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The Essentials of Effective Learning
Let’s start with the basics. What is mathematics?
Definition of mathematics: the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations
Of course, this lengthy definition may seem confusing, but maths is more abstract than complex.
Maths is the result of logical reasoning.
To create a better picture of what exactly mathematics is, we can name a few branches of maths. For example, there are triangles, which are analysed by Pythagorean Theorem, trig, algebra and geometry.
Organisation and a positive mindset are key! ¦ source: Visualhunt
There is also graphing, which uses math concepts such as transformations and translations, as well as linear equations, simultaneous equations, differential and polynomial equations, and integration.
Now we’re clear on what maths includes, let’s have a look at our
four recommendations for all learners, which apply to everyone, regardless of age or study level. Success is in the Details – So Be Thorough!
First of all, keep in mind that
learning the ins and outs of maths takes time.
But what does it mean to be thorough in this context?
Effective learning means exercising
self-discipline and making sure you cover every topic in depth.
For example, set a detailed revision timetable and
stick to it. Don’t forget to be kind to yourself and schedule enough breaks to keep you refreshed.
Understand that attending maths lessons or following maths courses is not enough. Revise what you have covered in class and
consolidate your knowledge, focussing on points you find slightly more difficult. Next, apply what you have learnt to example questions to test your maths skills.
If you make mistakes – that’s okay! Every mistake is an
opportunity to learn so that you don’t get tripped up on exam day.
Studying on a regular basis will fix your newly acquired knowledge into your mind and make it easier to recall this information. So don’t think you can twiddle your thumbs until the night before – if you want to do well, you’ll have to work for it!
Use Past Exam Papers to Revise
Past maths test papers are an
invaluable revision resource.
You can find them on the website of every major exam board including AQA, Edexcel and OCR. Working through exam papers can help you prepare for the real thing, as you get to know
what each board is looking for and how they tend to word problems. Don’t be tripped up by sneaky exam boards – revise with past papers! ¦ source: Visualhunt
Past exam papers will also help you spot the
key topics of your maths course, so you can know what to expect before you turn over the first page of your GCSE or A Level exam.
Exam boards also have answer booklets for each paper so you can see how you’re improving.
If you’d like to work through any math questions you got wrong, there are many maths teachers who put their working online so you can follow them to the correct solution, rather than going straight to the answers.
Tip: Make sure you focus on the most recent papers. The UK maths curriculum is changing all the time and it’s important that your revision is up-to-date. Work Out How Topics are Related
links between the concepts you’re learning will help you to see the bigger picture of mathematics and therefore potentially use a different approach to a certain type of maths problem.
For instance, why not find out how Pythagoras can be explained using polygons or where Pi comes from.
Making these kinds of connections when you learn math will not only help you in your understanding, but it will build a
firm foundation to further your maths education in the future. Be Well-Acquainted with the Basics
If you want to go far in maths, it’s really important to have a good grasp on what we call “
These are the kind of math skills that are
fundamental to the functioning of all facets of mathematics, such as addition and subtraction, multiplication and division, place value, factorisation, estimation, rounding, graphing and working with fractions.
A useful anecdote to explain this idea is the mechanic, who, without his toolbox, would not be able to make any repairs.
Equip yourself with the basic skills to support more advanced studies ¦ source: Visualhunt – Marcus Rahm
Maths mastery is down to building a
strong foundation. The more comfortable you are with using basic concepts, the faster your progress will be further down the line.
However, basic math concepts doesn’t just mean easy maths. Learning the multiplication table to revise aggregate function doesn’t make a lot of sense, since the level of study is so much higher. So
be sensible about what you choose to focus your energy on.
Whether you’re revising for your GCSEs, A Levels, or you’re in higher education at university, the math learning programme will be completely different.
While there is a whole world of printable math worksheets and exercises, it always helps to revise GCSE maths online with material based around a
specific syllabus. BBC Bitesize Maths is particularly helpful from KS1 maths to GCSE level, providing learner guides with math videos for qualifications all over the UK.
For GCSE and A Level math help, there’s
The Student Room, where students can discuss queries in forums and find teacher-approved resources. I’m a GCSE Maths Student
You’re in year 11 and preparing to sit your final GCSE exams this Summer.
