Preparing for Functional Mathematics

Ray SuttonJune 10th 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 mathematicsanalyse the mathematics, obtaining results and

solutionsinterpret the mathematical outcomes in terms of

the situationcommunicate 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 pictureFinal results for 2006–07

Hull City21st in the ChampionshipPlayed 46Won 13; drawn 10; lost 23Goals for 51; goals against 67Goal difference: –16Points: 49

Sunderland1st in the ChampionshipPlayed 46Won 27; drawn 7; lost 12Goals for 76; goals against 47Goal difference: +29Points: 88

www.problempictures.co.uk/examples

The development of process skillsAsking questions - MaggieAdapting questions to other contexts - MaggieCreating a story - RayLooking for the mathematics – picture activityWhat is the same? What is different? - RayJustifying decisions - IvorClassifying, ordering and sorting – Wendy ( and starter)Analysing solutions - WendyLanguage problems - Ray

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

Maths4LifePrinciples 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 24th 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.”

www.mathsinspiration.com/home.html

Rob 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 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 www.nrdc.org.uk (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.

- 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:

16-18 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 standardsCommunities – especially ‘Focus on

Numeracy’ in the East Midlands Subject Coaching Network community

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

www.pims.math.ca/pi/cartoons.html - copyright W.Krawcewicz, University of Alberta

ray.sutton@ncetm.org.uk