It’s all in the detail

Mathematics, as you will know from Theory of Knowledge, is at the top of the tree of knowledge. It is self-referential – that is, its theorems do not need to be proven by reference to the real world, but instead by starting with other axioms and theorems. Of course, maths has many real-world applications, and if you are starting out on the new Applications and Interpretations course, then you will spend a lot of time solving real-word problems.

Many of the problems students have with mathematics are not so much to do with applications, but because so much of it can be high-level, conceptual, abstract. Algebra can be bafflingly complex, and full of little rules: yes, you can cancel the x‘s in the numerator and the denominator in this case, but not in that case. Negative powers don’t give negative numbers, but reciprocals. Even numerical work isn’t necessarily straightforward:  how many significant figures is the number 4000 rounded to? Depends. If there are exactly 4000 ball bearings in this box, then it is correct to 4SF. But if it is an approximation to a village population of 4032, then the first zero is significant and the other two aren’t.

So why do I say it’s all in the detail, when so much of what you need to know is conceptual, broad brush? Well, when it comes down to answering questions in tests and exams – it’s all (well mostly) in the detail! The smallest detail can trip you up and lead you down the wrong path, details such as: misremembering a formula; not applying a minus sign throughout a bracket; typing -4.1² in your calculator instead of (-4.1)²; using sin instead of cos; solving 6x = 3 as x = 2. Some of these are careless slips, and teach you to check your work carefully. But in many cases you’ve misunderstood the method, used the wrong method, carried out incorrect algebraic working – how can you put these right, and get them right in the exam?

The problem is that if your brain leads you down the wrong path, the same thing will happen next time you are solving a similar problem, so you must “re-train” your brain. “Ah”, you’ll say when your teacher corrects your working, “I’ll remember for next time.” But the chances are that you won’t, because you forget about 80% of the detail within a week. So, you must write down the things that you do wrong, and how to put them right. Do this every day, and discipline yourself to look through the list (hopefully not a long one!) every evening. Try and find some similar problems and work through them to “reset” the brain pathway. At the end of the week, consolidate your notes and they can then form part of test and exam revision.

Have a look through recent maths exercises and tests, and I’ll bet you can find plenty of instances where you have lost marks because of poor attention to detail. Remember, every detail you put right will be at least one more mark in your exams!