The jump from Year 10 Maths to Year 11 Maths B feels more like a leap across a great chasm, the shock of which leads many to fall far from the other side. A great number of students pre-emptively drop to Maths A, many of whom are discouraged by their teachers or even parents.
For those who think they’re just not cut out for Maths and Science: yes, there are subjects which come naturally to some, and other subjects less so. While this is may constitute an excuse to quit, it is certainly not a justified reason.
As one of our highly valued students have said, you can’t always decide to ignore the things you find difficult in life – you have to push through them if you’re going to succeed.
The good news is it is possible to not just pass, but rather to do well and get an A in Maths B – if you put in consistent time and effort.
As a humanities and language-based person, mathematical concepts were so non-intuitive and abstract to me. Yet I graduated high school with Maths B and Japanese as the highest grades out of all my subjects – unexpectedly not in English, a subject which I loved.
If your last maths exam was a blemish to your otherwise perfect report card, or you’ve always had difficulty with mathematical concepts, here are 7 things that will help you to get an A in Maths B.
1. Do All The Different Questions For Each Math Section
In Maths, each section teaches a very specific principle – for example, solving linear algebraic equations. Once the principle is grasped, the basic level questions are easily solvable.
Within each section, however, there are variations of the basic question that take it to the next level – some of these may incorporate principles taught in previous chapters.
It’s vital to attempt these tricky questions, and learning from these will develop a complete understanding of the mathematical principle.
Ideally, students should review their thought process and work backwards with the answer provided to figure out how to correctly solve the tricky questions. This can be a time when collaboration with peers comes in (see below).
Lastly, they should be marked down to be discussed with a tutor or your teacher in class.
2. Collaborative Learning
Working with others might be an unwelcome necessity in the workforce, but collaborative learning in study shouldn’t be considered a challenge to overcome. If the right people are gathered, in the right situation, and the right environment, studying in groups and collaborating with other students can be an incredibly rewarding experience. It’s one of the absolute best ways to make those really difficult subjects enjoyable!
Every student, obviously, is an individual, and has different strengths and weaknesses. One of the greatest benefits of group study is that students can learn from each other’s strengths, and support their weaknesses.
Helping other people is one of the most rewarding experiences – and we would know, having worked primarily in the field of helping others. Learning how to do this early on is not just useful for school, but will continue to be a beneficial skill into life afterwards.
Finally, in Maths B – and all other subjects, really – a harmonious study group encourages you to actively engage in problem solving. This is the absolute core principle of maths, as opposed to being spoon-fed the method and answer at every step.
Teaching others is proven to help solidify core knowledge in your brain, as it helps transfer information from short-term memory to long term memory.
As you can see, rehearsal of content helps shift it from short term memory to long term. Continuous rehearsal – say, helping others with their work – is sure to build up a strong foundational knowledge base!
“But how do I find someone to study with?”
Well, your friends may be the first thing that comes to mind, but this is often not the most optimal choice. The best choice is someone friendly and familiar, and someone who you know is very passionate about improving their marks, or maintaining already good grades. Making this decision requires a bit of maturity, and it can be daunting to ask, but taking the leap is incredibly rewarding!
Another noteworthy point is the everyone’s level of knowledge should be around the same, with only slight variations. If someone’s knowledge is too high, they can become a lecturer; meanwhile, those around them at a lower level can be seen as leeches, sucking free knowledge from others without putting back. This kind of relationship will only build resentment from the former, and guilt from the latter. A truly symbiotic relationship is one where both parties are co-dependent and working concurrently.
3. Have A Good Relationship With The Teacher
Teachers make a big difference in any subject, but in maths, improper communication can be like learning in a different language.
Being in the teacher’s good books isn’t so they’ll give you the exam questions. It’s more about learning in an atmosphere where you will feel comfortable to ask a question.
We’ve all heard teachers say there’s no such thing as a stupid question. That doesn’t dispel the angst of asking a teacher who makes you feel like you’re holding the class up or wasting his time. The reality is, teachers do make us feel like this sometimes, even if just through body language. This occurs if they perceive the student as insincere, which usually happens if they think you do not pay attention in class.
