Q. I am supporting a nine-year old girl in maths who is about three years behind in maths because of family circumstances. She has no real concept of numbers. Have you any suggestions that might help her? I work with her one-to-one so can extract her from class, if necessary.
A. Let's call your pupil Gemma. Perhaps the first activity is to begin a diary with Gemma so that she can plot her progress. This will enhance praise you give for her progress as you will be able to refer back to breakthroughs that she makes.
Discuss with Gemma what she thinks numbers are, show her that numbers come in different formats: * a picture of a number of items, eg a group of horses in a field or dots on a page; * the name of a group of items as a digit or word, eg 5 or five (numbers denoting quantity are called cardinal numbers); * the numbers that suggest position, eg the picture of someone coming "first" in a race (these are called ordinal numbers as they describe order or position).
What we want is for Gemma not only to develop her own real sense of number but also to realise the importance of number in the world. Prepare some representations of, say, five and six, in picture, dot, word and digit formats - be inventive, include variations of the picture, for instance the objects arranged differently and different size digits for 5. Show these, the "fives", to Gemma and talk about them. Next, show her the "sixes" and talk about these; ask her if they are different from the "fives" and why she thinks so. Make a summary of this conversation for her diary and include some of the items you created to help with the illustration.
Next, shuffle the two sets together and ask her to sort out the "fives" and "sixes".
Gemma needs to be helped in seeing numbers outside school. This should be a fun activity, rewards are always welcome but there will be real joy at each new discovery. To do this, provide her with a scrapbook, with a title on it such as "Numbers for Life".
Set Gemma the challenge to "collect" numbers in her scrapbook. Ask her where she has seen numbers. If she isn't sure what is expected of her, a note home might be useful but make sure you emphasise that it must be Gemma who finds the numbers.
The resulting items could be photographs, pictures from magazines, leaflets or print-outs from the internet. As the weeks progress you should contribute as well. See which of you can come up with the most unusual number.
Having introduced the notion that number is important now you need to work on her sense of number. Before doing this activity you might need to show her how to use PowerPoint on the computer. In particular, how to paste a picture, shrink or enlarge the picture, how to copy and paste multiple images.
With Gemma, take some pictures with a digital camera or scan in a picture of her choice. Ask Gemma to use the computer to create slides of numbers, a different number for each slide using multiples of the image she has chosen as her original. Print the slides when she thinks she has made as many as she can or give her a time limit to work to.
Discuss the slides she has created; there may be some that are in fact the same number but with different sizes of image, alternatively there might be the same number of images arranged in a different pattern. The nice thing about having these on slides is that you can cut out the images and let her rearrange them to match the duplicate number.
Next, ask her to put the slides in order of size of number and to write the digit for each collection on the picture (give it a cardinal number). The next step is to ask her if she can use two slides to create another slide.
Encourage her to write the equation - eg 3 + 4 = 7. At each stage of success, get Gemma to take a digital photograph of her solutions for her diary - much more fun than lots of writing!
Though I have set this as an answer for the support of a nine-year-old, the activity could equally well be carried out by people of other ages as the images they create are their own and the discussions are flexible as far as conversational competence is concerned.
David Whitefield, a teacher in Enfield, has made some excellent resources for use with laptop and projector in the classroom available on his website in the "teacher resources" area at www.lgfl.netlgflleasenfieldschoolssouthgate accountsstaffdwhitfieldwebpagesteacher_resources_contents.html
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 firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX