn is
  influenced by the tasks pupils are given).

14
Back to our question

• What kinds of opportunities are given to students
  to learn mathematics (and to connect) and how
  do these relate to their identity construction as
  a learner of mathematics?

15
Typology?

• What are the resources available to students as
  they seek to identify or develop or construct
  their identities?
• Can we identify typologies (of tasks) that are
  likely to influence students in their
  construction of identities, such as
• Instrumentalist
• Developmentalist
• Negotiator
• Conformist
• Connector
• ?