Making your teacher acknowledge your questions and diligence is simple – demonstrate you are working hard.
Take note of what you don’t understand in class (write them down if you’ll forget), and ask questions during the brief pauses teachers indicate they want you to ask a question. Other than that, students should clarify about homework and show teachers their worked modelling and problem solving (MAPS) questions.
Even though it will be rare, you may get a teacher with whom you just don’t click. Their style of teaching may be in opposition to your learning language, or they may have a pre-existing bias against you.
Whatever the case, there are times when it is best to request a change into another class. If you have a history and reputation of taking your study seriously, carefully considered communication with school authorities will give a positive result.
4. Learn How To Properly Show Working
From Year 10 onwards, the use of mathematical language to show working is just as important as being able to solve the question itself.
From a marking point of view, the most you can get with just the correct answer is a D, even if your thought process was 100% correct. With minimal working that goes up to a C, and once the principles of mathematical language are understood, A’s are usually achieved.
For such an important part of Maths, it’s ridiculous to think that it’s not actually formally taught per se – there isn’t one class dedicated purely to teaching mathematical language.
“So,” I hear you ask, “how do I learn to show working then?”
Pay attention to the teacher’s full worked examples of MAPS questions.
Sometimes, the whole class is stumped by a particularly challenging MAPS question, in which case the teacher does it on the board.
Take this opportunity to note the teacher’s use of mathematical language – it will be an A-level example of what the teacher expects in the exam. If you know this is a critical area for you, copy it completely so you can go through it again.
Mathematical language is something slowly developed for as long as you do maths. This is because each teacher’s expectations vary somewhat, and you must adapt their requirements.
It’s always wise to do get validation from your teacher after you’ve done a full MAPS question. Apart from checking the answer, ask them what they think about your working, and how you could improve.
Lastly, observe your study group’s working and incorporate what you like into your own style of mathematical language. As stated above, collaboration is a powerful tool that can facilitate and enrich learning. BOOK A MATHS TUTOR TODAY
5. MAPS Strategy and Study
Have you ever studied long and hard before an exam, only to eventually get to the test paper and think to yourself,
“What the heck? This is nothing like what I learnt in class!”
Say no more. The MAPS questions we’ve been referencing throughout this blog can be quite tricky to figure out, but they do have their own strategy and principles.
The reason Modelling and Problem Solving can be tricky is because they combine multiple mathematical principles that you learnt throughout the term. Not only that, they’re presented as real life situations, in ways that are often unconventional.
It’s important that you analyse the problem beforehand. This will save you any precious time that might get wasted if you had rushed in, and gone down the wrong path.
Our maths tutors teach their students certain systematic strategy for tackling MAPS questions with maximum time efficiency.
5-1. Highlight the key information
Using highlighters when reading will save you the time needed to go through the passage again and locate key information. The use of colours will stimulate your brain to take note of the highlighted information. You can also choose to use different colours for known and unknown variables, which helps the brain organize the information.
5-2. Draw a sketch
At this point you likely won’t know how to approach the question yet. A sketch will present the information you’ve highlighted in another form, further stimulating memory and creativity. Even if you think you’ve got the question in the bag, you may realize you interpreted the question incorrectly once the sketch is done. If you rush in skipping this step, you will waste precious time realizing your mistake later.
5-3. Identify the relevant mathematical principles and formula
Once the sketch is done, determine what formulae you will use and steps to be taken to solve the question. This is a key step which will test your understanding of the knowledge and creative thinking.
Think about the problem both forwards and backwards, considering the given variables and steps to solve for the unknown and vice versa. If you are still stuck after this, continue to the next step, but you will have to revisit this process to figure out if you’re on the right track or if adjustments are needed.
5-4. Solve the question in logical steps
At this point, the answer is at your fingertips, and you must make sure to solve it in the correct steps. For example, you might first need to find the optimum quantity of production out of cost and profit equations, then use that value to solve for maximum achievable profit for the company.
Remember to use appropriate mathematical language!
