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@educ.keele.ac.uk http://www.keele.ac.uk/depts/ed/iaw/

2. 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 person’s willing expression’ (Kendon, 2000). Starting point for work on gesture 1

3. 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’. Starting point for work on gesture 2

4. 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. Data collection methods 1

5. 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. Data collection methods 2

6. 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 The first 35 lessons

7. 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 learner’s desk and the engagement of brain as the intermediary as seen in the use of artefacts, gesture and multi-modal learning. The first 35 lessons

8. 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. Investigation of gesture

9. 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 Gesture types

10. 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. Findings from first 35 lessons

11. 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. Findings from first visit to 7 schools

12. 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. Findings from second visit to 7 schools

13. Findings from second visit to 7 schools

14. 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. Findings from both visits to 7 schools

15. 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. Findings from second visit to 7 schools

16. 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. Conclusions

17. 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. Conclusions and the way forward 1

18. 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 Conclusions and the way forward 2

19. Enhanced secondary mathematics teaching Gesture and the interactive whiteboard Dave Miller and Derek Glover eda19@educ.keele.ac.uk http://www.keele.ac.uk/depts/ed/iaw/