Mathematics and ICT - PowerPoint

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pedagogy and ICT
David Wright
How ICT helps learners learn mathematics
(National Council for Educational Technology
(NCET) 1995)

 Learn from feedback
 Observe patterns
 See connections
 Work with dynamic images
 Explore data
 „Teach‟ the computer
Learning from Feedback
   Effective feedback allows:
    A  context of exploration
     A contingent claim to knowledge (it‟s ok to be
   through
     non-judgemental     and impartial messages
     possibility of privacy
Observing patterns
   The rapid production of results generates
    opportunities for:
     explanation
     justification
     proof

   Develops skills of enquiry and
Seeing connections
   Multiple, dynamic representations (for
    example, linking formulae, tables of
    numbers and graphs) give opportunities
     students making their own understandings
     gives the pupil a sense of power and control
      over the mathematics
Working with Dynamic Images
   Manipulation of diagrams dynamically:
     Unlocks   the power of visual imagery
     gives a sense of authorship to the pupil
     fosters a sense of confidence in one‟s ability
      to visualise mathematics and hence to think
Exploring data
ICT allows pupils access to real data and its
  representation, interpretation and modelling
    ownership of this process enhances the
     pupils‟ sense of authority
    access to different models encourages
     reflection and critique about models used in
     other situations
    access to multiple representations
     encourages reflection and critique of other
“Teaching the computer”
   In order to make a computer achieve a
    result pupils must express themselves
    unambiguously and in correct order
     They  make their thinking explicit as they
      refine their ideas
   Pupils are able to pursue their own goals
     theydevelop a sense of authorship and
      personal authority
Evolution of ICT in education
   Type 1 The learner and
    the computer                    Learner


   Type 2 The learner, the
    teacher and the computer        Learner      Teacher


   Type 3 (emphasising the
    „C‟ in ICT)                Learner


                              Dynamic     Autograph



               Low             Curricular specificity   High

      Johnston- Wilder and Pimm (2005)
Current research
   Small software on handheld technology
     WithPam Woolner and teachers at St
      Thomas More High School, North Shields
Two class sets of TI84+ calculators
have been supplied to the school. One
class have been given personal
ownership, the other set is used by the
department with a range of classes.

The school has also been supplied with
a range of software, including the TI
Smartview emulator and a range of
small software programs for the

TI has supplied its Navigator system
which will allow the calculators to be
networked wirelessly with the teacher‟s
computer and the projector.
Small software
„Navigator‟ network
Research focus:
 A socio-cultural analysis of the integration
  of ICT into the mathematics classroom
 An analysis of the mathematical meaning
  of the GC as an instrument in relation to a
  problem-solving task
Two theoretical frameworks

   Valsiner‟s zone theory (Valsiner, Goos)

   Instrumentation theory (Verillon &
    Rabardel, Artigue, Trouche & Guin)
Valsiner‟s zone theory
The zones
   ZFM – environmental constraints
      Resources
      Access to learners
      Technical support
   ZPA – activities which promote new skills and
   ZPD – the possibilities for learning
Instrumentation theory (Guin &
    The instrumented activity system model
    (Verillon & Rabardel)
                                   Instruments emerge through a
                                   dialectical interplay between the
                                   technical demands of mastering a
                                   device and the conceptual work of
                                   making that device meaningful in the
                                   context of a task (Artigue, 2002)

                       Utilisation scheme (theorems-in-action)
Instrumentation theory
“Instrumental genesis thus makes artifacts meaningful in the context of
activity, and provides a means by which users make meaning of that
activity” (White, 2008)
   An instrument is more than object/artifact – it is a psychological
    construct consisting of a dialectical process of:
      Instrumentalisation –
          Oriented towards the artifact – this is the process by which
           an artifact becomes the means of achieving an objective,
           solving a problem etc.
      Instrumentation-
          Oriented towards the user - the user develops the schemes
           and techniques through which the artifact can be
           implemented in purposive action. “Instrumentation is
           precisely the process by which the artifact prints its mark on
           the subject …” (Trouche, 2004)
Utilisation schemes
   Comprise both the rules and heuristics for applying an artifact to a
    task and the understanding of the task in the form of „theorems in
   “Theorems-in-action take shape as the domain-specific propositions
    on which learners rely as they interpret the capabilities [affordances]
    and constraints of a tool in relation to the features of a problem-
    solving task” (White, 2008)
   Hence the possibility of research focused on „theorems-in-action‟ as
    a mechanism for linking the learner‟s instrumented activity with
    learning goals and curricular content.
Artigue, M (2002) Learning mathematics in a CAS environment: The genesis of a reflection about
     Instrumentation and the dialectics between technical and conceptual work International Journal of
     Computers for Mathematical Learning 7:245-247
Goos, M (2005) A sociocultural analysis of the development of pre-service and beginning teachers‟
     pedagogical identities as users of technology Journal of Mathematics Teacher Education 8:35-59
Guin,D and Trouche,L (1999) The complex process of converting tools into mathematical instruments:
     The case of calculators International Journal of Computers for Mathematical Learning 3: 195-227
Johnston-Wilder,S and Pimm,D (2005) Teaching Secondary Mathematics with ICT. Maidenhead:Open
     University Press
National Council for Educational Technology (1995) Mathematics and IT: A pupil’s entitlement NCET
Trouche,L (2004) Managing the complexity of human/machine interactions in computerised learning
     environments: Guiding students‟ command process through instrumental orchestrations.
     International Journal of Computers for Mathematical Learning 9(3): 281-307
Valsiner,J (1997). Culture and the development of children’s action: A theory of human development.
     (2nd Ed) New York: John Wiley and Sons
Verillon,P and Rabardel,P. (1995) Cognition and artifact: A contribution to the study of thought in
     relation to instrumented activity. European Journal of Psychology in Education, 9(3): 77 – 101
White,T (2008) Debugging an Artifact, Instrumenting a Bug: Dialectics of Instrumentation and Design
     in Technology-Rich Learning Environments International Journal of Computers for Mathematical
     Learning 13:1-26