We all know that the best way to study for any topic is slowly, with many repetitions over time. Of course, few of us create the perfect revision timetable and manage to maintain it over a course's entire duration. So when you are looking at ensuring you know your stuff, how should you best looking at tackling your NCEA maths revision?

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What are you Studying?

An essential thing with revision and study is to be clear about what your goals are. Without knowing why you are studying and what you are trying to learn, you will waste your time. In New Zealand, we are lucky – the exams we sit for NCEA maths are not designed to trick students. There are no tricks in either internal or external testing. In fact, the NZ Government has even set up “Study It” to help students sitting NCEA Maths level 1, 2 or 3.

Revising NCEA with laptop and paper
Maths homework image by Eclipse Images

Understand the basics.

Some techniques are applicable to study across any subject, while others are more specific to maths. If you are starting early enough, the top tip to ensuring that you will go into any NCEA maths test with justified confidence is to make sure that you have “mastered the basics”. Yes, get someone to test you on your timetables and download a fun brain-teasing app that solidifies those old basic facts.  You can have all the flashcards full of mathmatical formulas, but if you still need to use your fingers to work out what 7 + 3 equals, it is hard to feel confident.

Looking at specific examples from the NCEA syllabus.

If you are struggling to understand a concept in class, talk to your teacher, peers or an external tutor. There is absolutely no shame in being the last person to really understand a concept. However, it can be frustrating, and sometimes you're not getting it because of how it's being explained.

Talking with a private tutor gives you all the time in the world to really come to grips with a concept, and a good tutor can find different ways of explaining things. So, ask questions, and if you can't work things out on your own at home, ask more questions. You can find tutors via school or Facebook, and more experienced maths tutors through specialist sites like Superprof.

The NZQA provides really clear examples around what you need to know for every subject. With maths revision, using online resources is not a substitute for real-world learning, so go through the standards and make sure you understand what you need to know, even if you don’t yet understand what you’re actually doing.

For example, with the Unit “Apply numeric reasoning in solving problems”, the achievement standard requires you to be able to “apply numeric reasoning”. Reading through the details of this standard, you will get advice on what problem-solving techniques you will need to be able to show.

You could have to answer a real-world question that shows you can calculate the compounding interest rates for a superfund contribution. Or you might be given a mathematical question designed to allow you to show your understanding of calculating fractions.

NCEA Maths Revision Tips From the Source

When you are going through your practice exams, start with the questions you can answer first. Check that you are getting your basic number skills right. Then move on to the more difficult questions.

Use bullet points to show your working and answer the questions in a logical manner. This means if you are asked how long it will take Max to save for an Electric Bike, break the question down. E.g.:

  • Max earns $500 a week after tax. He is going to save 10%.
  • 500 x 10% = $50 saved each week.
  • The eBike Max wants is $1,500
  • 1,500 / 50 = 30.
  • It will take Max 30 weeks to save for his eBike

Wait until the end of your working before rounding.

Have an attempt at every question. Even if you don’t get the answer right if you can show your working and are on the right track, you are more likely to get at least a partial credit for the question.

Difficult maths problem
Frustrating maths problem Image by DNY59

Show your maths knowledge.

Use the "appropriate mathematical statements" is one of the key things that you will be tested on. One of the challenges with many maths problems at NCEA level isn't finding the answer but working out what the question is!

When you are given a story with information and then asked to offer a solution, examiners aren't looking for the final figure. They want to see how you got to that figure. However, they also want to know that you really understand what is being asked, and could come to the answer using different methods.

One of the examples offered to study is asking students to calculate how much money two friends travelling around Europe need to save and how long they will have to save for:

  • Hui earns $850 per week and saves 2/5 of this: 850 x 2/5 = $340 per week.
  • Mike earns $790 per week and saves 35% of this: 790 x 0.35 = $276.5 per week.

In order to get a better grade, you will need to show that you understand how to use different methods. In the example above, the student was able to clearly show they could successfully complete mathematical calculations for fractions and percentages.

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Don’t recreate the wheel

While often students will spend a lot of time ‘practicing’ by trying to work out unsolved examples and checking the final result, this isn’t the best way when you are trying to ensure you have great understanding. Instead, work through examples that are already (correctly) solved. This way, you can ensure that you are using the right workings, as well as coming to the correct answer.

Again, maths tests and exams are NOT trying to trick you; they are there to help ensure that you have grasped the concepts – and as the saying goes, practice makes perfect. However, if you aren’t practising correctly, you will be solidifying the wrong information in your brain – and that won’t help you pass NCEA maths at any level.

Teen Girl Excited To Understand Maths
Excited young woman by Bulat Silvia

Sit Up Straight

While the typical pose for a relaxing studying session is depicted as lounging upside down on the couch or sprawled on a bed, this is not going to help you remember what you’re studying.

Research has now proven that sitting up straight, with your feet flat on the floor, actually helps you focus. Other research has shown that great posture even reduces anxiety – specifically around maths!

Move Your Body

If you find that you are stuck on a question or re-reading the same sentence without actually reading it, stand up! While a brisk 5-minute walk in fresh air is the best to help you regain your focus, just standing up and stretching can help.

Find a youtube video for 5-minute yoga routines for focus, do 20 jumping jacks, or just stretch up tall then touch your toes. You are trying to clear your head and get your blood moving a bit in order to give your brain a chance to refocus.

You can also use a five-minute break to summerise and reflect on what you’ve learnt so far.

Teenager doing Yoga to improve recall
Teen girl doing yoga prayer pose image by Courtney Hale.

Regular exercise is great for maths revision.

You are probably sick of being told – but getting regular exercise really is good for you. Maybe instead of wasting time creating a revision plan that you’re probably not going to stick to, try creating an exercise plan. Kids and teens who get regular exercise are better able to focus without being distracted.

A study in 2003 out of the University of Georgia was able to show that only 20 minutes of light exercise is all it takes to boost your ability to concentrate overall. That’s a pretty good trade-off for walking home from school.

Pomodoro Technique

One popular technique for concentrating is to break it up into chunks of time. In the 1980s, Francesco Cirillo developed the “Pomodoro Technique” for time management. This has been revamped a bit for a modern audience, but the basic principle remains the same.

Set a timer for 25 minutes, turn your devices onto aeroplane mode, and work solidly until that timer goes off. Keep a notebook beside you for when your brain tries to interrupt with something vitally important – write the idea down, and deal with it later.

If you search Spotify, YouTube or your favourite music provider, look for “binaural beats”. There are a lot of different options and styles. Still, generally, the idea is that by feeding two slightly different frequencies, one to each ear, the brain getting confused enough to tune out distractions and allow you to focus.

While you may find that you can’t concentrate for the full 25 minutes, by having a visible timer, it becomes easier to stay focused. You will likely discover that the most productive time is during the last ten minutes when your brain has finally resigned to completing the task. While it can be tempting to ‘go with the flow’ and carry on, by stopping when your timer goes off and taking a 5 minute brake to move and stretch you will be able to carry on productively for longer.

Tackle Maths Problems TL;DR

  1. Understand what your goals for learning are
  2. Break down the question into manageable chunks
  3. Always show all of your working
  4. Work through examples that have already been solved (correctly)
  5. If you get stuck, ask! A teacher, peers, tutors - just don't do it alone.
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Alison