For a lot of students, the math exams are the ones that cause them the most worry.
No need to panic. Just like maths,
every problem has a solution.
Year 11 maths is all about algebraic equations, number sense, and graphs. Sub-topics include inequalities, linear equations, theorems, indices, square roots, reasoning, ratio, loci, vectors, probability and math problem-solving.
How did these topics become GCSE nightmares?
It’s all down to the way you learn.
If the methodology of your educator doesn’t suit the way you think, it makes you think you’re less capable than you are.
When it comes to learning math, low self-esteem can be incredibly detrimental, so you need to find revision strategies that suit your style of learning.
Where to Find the Best GCSE Maths Revision Materials
BBC Maths is a brilliant free math resource as it tailors revision materials to the specific math curriculum for each of the four countries that make up the UK. Studymaths.co.uk has revision notes, maths worksheets, key formulae and even a glossary to help you get into the swing of practicing maths and understanding mathematical vocabulary and scientific notation. If you want to move away from textbook maths and learn in a more interactive way, this website has puzzles and free online maths games to help you learn key concepts. Then when you feel ready, you can have a go at some exam-style questions from the question bank to see how you’re getting along.
These days, everyone has a smartphone or tablet – you can use these for revision!
Gojimo, the free interactive math app, can help you prepare for upcoming exams with personalised maths quizzes and the ability to track your progress. The app focuses on topics and maths questions from whichever exam board and qualification you select, so you can do effective revision on-the-go! I’m an A-Level Maths Student
studying maths and perhaps related subjects such as physics in year 12 or 13.
There’s plenty of help out there for you, too.
Of course, you’ll have work a lot harder for your maths A Level qualification than you did for your GCSE. The key to successful revision is
keeping it fun.
Even though differentiation and calculation of probability and statistics don’t scream ‘fun learning’, this means finding interesting ways to learn each topic, aside from re-reading class notes. For example, why not
work with a classmate and create flashcards to test each other? Or you could both attempt the same exercises and compare answers as a form of peer mentoring.
The internet also has some great maths websites and downloadable online math resources to help you.
Exam Solutions (maths made easy) provides subscription-free maths help for GCSE and A Level students, focussing on specific exam questions from real past papers. The teacher films himself working through maths exam questions step-by-step, so you’re free to pause, rewind and fast-forward the maths videos. So if you’re looking for a solution to question 3 of the Edexcel C1 paper from June 2014, you’ll find it. Another handy feature is the ‘ helpful tutorials‘ placed next to each exam question, so you can revise further if needed. The internet offers lots of help for maths students ¦ source: Visualhunt – Anna Demianenko
You can also use the Gojimo app for A Level maths revision. Just like for GCSE, you can focus on a specific exam and revise with maths quiz questions with instant explanations on-the-go!
I’m a Foundation Year, Undergraduate, or Masters Student
For you, A levels are long gone. You may be aiming for a career in
finance, research or engineering, so you’re destined to be a mathematician in some form.
As your level of study is so advanced, revision tools can be hard to come by – but
they do exist!
Mathematical Institute at the University of Oxford has a range of practice math problems aimed at those starting a maths degree. Each worksheet provides an opportunity for foundation year students and even undergrads to familiarise themselves with degree-level maths.
For those studying
economics or finance, the University of Warwick has put together a handy page of notes, exercises and quizzes. These are aimed at helping you with the mathematical aspects of your degree course.
When you’re studying for a degree, your lecturers will provide information on the format of the exam and will give you access to past exam papers as well as sample questions.
It’s down to you to get the most our of these somewhat limited resources.
Do every question – even the optional (often more difficult) ones. When you make a mistake, try again. See where you went wrong and learn how to avoid being tripped up next time.
Ultimately, academic success is down to the learner.
Of course, having the right resources is key, but the most successful students also know how to get the most out of them.
Maths is a subject based on logic. It’s very
interesting, but by nature, there is a risk of it becoming boring. Good learning happens when the student is interested in the course content, so know how to keep your degree interesting and most of all, enjoy it!
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