Q: My class is sound on general maths skills, including number bonds to 10, but children have had problems understanding and applying 'bridging through 10 when adding single-digit numbers'. The problem seems to lie in the splitting up and rearranging of numbers. Have you any suggestions?
A: Bridging through 10 occurs when two single-digit numbers are added together to make a quantity bigger than 10, eg 7+8. A number of mental strategies can be used to create the answer, eg 7+10-2=15; 10+8-3=15; 5+2+5+3=10+5=15.
Children's ability to use mental strategies successfully is strongly related to their experience of number. Too quickly we confine them to number lines and grids, which can cause confusion as it is not a natural progression for them.
Primary senco Mecky Turner sent me a copy of a project about tally marks.
She explained why visualising quantities is closer to formation of a number concept than number lines or grids. She suggests that some six-year-olds with plenty of experience of seeing sets of objects fail to grasp numerosity: "Tally marks are an ideal representation of quantities because they can be lined up easily. A bundle of four sticks plus one lying across gives the image of 'five' a visual closure and makes five an easy quantity to scan for. With tally marks, they can begin to see and understand relationships between numbers."
These ideas provide a sound grounding for developing mental strategies based on this representation. Sticks can be used to represent the sum 7 + 8. Children should be encouraged to encode one number first and then the second. Here is the example I showed earlier, 5+3+5+2. If pupils have been using tallying to develop their understanding of number it is very likely that they will recognise the two groups of five as 10 and will be able to add the second set of five. I would be interested to know if tallying leads to them using particular mental strategies in the first instance. I have included Mecky's paper on www.mathagonyaunt.co.uk.
I am also working with Bristol choreographer Tamara Cater to represent numbers in a variety of different dance arrangements and developing a dance for "bridging through 10". This will be available as a video clip on the same website for stimulating the creation of dances in primary schools.
Q: I am a third year BA primary education student with QTS status specialising in maths. I am also a parent and like many of my friends I have struggled with helping my children with their homework because of the differences between the strategies they have been taught and the ones I was taught 20 years ago. Do you know where parents could seek help?
A: Now that we have the world wide web there are a lot of materials that I could recommend. A numeracy consultant for Leicestershire recommends the website Mathsweb which offers documentation in the parents' section entitled 'Sums and things. Some help for parents'. This enables parents to understand the approach to calculation in many schools, as well as other aspects of mathematics. www.leics.gov.uk educationngflnumeracy
I wrote the following poem for a recent seminar in Torquay and was asked to include it in my column:
Algebra in an Envelope
Maths, some think, is really quite bland
Algebra is a concept they don't understand
The teacher says, "a and p, apples and pears"
Is there anyone in class who really cares?
Consider carefully, does it really explain
Is the actual meaning made quite plain?
With envelopes it's teachable
And the concept is reachable.
I'll surprise you, it's not quite as difficult as you think
Especially when the explanation provides some link.
A way that is much better
Linking any number to a letter
These envelopes hold a secret surprise
Letters not for the wordwise, but an algebra in disguise!
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX