The Cornwall Post-16 The Cornwall Post-16 Mathematics ProjectMathematics Project

Main Findings and Implications for Effective Mathematics Teaching at

Post-16

‘…..all learners are truly able to recognise pattern, to generalise, to imagine, to reason…., to connect ideas…. and to do the numerical and spatial reckoning….

We need to give them all the chance to do so’

Anne Watson, Mike Ollerton: Inclusive Mathematics

‘Simply because a teacher is teaching does not necessarily guarantee that a child is learning ……. Conversely, a child often learns when the teacher is not teaching’.

Ainscow & Tweddle (1979, 1988)

‘Pupils bored by practising techniques modelled by the teacher.

[They] accumulate skills but do not make important conceptual connections…’

From ‘Weaknesses and barriers’

Jane Jones, HMI

‘For example, when you’re with a group you feel like you don’t know some things, because you’re not an expert, and someone helps you and that way you learn stuff…..and the thing you learn sticks inside and it never comes off because it sticks to the other ideas you’ve already got.

Our ideas are in our head. Now we know more than before – all of the ideas are stuck to each other and we all know them. We’re friends who know different things’.

Francesco, aged 5-6 years

‘Activities were well thought out and made me think. I didn’t get bored which sometimes occurs in textbook work’

‘it really helped me being able to visualise the bigger picture. See more clearly the goal and the starting point’

‘I enjoyed actually having to think through the processes of it’‘We should do more things like this. We learnt and understood

a lot more in the period of time we had’‘helped to make the connections and see why the different

processes happened’‘working with others and with equipment rather than working

in exercise books or off the board really helped’‘it helped trying to work the answer out for myself, without

being told what to do’‘it was fun!’

Feedback comments from students who were part of the Cornwall Project

Structure of Project• Launch – session 1 (Nov 06) – pilot group of 6

secondary schools & 1 FE college (two teachers from each). Clarify project aims & success criteria / methodology (co-coaching approach) / ‘showcase’ approaches / standards unit materials etc

• Set up NCETM portal community / secured funding• Session 2 (March 07) & session 3 (June 07)• Collaborative planning & teaching• Multimedia Product – 3 schools• County-wide launch event – led by the pilot

teachers – 4 December 2007• Evaluation

The NCETM web portal community was an integral part of the project. It was a forum for communication within the project (an issue in a large, rural county such as Cornwall) and resources developed by the project team were uploaded and made available from there.

The materials from the collaborative lessons were also uploaded, along with lesson plans to allow other schools to trial the lessons.

Teachers from the pilot project uploaded activities and other resources that they had devised – there

are currently over 50 different activities on the

community

Main FindingsMain Findings• The learning is NOT in the activity; it’s in what you do with the activity• Teacher role – questioning, encouraging, prompting, ‘devils advocate’…. learning!• Consistently true that planning for student centred learning revealed fresh insights• Gap (in progress and participation) between most and least able narrows• Power of paired work / paired talk• Time to think / not prescribed• Importance of planning / planning for dialogue / planning key questions• Activities work best on specific aspects, then link together• Think about range: matching, grouping, unjumbling, sequencing, posters…• ‘Cold’ starting points with no input….• Use blank cards (and at different points)• Build in different starting points• Easily translated to other post-16 courses (FSMQ, GCSE) and to KS4 and KS3….• Very effective for revision too, but students need to be ‘taught’ to reflect effectively on

their learning

It’s difficult to avoid the conclusion that a significant inhibitor to student progress / attainment may be the prevalent learning approach traditionally adopted in the teaching of post-16 mathematics

Collaborative planning & teaching• Took place in-between the ‘formal’ sessions• LA Adviser visited all the project schools between

February and June 07, jointly planned and taught a lesson with the usual class teacher.

• Students completed evaluations• LA Adviser uploaded resources and lesson description and

evaluation on portal• Teacher responded with their reflection on the lesson• A key component to the project – demonstrated to us that

the approaches would work with any (some very unpromising!) topic area!

In addition, we uploaded evaluations of a number of lessons taught using these approaches –

the lessons were planned & taught collaboratively. The evaluations included student voice, pictures and teacher evaluation.

Student feedbackTeacher reflection

Teacher Reflection / Evaluation• ‘The students’ ability to explain the whys and wherefores

developed before my eyes’

• ‘…really helped think about what we were trying to get the students to understand… it’s easy to focus too much on what the exam question will look like rather than thinking about the learning you want to take place’

• ‘this lesson certainly taught the understanding of what is required to solve trig equations rather than just teaching the steps required’

• ‘I have certainly changed many of my approaches to topics I have taught in the same way for a few years now’

• ‘all the pupils were fully involved’

• ‘the following lesson proved how much understanding the pupils had gained’

• ‘the students enjoyed working together in small groups and really benefited from discussing the problems’

• ‘the tasks were challenging but all the students got stuck in and wanted to do everything and this has consequently spurred them on to even more revision’

• ‘I have to say I cannot remember a better lesson that I have taught’

Where do we go from here?• Multimedia CD/DVD Rom

– Video clips from session 3 (21 June) where teachers are presenting to their peers

– Video clips from three lessons + ‘talking-head’ teacher reflections on the process / approaches

– Downloadable resources + those from the three lessons

– Prompts and support for CPD for departments wishing to implement these approaches

• Wider launch (with resources pack + CD) – 4 December 07

• Generic qualities? Links with science etc…

In Conclusion• Potential for a significant change in:

– Perceptions of effective mathematics teaching (student & teacher!)

– Student engagement & motivation– Student achievement especially ‘less able’ students– Identifying wider benefits KS3, 4, 5– Effective models for teacher CPD– Post 16 / HE recruitment & retentionFurther details: contact Lee Northern, County Maths

Adviser at lnorthern@cornwall.gov.uk