Q Can you give me some advice for teaching 8 to 14-year-olds please? I'm looking for ideas for introducing the history of maths and cultural differences in maths. Can you also suggest a source of open-ended questions to stimulate creative thinking?
A The British society for the History of Mathematics has links to lots of information about various areas of mathematics on its website at www.bshm.org. This provides some good background information. The approach I use to seek out materials for a particular cross-cultural topic is by searching on the internet under the country for which I wish to seek lesson ideas. For example, I typed "mathematics from Africa lesson ideas" into the search engine which led to multicultural lessons and resources, clicking this site www.cloudnet.comedrbsassedmulticult.htmNoNomath and then "Maths" opened a link to learning about a method of addition used by the Mende people of West Africa (www.deltacollege.edudeptbasicmathMende.htm).
There were many other options. I suggest that you would find this a really good way to source the materials for investigations to introduce history of maths and a cross-cultural element to your lessons.
Open-ended questions can be found at www.nrich.maths.org.uk There is a "past issues" date search on the home page. One problem from October is "How many triangles can you make using sticks that are 3cm, 4cm and 5cm long? Each side can only use one stick but a triangle can use more than one stick of the same length", you can click on the rods and manipulate them.
This problem has different solutions. Pupils could play with this one using straws. Pupils' solutions are posted on the site the following month and provide some interesting insights into their different approaches. An interesting example is one called Coordinates and Patterns from September (the solutions are found under October 2004). Other examples of puzzles and problems can be found at a site created by www.ex.ac.ukcimtpuzzlespuzzindx.htm
Q We teach children about odd and even numbers as early as possible and this is often a struggle for teacher and pupil. What is the purpose of knowing about odd and even numbers in adult life?
A It is important for us to understand the properties of numbers to understand the structure of number. Even numbers can be divided by two leaving no remainder; odd numbers cannot be divided exactly by two. Pupils can look at odd and even numbers using their fingers. Ask them to think of a number between one and 10 and then show you this number using their fingers. They can work out if it is even by matching fingers, sorting them into pairs. If one is left over then the number is odd, if they are all paired then the number is even.
Another good way of doing this is by asking pupils to create numbers in groups of pupils, and then ask if they have made an odd number or an even number. They can check by creating pairs, if one person is left then the number is odd as before. When learning about money pupils can look at even and odd numbers using two pence pieces.
Your question made me think of all the times that I find it helpful to use these facts about numbers. For example, door numbers tend to be numbered odd on one side of the road and even on the other side of the road.
GCSE revision A pupil who had been studying for a November GCSE sent me the following poem, which I thought would be really good as an introduction to discussing exam revision with a group. Pupils' feelings about taking an exam can have a huge impact on the final result. The opting out described in this poem shows the writer's frustration at not clearly understanding why she is studying the maths. Is this an illustration of "fear of failure"? A real condition that encourages lack of study as then the learner cannot be blamed for any subsequent failure.
Maths exam stress
Is this mathematics what I need?
So much info to my head they feed.
How do I need this?
I'll just give it a miss.
It isn't clearly plain to see
how this work is helping me.
Making sense of the text,
who really cares about "x" or about
variables and y.
The stress just makes me cry.
But work or no work it's still an
Revising - not me! I am who I am.
Whether I like it or not, adults all say
"you will take your mathematics