**An idea for Maths Exams**

**What is mathematics?**

*the science of quantity.’*This and other definitions which focus on magnitude and counting fail to account for much of the content subject. Many areas of mathematics, of course, bear no obvious relation to measurement or the physical world.

*Mathematics is the manipulation of the meaningless symbols of a first-order language according to explicit, syntactical rules’*(Snapper, 1979). However, formalist definitions seem to make the symbols and notation the object of study. These definitions ignore both the physical and mental meaning of mathematics.

*‘Mathematics is the art of giving the same name to different things.’*This quote hints at one of the essential ideas in our subject: the act of generalisation. Taking the specific, spotting patterns and relationships and extracting an abstract generalisation that is independent of the specific. Karl Freidrick Gauss took the perspective that mathematics was about ideas, famously arguing that ‘

*What we need are notions, not notations*’.

*‘It would be bad enough if the culture were merely ignorant of mathematics, but what is far worse is that people actually think they do know what math is about— and are apparently under the gross misconception that mathematics is somehow useful to society! This is already a huge difference between mathematics and the other arts. Mathematics is viewed by the culture as some sort of tool for science and technology. Everyone knows that poetry and music are for pure enjoyment and for uplifting and ennobling the human spirit (hence their virtual elimination from the public school curriculum) but no, math is important.’*

**What does a mathematics qualification suggest about a pupil’s competences?**

**What do I propose for assessment?**

__Concept Focused Multi Choice__

__A range of questions like just now__

__A Mathematical Thinking Section__

*“it is perfectly possible to have all of the necessary techniques safely inside your toolbox and yet not see how they could help you solve the problem you are tackling. The teacher feels frustrated, because they think that the students ought to be able to solve the problem. They apparently know everything they need to know, but they do not mobilise it in the particular situation they are presented with.”*

This is something that I’m sure many teachers can relate to. He continues:*“One reason for this may be that the students have met the relevant content only in a narrow range of contexts and have not seen how it might be applied more widely. Another reason may simply be that they have encountered the relevant content too recently. When learning a language, students do not spontaneously and fluently use the vocabulary they have just learned. It needs time to bed in. Similarly, if we want students to make sophisticated use of what they know, it might be better to rely on mathematical content that was learned some time ago and is quite robustly known. Content learned 2 years previously is a rough rule sometimes used at the Shell Centre in Nottingham. … It also acknowledges that if the problem-solving demands are high, other demands, such as procedures and concepts, may need to be lower.”*

**well**

**established**for National 5 pupils. However, they require pupils to reason with these ideas on a sophisticated level and apply problem solving strategies. The two questions below would be quite difficult for an S2 pupil, but provide just the right amount of challenge for a National 5 candidate to apply their previously learned material in a problem solving context.

**Conclusion**