Would you like to enthuse and challenge your more able mathematicians? Welcome!

Course objectives.. To Identify more able mathematicians To know the characteristics of more able mathematicians and reasons why some do not make good progress To plan for more able mathematicians To have practical KS1 and KS2 maths activities which develop higher order thinking

Mathematics is not only taught because it is useful. It should also be a source of delight and wonder, offering pupils intellectual excitement, for example in the discovery of relationships, the pursuit of rigour and the achievement of elegant solutions. Pupils should also appreciate the creativity of mathematics. DFEE 1988

Who are more able children?

Identifying more able mathematicians

Mathematically More Able Pupils What are the key characteristics displayed by mathematically able pupils? How do they differ in their approach to mathematics when compared to other children?

What opportunities could you offer in maths lessons to develop more able mathematicians? “Pupils with high mathematical ability will only show their special talent if stimulating opportunities are provided … a child who is capable of detecting patterns and generalising will only do so if suitable activities are provided.” Koshy (2001) Co-director of the Brunel Able Children’s Education Centre What are we trying to encourage? What sort of mathematics appeals to the More Able? What could the problems look like? What thinking are we encouraging? What kinds of questioning would help?

Types of problems......

How many 5p coins are needed to make 45p? Kind of Knowledge Details Known The final amount of money 45p UnknownThe number of coins? Restrictions All coins have the same value 5p How could the problem become more open?

How can we ensure that opportunities are provided to challenge all learners and that higher levels of thinking are developed?

Anderson and Krathwohl (2001) produced a revised taxonomy: What do tasks that encourage higher order skills look like?

Look for evidence of the range of number properties children choose to use, for example, when they sort numbers for a partner to work out their ‘rules’ or criteria. Look for children choosing criteria such as multiples of 10, even or greater than 20, and applying them consistently and accurately. Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000 I know the 2, 3, 4, 5, 6 and 10 times-tables and use them for division facts I recognise multiples of 2, 5 and 10 Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000 I know the 2, 3, 4, 5, 6 and 10 times-tables and use them for division facts I recognise multiples of 2, 5 and 10

LET’S GET PRACTICAL… Task: Investigate the properties of a group of numbers – how many different sets of numbers exist within your group?

Paragraph 235 of the Williams Review (2008) stated that “in-class provision is sometimes not stretching enough for the gifted and talented pupils. Part of the reason why in-class provision might not be stretching can be attributed to teachers’ lack of knowledge of what might be possible and of the types of activities that would allow the most able to flourish, for instance open-ended investigative tasks. In discussion with Ofsted, it has become clear that many primary teachers lack confidence at this level of mathematics and are often unaware of the bigger picture and network of interrelationships.”

How can Teachers use the Primary Framework Learning Overviews to design an investigation that meets the needs of all – including the most able? Primary Framework Y4 Block B Unit 1 Learning Overview Assessment focus: Ma1, Reasoning Look for evidence of children’s reasoning about shapes and look out for children who can visualise 3-D shapes and changes made to them. For example, identify children who can visualise a solid cube, imagine using a saw to cut the shape in half and then describe the two new shapes that have been created. Look for children who can explain what they see in order to justify their response and for children who can pose similar problems for others to respond to.

LET’S GET PRACTICAL…

What can you work out (from the information)? If you know that, what else do you know? Can you tell me what your thinking is? Shall we test that? Does it work? Do you still think it is... ? Do you agree that... ? Why is that bit important? So, what must it be? Prompts to guide children’s reasoning…

it could be..., because... it can’t be..., because... it won’t work, because... if... then... it would only work if... so... in that case... and phrases like: since, therefore, it follows that..., it will/won’t work when... Language of reasoning...

Resources! NRich ABOUT NRICH The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRich team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. On our website you will find thousands of free mathematics enrichment materials (problems, articles and games) for teachers and learners from ages 5 to 19 years. All the resources are designed to develop subject knowledge, problem-solving and mathematical thinking skills. The website is updated with new material on the first day of every month.

Plus poster problems More detailed menu

Resources! Circa ABOUT CIRCA MATHS Circa Maths publishes two mathematical magazines for children; Buzz, a new magazine for Key Stages 1 and 2 and the much acclaimed CIRCA for Key Stages 2 and 3. Both are informative, challenging and jam-packed cover-to-cover with mathematics. BUZZ is an A5 (148x210mm) 16 page magazine printed full colour through out. CIRCA is 16 pages printed in full colour and are supplied with teacher's notes. Each issue of CIRCA comes with a FREE 4- page booklet of Teacher's Notes. These show the content, levels, answers and, where appropriate, additional information on a topic with suggestions for further work. There is also a reproducible worksheet which is often a starting point for a wider investigation.

“There is very clear evidence that focusing sharply on what the most able children can achieve raises the expectations generally, because essentially it involves careful consideration of the organisation and management of teaching and learning.” OFSTED I love maths!!!