Mathematics focus: improving the score and enjoying the game! Ray Sutton Jan/Feb 2009

Objectives To affirm and model the principles of effective learning and teaching in mathematics. To identify some common themes in recent curriculum developments in mathematics. To consider the implications for professional learning. To become more familiar with the Ofsted report on mathematics (Sept 2008), the National Centre and portal, and exemplar resources

2009 Nice or nasty?

What is there to follow up? What questions can I ask?

“My mum does numerology and 2009 is a number 2” “I like it because it has my age in it” , can you think of some more?

I noticed that 9 is a square number but 2 isn’t What is the nearest square number to 2009? How far away is it from 2009? ……… = – 16 = 2009

x x 7 x 41

Socks in the dark (1) There are two sock colours. How many socks do I need to take out before I have a pair of socks that have the same colour? How many do I have to take out if there are three colours and I want to get a pair that are the same?

Socks(2) What question should the teacher ask next?

Socks(3) If your partner tells you how many colours there are, how can you find the number of socks to take out? Try this with your partner and decide together what to write down.

Socks(4) I am a three-legged monster and I need three sock that are the same colour. Try this out using the bag of socks with two colours.

“The implications for teaching and learning are significant and will need to be introduced gradually and thoughtfully, but they do not threaten aspects of existing good practice. Helping learners to become more ‘functional’ is supported by existing practices including: learning through application learner-centred approaches active learning and a problem-centred approach partnership learning assessment for learning.”

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

“Good curricular planning provided pupils with opportunities to apply mathematics to a variety of interesting tasks, enabling them to choose approaches, reason and refine their thinking in the light of their solutions. Teachers encouraged pupils to discuss mathematical problems in depth and this helped to build their confidence. In a primary school where developing pupils’ understanding was promoted effectively, pupils were confident in ‘thinking aloud’ and were not afraid to have their mistakes used to help others.” - Ofsted: ‘Mathematics: Understanding the Score’, Sept 2008

Pressing the right buttons Poster Pictures and stories Piece of A4 paper People maths Putting things in order Pay off for me Play dough Piece of string

Creating comfortable challenge Pushing for new language and description Thinking while doing Writing things down Adding a new twist or different dimension Collaborating and comparing Creating questions for one another Explaining why and giving reasons

Principles for effective teaching and learning in mathematics(1) 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). 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). 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). - From Maths4Life ‘Thinking Through Mathematics

Principles for effective teaching and learning in mathematics(2) uses higher-order questions Questioning is more effective when it promotes explanation, application and synthesis rather than mere recall (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.

The National Centre for Excellence in the Teaching of Mathematics provides strategic leadership for mathematics- specific CPD. It aims to raise the professional status of all those engaged in the teaching of mathematics so that the mathematical potential of learners will be fully realised.

The NCETM portal Primary newsletter and ‘Up2d8 Maths’ Self evaluation – subject knowledge, subject-specific pedagogy Exemplification of TDA standards Communities and regional pages Mathemapedia, research, resources, blogs, news, events.

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

Events Mar 24 Maths Inspiration for year 12 and year 11 at Nottingham Playhouse

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

Objectives To affirm and model the principles of effective learning and teaching in mathematics. To identify some common themes in recent curriculum developments in mathematics. To consider the implications for professional learning. To become more familiar with the Ofsted report on mathematics (Sept 2008), the National Centre and portal, and exemplar resources

- copyright W.Krawcewicz, University of Alberta