Enhanced secondary mathematics teaching Gesture and the interactive whiteboard

1
Enhanced secondary mathematics teaching Gesture
and the interactive whiteboard

• Dave Miller and Derek Glover
• eda19_at_educ.keele.ac.uk
• http//www.keele.ac.uk/depts/ed/iaw/

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Starting point for work on gesture 1

• How does gesture support, enhances and emphasise
  learning?
• Gesture use is related to the taken and shared
  ways in which a classroom community reasons,
  symbolises and argues (Cobb and Yackel, 1996).
• This means that there is wide recognition of the
  range of visual bodily actions that are more or
  less, generally regarded as part of a persons
  willing expression (Kendon, 2000).

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Starting point for work on gesture 2

• Abrahamson (2003) sees this as part of the use of
  bridging tools that establish artefacts for
  further mathematical development with embodied
  cognition from their hands on experience but in
  doing so they communicate their discussion and so
  use gesture.
• Rasmussen et al (2004) develop Pea (1993) by
  suggesting that knowing rather than being located
  entirely in the mind is distributed across
  activities involving tools, utterances and
  symbols and so focusing on the function of
  gesturing in the collective development of
  meaning can be important.

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Data collection methods 1

• Initially lesson observation was undertaken by
  visiting staff, supported by the use of
  video-recorded lessons.
• Since 2003 all investigations have been made
  through the analysis of video-recorded data.
• All this is supported by staff interviews and
  some pupil interviews.

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Data collection methods 2

• Initial 35 lessons were with teachers who had
  volunteered to be involved or had been
  recommended as good IAW practitioners.
• Next 42 lessons were associated with 7 schools
  who were selected for involvement in a project.
• Final 46 lessons were recorded in same schools as
  previous 42 lessons.

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The first 35 lessons

• Interactivity is the key to enhanced learning
  with IAW technology. It was felt to exist at
  three levels
• teacher-learner reacting to each other,
  especially as seen in the use of questioning
• pupils working together or individually in
  solving or developing IAW based concepts, as
  seen in the development of discussion
• at the board, on the desk

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The first 35 lessons

• Interactivity is the key to enhanced learning
  with IAW technology. It was felt to exist at
  three levels
• the process observed in individual learning in
  the complex of understanding between materials on
  the IAW, materials on the learners desk and the
  engagement of brain as the intermediary as seen
  in the use of artefacts, gesture and multi-modal
  learning.

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Investigation of gesture

• How far is gesture an important part of
  teacher-learner interaction?
• Although differing from person to person, is
  there any commonality in the way in which body
  language mediates the IAW to the learners?
• Analysis would be from a practitioner rather than
  a psychologist viewpoint.
• We would dissect video-recorded lessons.
• We would also record intensity of gesture.

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Gesture types

• Invitational
• offering the pen for use, showing a step and
  offering an opportunity for participation
• Displaying
• with hand gestures pointing to material on the
  IAW and then using movement
• Blocking
• putting a barrier between the pupils and the IAW
  often as a result of mistakes
• Sequencing
• indicating progression by using gestures to pose
  a question and then work it through

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Findings from first 35 lessons

• Reflection on the 35 lessons from the original
  investigation had led to the view that
• teachers working with IAW technology were more
  likely to be physically active in promoting
  learning through their enthusiastic approaches to
  the materials available.

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Findings from first visit to 7 schools

• 42 lessons
• 5 showed lively use (episodes described by pupils
  as fun) - drawing upon the full range of
  learning opportunities offered by the IAW.
• 23 lessons were characterised by didactic
  approaches with minimum use of the interactive
  elements.
• Typically - examples from the text book, teacher
  talk about processes, work through two or three
  examples with ordinary handwriting and then set
  pupils on exercises.

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Findings from second visit to 7 schools

• 46 lessons
• 16 of the lessons were characterised by lively
  teacher presence at the IAW and by a full use of
  supporting gesture throughout the lesson.
• 5 lessons the IAW was being used but with minimal
  staff gesturing.
• 7 lessons there was some attempt to interpret
  through gesture but usually only with blocking
  gesture.

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Findings from second visit to 7 schools
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Findings from both visits to 7 schools

• From this it would seem that as teachers become
  more involved in the use of the IAW as the focus
  of their teaching they also become livelier in
  their approach and make increasing use of a range
  of gestures.
• By re-visiting the recordings it seems that
  teachers develop their own vocabulary of gesture
  and although this may not be the same teacher for
  teacher pupils respond to the known gestures for
  their teacher at any one time.
• This was seen in one school where in teaching
  three lessons the teacher made similar
  invitational, displaying and sequencing gestures.

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Findings from second visit to 7 schools

• Teachers taking part in both sets of recording
  report an 85 increase in discussion of
  mathematical concepts and 64 record a fall in
  pupil copying and similar activities.
• The teachers reporting enhanced discussion were
  also those where there were intensive periods of
  gesture especially during the development of a
  concept such as teaching balance in equations and
  the relationship between internal angles and the
  number of sides of a polygon.

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Conclusions

• Our evidence throughout the three stages of the
  work outlined points to livelier teaching as the
  IAW becomes standard in mathematics classrooms.
  This liveliness is marked not only in the use of
  materials at the IAW but also by greater use of
  gesture whether intentional or not. The comments
  of one teacher suggest that they too share the
  motivation that pupils have noted.
• The validity of our conclusions will be tested as
  more evidence becomes available but we believe
  that there is a vocabulary of gesture that has
  developed as teachers work with the IAW in
  mathematics.

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Conclusions and the way forward 1

• It is our belief that we should be moving to
  helpful generalisation in that professional
  development of IAW use should include some
  element of gesture awareness.
• This calls for much deeper analysis and
  psychological interpretation based upon knowledge
  of learning but our early evidence is that once
  teachers become aware of the benefits of
  kinaesthetic as well as verbal and visual
  learning they are more ready to support what they
  are saying by showing it as well.

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Conclusions and the way forward 2

• Much more remains to be investigated if we are to
  offer professional development that can make a
  real difference to classroom experience.
• Our evidence from 4,500 pupils before and after
  being taught mathematics with the IAW is that
  teachers are more lively, more ready to seek
  alternative ways of offering explanation and
  example, and more responsive to learner need.
• Gesture may be a product or a prompt in achieving
  this

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Enhanced secondary mathematics teaching Gesture
and the interactive whiteboard

• Dave Miller and Derek Glover
• eda19_at_educ.keele.ac.uk
• http//www.keele.ac.uk/depts/ed/iaw/