Preparing for Functional Mathematics Ray Sutton June 10 th 2008

Objectives: functional mathematics To understand the employability drivers and the assessment developments To experience and reflect upon some activities that support the development of process skills To identify the implications for learners, teachers, and professional development

What is functional mathematics? Huw Williams, Senior Engineering Specialist, JLR Research

Process skills recognise situations in which mathematics can be used make sense of these situations (and represent them) describe the situations using mathematics analyse the mathematics, obtaining results and solutions interpret the mathematical outcomes in terms of the situation communicate results and conclusions

Picture it!

Why are pictures useful in mathematics lessons?

Picture it! Work in pairs. Decide whose picture has the most mathematical potential. Identify and write down all the mathematics you can in the picture or deriving from it. Write down some problems, of increasing complexity, based on the mathematics you have identified. What is the most open problem you can create?

‘Levelness’ the complexity of the situation or problem the learner is tackling the familiarity to the learner of the situation or problem the technical demand of the skill required the independence of the learner in identifying and selecting the skills they will need, and in tackling the situation or problem

It doesn’t have to be a picture Final results for 2006–07 Hull City 21st in the Championship Played 46 Won 13; drawn 10; lost 23 Goals for 51; goals against 67 Goal difference: –16 Points: 49 Sunderland 1st in the Championship Played 46 Won 27; drawn 7; lost 12 Goals for 76; goals against 47 Goal difference: +29 Points: 88

The development of process skills Asking questions - Maggie Adapting questions to other contexts - Maggie Creating a story - Ray Looking for the mathematics – picture activity What is the same? What is different? - Ray Justifying decisions - Ivor Classifying, ordering and sorting – Wendy ( and starter) Analysing solutions - Wendy Language problems - Ray

In what ways are these activities useful for developing process skills?

Maths4Life Principles guiding the development of the resources Teaching is more effective when it… ● builds on the knowledge learners already have This means developing formative assessment techniques and adapting our teaching to accommodate individual learning needs (Black and Wiliam, 1998). ● exposes and discusses common misconceptions Learning activities should expose current thinking, create ‘tensions’ by confronting learners with inconsistencies, and allow opportunities for resolution through discussion (Askew and Wiliam, 1995). ● uses higher-order questions Questioning is more effective when it promotes explanation, application and synthesis rather than mere recall (Askew and Wiliam, 1995). ● uses cooperative small group work Activities are more effective when they encourage critical, constructive discussion, rather than argumentation or uncritical acceptance (Mercer, 2000). Shared goals and group accountability are important (Askew and Wiliam, 1995). ● encourages reasoning rather than ‘answer getting’ Often, learners are more concerned with what they have ‘done’ than with what they have learned. It is better to aim for depth than for superficial ‘coverage’. ● uses rich, collaborative tasks The tasks we use should be accessible, extendable, encourage decision making, promote discussion, encourage creativity, encourage ‘what if’ and ‘what if not?’ questions (Ahmed, 1987). ● creates connections between topics Learners often find it difficult to generalise and transfer their learning to other topics and contexts. Related concepts (such as division, fraction and ratio) remain unconnected. Effective teachers build bridges between ideas (Askew et al., 1997). ● uses technology Computers and interactive whiteboards allow us to present concepts in visually dynamic and exciting ways that motivate learners.

News Maths Inspiration comes to Nottingham On Tuesday afternoon March 24 th 2009 (to be confirmed) “It's a chance for Year 11s and sixth formers to experience the UK's most inspiring maths speakers live, in big venues, presenting mathematics in the context of exciting, real- world situations.” Rob EastawayRob Eastaway is an independent lecturer and author whose books on everyday maths include Why do buses come in threes? and How to take a Penalty and he is often to be heard on radio talking about the maths of everyday life. He has also written books on memory, creativity and cricket. Colin WrightColin Wright graduated in Pure Mathematics at Monash University, Melbourne, before going on to get a PhD at Cambridge. While there he learned how to fire-breathe, unicycle and juggle. These days he is director of a company that specialises in software for marine radar, but takes out time to give juggling talks all over the world

News Action research projects: Portland College – “Support each other through Action Learning Sets” Leicestershire ALS – “Understanding the language needs of ESOL Numeracy learners” Castle College - “Developing Key Skills teaching and learning into Functional Skills teaching and learning” NCETM grant: Leicester ALS in partnership - “Teachers collaborating to improve maths learning and teaching for ESOL learners”

News “Learning Mathematics Outside the Classroom” – see NCETM homepage The future – continuing strong links between Mathematics, Science and Engineering (STEM subjects) and between Mathematics and Numeracy

News “Improving Learning in Mathematics” boxes still available “Thinking Through Mathematics” folders now in short supply Many Maths4Life resources still available at (including ‘Topic- based teaching’)

Key processes in Mathematics In the new programmes of study at Key Stages 3 and 4 there is much greater emphasis on the key processes, and attainment target 1 is different, now entitled Mathematical processes and applications. Key processes lie at the heart of the new Secondary National Curriculum in mathematics and should be embedded in all units of work. They should influence the nature of mathematical activities to be undertaken and provide powerful guides to teachers making choices about pedagogical approaches and classroom organisation. The key processes are: Representing Analysing - use mathematical reasoning - use appropriate mathematical procedures Interpreting and evaluating Communicating and reflecting. To inform your understanding of the key processes, the document Mathematical processes and applications objectives explains how the key processes relate to the former 'Using and applying mathematics'. It describes the role of the key processes in problem-solving and makes links to applications and to progression in functional mathematics.Mathematical processes and applications objectives - From the renewed Secondary Framework

Update from the awarding bodies Garry Haynes, Professional Officer, Qualifications Division, OCR

Changing curriculum and assessment What changes do we envisage for learners: L1, L2, L3? 19+ E1 E2 E3 L1 L2? ……and what changes for teaching? ….and what should teachers be doing?

The NCETM portal Self evaluation – subject knowledge, subject-specific pedagogy Exemplification of LLUK standards Communities – especially ‘Focus on Numeracy’ in the East Midlands Subject Coaching Network communityEast Midlands Subject Coaching Network Mathemapedia, research, resources, blogs, news, events.

Things that subject learning coaches get upto

Action to support process skills Think about: What you are doing now? What is going well? How and why it is going well? What you would like to do more of? Identify: -what has worked well previously. -your existing useful skills and qualities. -your ‘vision’ and what the ‘improved future’ will be like. -what you could do differently and how you could do it.

Developing ourselves and our teams in preparation for process skills - options Exploring the post-16 on-line module (max 10) Action learning sets to support coaching and leadership back at base A look at the QIA Excellence Gateway and ‘Learning Mathematics in Context’ Planning a session based on an idea from a pilot assessment paper (pairs only)

Reflection activity from QIA Action Planning Evaluation

Action to support process skills Think about:- What you are doing now? What is going well? How and why it is going well? What you would like to do more of? Identify: -what has worked well previously. -your existing useful skills and qualities. -your ‘vision’ and what the ‘improved future’ will be like. -what you could do differently and how you could do it.

Be creative with....organising learners and learning..trying out new approaches..variety in the lesson..finding out what learners think..making mathematics attractive..supporting other teachers and assistants..your own learning

- copyright W.Krawcewicz, University of Alberta