Initial impetus

1. History of Mathematics and the Collaborative Teaching Practice at KS3St. Edmund’s Catholic School, Dover, KentSimon Langton Grammar School for Boys, Canterbury, Kent2007

2. Initial impetus Previous studies have shown that the history of mathematics helps learning in the following ways: • The skills pupils learn acquire ‘meaning’ • Pupils’ memory of covered subject-matter increases when they learn about the context in which this first appeared • Pupils start making links between mathematical concepts through the historical development and personalities they learn about • Role models facilitate and encourage pupils identification with successful examples, thus providing greater motivation for the learning of mathematics.

3. The pre-history of the project • The prevailing modern view of mathematical ability one which entails creativity and transcends the more limited concept of technical ability • little widely available material to introduce the secondary school age children to the world of ‘creative’ mathematics in historical context • this project’s main aim was to inspire young mathematicians • help them gain an insight into the various techniques of research, analysis and synthesis of mathematical thought • majority of the current resources university and post-graduate level students • some resources can be used by teachers but very few by children

4. Gatsby Fellowship in Mathematics 2004/5 • Work developed through the link with the British Society for the History of Mathematics (especially as Education Editor, Bulletin) • Benefits of learning mathematics in historical context (work done with the HPM - History and Pedagogy of Mathematics group, part of ICMI).

5. Aims of the project TEACHERS - CPD • Increase teachers’ subject knowledge in terms of historical context • Increase motivation to undertake individual research and CPD • Introduce Collaborative Teaching Practice as a CPD model for the school • Develop a range of technical and IT skills (dynamic geometry software, use of video and media clips in teaching, website development PUPILS • Increase pupils’ motivation in learning mathematics • Improve pupils’ understanding of the subject through contextual learning • Enable pupils to gain skills in structuring their knowledge and • Enable pupils to link their understanding of different mathematical concepts

6. Time and place • The first half of the project ran 2006/7 St. Edmund’s Catholic School, Dover • The second half of the project from January 2008 to July 2008 at Simon Langton Grammar School for Boys in Canterbury, Kent.

7. Example: angles on parallel lines • We decide to do the topic as it offers possibilities for varied historical explorations as well as the use of modern technologies (Euclid, his Elements, timeline, use of dynamic geometry software) • We divide tasks for the production of resources • We share the resources • Collaboratively asses them (in the event a series of presentations was made – one which offered slight historical element, and another which was used as a starter on recognition of angles) • We adopt the resources including the dynamic geometry files • Train the members of the team who did not know how to use Geometer’s Sketchpad • Discuss the possible historical approaches • Teach collaboratively - film the lesson • Analyse the lesson and make final set of resources • Ask students to complete the questionnaire on their assessment of the lesson and the resources.

8. Lessons learnt - the good ones • Collaboration aided differentiation between ability groupings, which allowed us to develop ‘graduated approach’ • Historical elements were used to complement and enhance lessons, pulling concepts from different historical contexts. • Having a theme such as ‘historical context’ meant that we had an excellent opportunity to share ideas and subject knowledge, particularly for non-specialist teachers (two teachers from the Science department). • Opportunity to develop the use of ICT and interactive teaching methods in the classroom was further developed (but not at the expense of more traditional resources). • Confidence amongst teachers increased manifold through trying new things and working on new topics. • Discussions generated from collaborative planning process and subsequent feedback sessions were an excellent type of in-house CPD. • Children enjoyed the novelty of lessons with historical focus. • Quality of lessons was enhanced by detailed, collaborative planning. • Many benefits for SEN pupils.

9. Lessons learnt - what should happen… • There is greater flexibility in timetabling. School restrictions meant that the more structured timetable of planning, filming lessons and evaluating could not always be put in place, hence we had to work ‘around’ it which took up lots of time and energy. • More regular cycles linked to existing schemes of work which would require resources (teacher-time) to prepare would be very helpful. • The whole-department collaborative work was less successful than the lesson study group. These latter groups remained small (optimum number of 3) and more trust and support was developed in that way. • Evaluation of videoed lessons is more consistently focussed on learning and not teaching. This is more likely to happen in a small group (and perhaps when not overseen by senior managers). • If we had larger bank of resources for non-specialist Maths teachers they would have been able to do more (their subject knowledge had sometimes to be developed through piece-meal collection of details). • The students should be involved in a History of Maths project themselves in a more organised way (beginning of Year 7, good transition activity maybe!).

11. Talking with pupils during/after the first half of the project showed that… • pupils seemed to remember the mathematical skill and its application better when they learnt about the context in which the skills were first used • the acquisition of mathematical skills became more meaningful when they knew the historical background • the pupils started making links between mathematical concepts, the historical developments and personalities they learnt about • they were able to identify with the role models and gained greater motivation for the learning of the subject • They began to take ‘charge’ not only of their own learning process but were keen to transmit that to others via presentations.

12. Where next… • Still a half way to go - Simon Langton • Cooperation with the local primaries and secondaries • Using the resources we make to prepare something for publication (book and/or electronic) • Questions still to answer - techniques to develop • How do you measure quantitatively the qualitatively different type of teaching/learning • How do you do this in a short period of time • Can you actually measure such qualitative data other than in the way we did it in the first half of the project? • Are we moving forward in a positive way - and what are the benchmarks to show us this progress?

13. Thank you for listening. Please see NCETM portal ‘History of Maths’ for further information or get in touch by email snezana@mathsisgoodforyou.com