Developing maths at home Laura Clarke

Why can’t we be like Shanghai and Singapore? X

Are we just a nation who are not very good at maths? ‘A body of research on conceptions of ability has shown two orientations toward ability. Students with an Incremental orientation believe ability (intelligence) to be malleable, a quality that increases with effort. Students with an Entity orientation believe ability to be nonmalleable, a fixed quality of self that does not increase with effort’ Patricia Lineham, Purdue University

What helps to make children successful at mathematics? conceptual understanding—comprehension of mathematical concepts, operations, and relations procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately strategic competence—ability to formulate, represent, and solve mathematical problems adaptive reasoning—capacity for logical thought, reflection, explanation, and justification productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. (Kilpatrick et al, 2010)

Key ideas in early mathematics More and less Counting Subitising Part – whole

Counting … what’s involved? Knowing the number names in order (stable order principle) Giving each item one number (one to one correspondence) Know that the last number you said is the number in the set (cardinal principle) Know that anything can be counted (abstraction principle) Start counting anywhere (order irrelevance principle)

p a c b x w

p + a = c + p = x + a = a x c = w – b =

Number sense ‘feel’ for number (quantities, more or less) Relative size and position of numbers (when compared to 10s) Cardinal, nominal and ordinal aspects of number

3 Cardinal – how many Ordinal – the position (order) Nominal– used to name or label

Noticing (more or less, counting, subitising, part-whole)

Noticing (more or less, counting, subitising, part-whole)

Noticing (more or less, counting, subitising, part-whole)

Noticing – maths used every day

Noticing – maths in story books

How else can you help your child with maths? Noticing – what else? How else can you help your child with maths?