This advice is for those who are intent on obtaining an ‘A’ pass at Higher/Advanced level maths, but applies at whatever level you are studying.
Please read and implement today. So many students will read this advice but leave doing anything about it until only a few weeks before the exam when it will likely be too late to change the course of things — if you are reading this in April, a month before your exam, then you need advice other than that which is provided here.
Achievement in mathematics is much more easily realised than people would imagine, but it has to be earned through a steady effort.
Please also see my page How to have successful tuition
“Failure to prepare is preparing to fail.” — Benjamin Franklin as quoted by a Masterchef finalist
“The biggest mistake you can make is being afraid to make one.” — The voice of experience
“Mistakes are great. The more I make the smarter I get.” Buckminster Fuller
“Mathematics is not a spectator sport” — an observation made by many teachers of mathematics
“Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.” Paul Lockhart
“I was an ordinary person who studied hard. There’s no miracle people.” — Richard Feynman — Nobel prize winner in Physics 1965
“I feel that my main responsibility as a teacher isn’t to convey facts, but to rekindle that lost enthusiasm for asking questions.” — Max Tegmark
- get a coach — due to class size numbers it is unfortunately the case that students often do not receive the 1-1 help that they need, this is where a tutor comes in!
- remember you are learning maths so it is okay not to know how to do something but you must find out — the onus is on you!
- converse, talk, discuss, ask mathematical questions with your tutor/parents/classmates/friends
- become diligent — look this word up if you don’t know it
- work steadily
- develop grit — do not be put off by setbacks
- develop top-notch ‘C’ grade skills — basically things that can be improved by practice eg completing the square, rules for differentiation and integration, wave function finding k and a, etc
- maths cannot be learned passively you have to actively engage with it by doing problems
- put your effort into understanding rather than merely memorising maths facts
- take a wider picture of what is going on in maths
- develop a feel for the kind of thing to do in solving a problem, or in working through a question
- take the pressure off your memory
- review your work at regular intervals — I know this is a drag but it works, the more you look at something the easier it is to understand
- practise past paper questions regularly — this should help you to feel more confident in identifying topics in questions (which is a problem that many students have)
- become someone who takes pride in being able to give a full and clear explanation for the solution to any given problem
- invest in and read a maths dictionary such as Oxford Student’s Mathematics Dictionary which will help you to review earlier maths studies — NB this is important!
- consider using an app(s) that will help you improve your basic maths — this would make a big difference in helping you learn the new things in Higher
- try doing puzzles like sudoku, futoshiki, cryptic crosswords even — anything to get you using your brain
- consider to yourself: how can I ask better questions? Please note that I do not mean that you should self-censor your questions — ask away! But do consider, in a cool hour, what questions you want to ask and how you want to ask them. Pointing to a problem in a past paper and asking “How do you do this?”, is not a good question, in my opinion. Similarly bringing an exercise to a tutorial, from a worksheet or textbook, which contains “questions”, is not really asking a question. A real question is one you want to know the answer to, ie it comes from inside.
- learn to ask mathematical questions eg things like “why do we divide here?”
- see also Bill Shilito’s question prompts
- at the very least ask questions to yourself — “why” being the main one which will help you to review and hopefully consolidate your understanding
- “The cure for boredom is curiosity. There is no cure for curiosity.” Dorothy Parker
- as the exam approaches work through exam papers in a methodical manner
- structure your revision in order to aid retention of material, approaches and methods
- read your notes with attention — switch off social media
- do problems with attention — switch off social media
- GOOD TO DO
- read! put your phone down!– get interested in maths and science, literature, philosophy, art, music, technology, and politics!
- maths is part of human culture — see it as such. Reading books, in my opinion, is still the best way to learn about culture.
- as the exam approaches keep your focus on getting an ‘A’
- in a sympathetic way — lots of rewards for hard work, take breaks, etc
- maths cannot be learned passively you need to actively engage with it by doing problems — yes I know I’m repeating myself but this is important! Maths is not a spectator sport!
- work on a gradient — that is in any study session try easier problems first and work up to harder problems
- use your textbook as a source of notes and worked examples — use the method in the book to solve a problem you are stuck with
- similarly, and I would hope that this doesn’t really need to be said, use your teacher’s class notes and worked examples — a lot of maths at this level consists of copying — but copying with understanding hopefully!
- remember nothing is being hidden from you, everything is in front of you in black and white — but if you cannot see it, please ask!
- when revising, and a question or problem gives rise to a feeling of aversion or revulsion, this is a sign that this is a topic you need to revise! Find out how to answer it so that the negative emotion is dissipated! Doing this will boost your confidence.
- read the advice in the front of the Official Past Papers — browse it in W H Smith’s if you don’t want to buy it (the papers are available online after all)
- be optimistic “Winners are people who expect to win”, you need that energy to help you make the efforts that are required
- you want to maximise marks gained through knowing maths and being able to apply common sense
- you want to minimise marks lost through
- careless errors
- not answering the question by not reading it with sufficient care
- not setting out working in a clear and logical manner
- SERIOUSLY CONSIDER
- achieving success in school maths is not a matter of talent, more it is a matter of working effectively
- read a book on productivity hacks
- implement some of the hacks and see what happens to your results in tests
To sum up (some things I often say to beginning tutees):
“Consider from now on how you will communicate your solutions. The correct answer isn’t all that important; it’s a matter of understanding the process and communicating that you understand it, ie ‘showing your working’.”
“Don’t try to cover up what you don’t get; find out what it is that you don’t get, get it (you will be absolutely capable of doing this), and learn to communicate your understanding with confidence! ”
“Think: how can I best show, how can I make it really clear, how can I convince my reader that what I’ve written down as working, is correct?”
“Start by convincing yourself — by understanding.”