5-5. Work backwards to double-check your answer
Depending on your exam strategy, you may double-check answers after you’ve attempted the whole paper, or you may do it right away. Make sure to check by working backwards with the answer and/or subbing it back into the formula. If you go through your initial working again, you will tend to accept your logic whether or not it is actually correct.
During exam preparation, however, MAPS questions should be attempted in limited time. Timing yourself is a great way to simulate exam conditions. This will not only help you practice, but also give you a sense of how much time is necessary to solve each question. Unlike knowledge and procedure (KAPS) questions, MAPS require more than just muscle memory.
If students struggle to solve the questions within the assigned time-frame, they need to improve their understanding in knowledge, refine their MAPS strategy, and/or learn to think outside the box.
This is where we as tutors are able to assist students best. Not only do tutors help facilitate a good environment to practice MAPS questions, but they are actually trained to do mock exams with students under typical exam conditions. This kind of practice can prove invaluable to students in the long run.
6. Tips & Trick For Maths Assignments
Maths assignments are a sensitive issue that summons an atmosphere of competitive secrecy. Everyone is trying to achieve the top mark, the top place in the class – and assessments often present the greatest challenge.
This is a time when sources of external help – A Team Tuition tutors, for example – are the most valuable, as the same oath of secrecy does not bind us. Having said that, Maths B assignments require knowledge and problem solving not explicitly taught in class that challenges even high school maths graduates.
Before we discuss assignment tactics, it needs to be said that maths assignments particularly take a lot of time to complete.
You should always, always, always start your assignments early. Remember how we talked about MAPS questions, and the plethora of work they require to complete?
Well, assignments are like super-mega MAPS questions.
Never fear – remember, you are more than capable of accomplishing them! Contrary to popular belief, your teacher would not assign you an absolutely impossible task.
Start by identifying the mathematical concepts you will need to research and form the skeleton of the assignment. Complete a table of contents if that’s all you can do for now – but always start with the bare bones of the work, and build from there.
As you’re doing research and beginning the assignment, take note of specific mathematical jargon that need to be used. Use of correct terminology will make your assignment more concise.
Concise means precision; and precision is key.
“Why?” I hear you ask. Well, let me ask you a question in return: How often do you go over the specified word or page limit in a Maths assignment?
If you bit your lip and tried to avert your gaze, then I know the answer is at least more than once.
Being precise will allow you to be concise. Utilising key terms will cut down on words, and tools such as tables or graphs must be used to convey information, as they rarely contribute to the word count.
More importantly, the acceptable standard of mathematical communication escalates dramatically in maths assignments.
What would have been an A in the exam would at most give a B-. Students are expected to note every step in their mathematical process – this includes every sketch drawn, relevant observation made, and button pressed on the graphics calculator.
Maths assignments apply principles taught in textbooks to real life, in often seemingly meaningless ways. For example, I’ve seen assignments focused on the equations derived from the lines and curves on our hands. Regardless, it can be incredibly rewarding to explore such topics!
Note that, naturally, there are usually assumptions that must be made and limitations acknowledge in applied mathematics. Going back to the previous example, we may assume that the lines are always curved, while they may not truly be; or we may assume that every piece of data is accurate, while we are quite prone to human inaccuracy. Every single assumption and limitation must be clearly stated in the relevant section of the assignment.
7. Recognise When To Get Extra Help
The prerequisite for learning additional knowledge is that you know the basics. Sometimes, early difficulties can lead to falling too far behind in a section, chapter, or even a whole subject.
It is important to get back up after you fall. Before that, however, it’s possible to realize you’re about to fall and lean on someone to get you through the task.
How do you know when you need to get help?
Get extra help if you hardly understand anything from class and every lesson seems like a chore. Get help if absolutely nothing makes sense, and you’re struggling to keep up with the rest of the class. Get help if you need to push yourself from a C to a B, or from a B+ to an A.
What I’m saying is, get help whenever you can, and whenever you want.
There should never be any shame in asking for help. Whether you’ve struggled with the basics of mathematics from day one, or you’re acing everything except that one key area – it doesn’t matter. Help is available to you whenever you need it – from teachers, parents, or A Team Tuition, at any time.
by Chilly Peng