Semiotic Mediation and Mathematical Puzzles

1
Title

• Semiotic Mediation and Mathematical Puzzles

2
Literature Review

• Semiotic Mediation
• New Artefacts and Mathematical Meanings in the
  classroom - Maria Mariotti
  (2005)
• Mind in Society - Lev Vygotsky (1978)
• Radical Constructivism
• Radical Constructivism A way of knowing and
  learning Ernst von Glasersfeld (1995)
• Semiotics
• Introducing Semiotics Paul Cobley and Litza
  Jansz (2003)
• Issues in secondary school mathematics teaching
• Is Mathematics TIRED ? A profile of Quiet
  Disaffection in Secondary School Mathematics
  Elena Nardi and Susan Steward (2003)
• Reflection
• Reflective Practitioner Donald Schön (1983)

3
Research Question

• What Semiotic Mediations occur between Learner
  and Teacher with an Artefact which allows the
  learner to explore some mathematical
  concepts/proofs in the knowledge domain of
  triangles and squares?
• Subject to population sample

4
Design

• Build 5 Mathematical Puzzles which allow learner
  and teacher to engage in a mathematical dialogue.
  
• How will it help answer the research question.
• The dialogue will be recorded and the data
  analyzed to see what Semiotic Mediations occur
• Support the work of Mariotti in detail
• Use of an Artefact to create mathematical meaning
  
• Use of the Artefact to stop mathematical
  misconceptions

5
Design to investigate Semiotic Mediation in
support and teaching of Mathematics
Artefacts can act as a Semiotic Mediator by
Mariotti
What is meant by Semiotic Mediation ? How can we
qualify this term ? How can we measure this term?

Purpose of research need to build an artefact to
observe Semiotic Mediation
6
Informed by Radical Constructivism
Radical Constructivism
PLAY with Knowledge

• Radical Constructivism
• Knowledge is not passively received by senses of
  subject
• Knowledge is actively built up by cognitive
  procedures with the subject
• The function of cognition is biologically
  adaptive tending towards fit or viability
• This mental construction is a way of the
  subject organising their experience of the world
  not the discovery of an absolute reality.

7
Reflections on Metaproject
Metaproject Pythagoras without Mathematics
Using ideas from reflection I have reviewed and
improved the artefact I produced last year
8
The Artefact

• Puzzle Maths
• https//www.cs.tcd.ie/heapg/Dissertation/index.ht
  ml
• How does it show your technical competence?
• All puzzles are written in Flash 8 refined from
  last year with generalised features which allows
  a set of puzzles to be created
• Created a web site resources which includes
• 5 Mathematical Puzzles
• A PHP Journal for Reflection and feedback from
  participants and peers
• Teacher Support
• Digital Video of Research Data (only with my
  permission with express use for research purposes
  only)

9
Methodology

• Research methodology used
• Qualitative Case Study
• Data collection instruments
• Digital Video will record the dialogue between
  learner and facilitator and the interactions with
  the Artefact

10
( Expected ) Findings

• Initial findings or what do you expect to find?
• Need to define what is meant by Semiotic
  Mediation
• Need to analyse the data and show how or not that
  the data fits into this concept of Semiotic
  Mediation
• I expect to find that the interaction with the
  artefact does allow the learner a different
  perception of mathematical concepts and the
  construction of mathematical proofs.
• I would like that perception to be positive !