A Bit About Myself…

My name is John Armstrong and I am a fully qualified and experienced tutor and classroom teacher of A Level Mathematics and Further Mathematics. I also tutor university entrance exams such as STEP, TMUA and MAT.

As you can probably see from the sheer amount of A Level Maths and Further Maths resources on my site, I am passionate about students and tutees having access to the best resources. Take a look, just for example, at the A Level Maths exam questions by topic that I have collated, my A Level Maths revision notes or the equivalent for A Level Further Maths or my proudest achievement resource-wise: The Ultimate Study Tool for A Level Maths; I am absolutely dedicated to delivering the best for my own (and all other) students and tutees.

I have been professionally tutoring on a one-to-one and small group basis for many years now, refining and perfecting my tutoring approach over my many years. My classroom teaching experience is mainly in Sixth Form Colleges teaching A Level Maths, Further Maths and preparing students for entrance exams such as STEP, MAT, TMUA among others.

My Tutoring Approach and Philosophy

When it comes to A Level Maths and Further Maths, high grades come with hard work. In all my teaching experience, it is always the students that put the most work in that get the best grades. As an A Level Maths tutor, it is my job to help you thoroughly understand the material, giving you the knowledge, self-confidence, and of course, the resources required to practice what we go through in sessions and, ultimately, get the grades. I will help you to uncover which areas need work and will guide you through exactly what approach is needed to get the best grades in A Level Maths. Naturally, I will need to modify my tutoring approach depending on your needs and the situation you are in, so if you would like more information and examples of how I would do this, please read this article I have written on how I adapt my tutoring approach to student needs. 

The Roles of an A Level Maths Tutor

A tutor can perform many roles. As an A Level Maths tutor, I have to be able to adapt to whatever your individual needs and circumstances might be. From my years of experience, I firmly believe that a good A Level Maths tutor must be able to perform any of the following roles depending on the needs of the student at the time:

• A subject expert: over the course of my career, I have heard many stories from my students who had previously taken on tutors who were very good and accomplished mathematicians (university lecturers or PhD students, for example) but who didn’t have an in-depth knowledge of the A Level syllabuses which they tutored. Knowing the syllabuses inside-out – their idiosyncrasies, how the marking guidance has developed over the years, the differences between syllabuses – is key and fundamental knowledge for an A Level Maths and Further Maths tutor to be effective. An effective maths tutor should be adding value by giving students sound, expert guidance on how to improve both subject knowledge and technique ultimately leading to a boost in exam performance. A tutoring session should not simply consist of the tutor and student muddling through questions together session hoping that an improvement will be seen.

• A teacher: a tutor may have all the above attributes but, to be effective, an A Level Maths tutor must also be skilled in being able to impart this knowledge upon their students. An effective A Level Maths and Further Maths tutor should have experience in both teaching and delivery to be able to engage and deliver content in a way that you understand. A well-practised classroom teacher of A Level Maths and Further Maths will be able to recall at a moment’s notice all of the content required and be able to instantly help students with any problems they may be facing.

• A mentor: it is important that you choose an A Level maths tutor who can help motivate and drive you to success; a tutor who can get to know not just your mathematical strengths and weaknesses, but actually get to know you as a person and truly understand what makes you tick. Such a tutor will be better at helping you do what needs to be done to achieve your full potential in A Level Maths.

As an A Level Maths tutor and an experienced classroom teacher of A Level Maths, I have seen many different reasons why a parent would want a A Level Maths tutor. However, choosing a tutor with the right approach is always a worry and it can seem like a daunting task. I will now outline some common scenarios, one or more of which will probably ring true. Each individual student needs a personalised approach as each personality is different, however, in order to give you an idea roughly of the approach that should be taken by a tutor in a range of circumstances, let me give a few case studies of the different types of students and how a tutor may help.

Example Student #1: Underconfident and Scared To Ask For Help In Class

Laura (a hypothetical student) lets things get on top of her; she feels she understands most things to an extent in class but when it comes to things she doesn’t understand, she rarely asks the teacher. The thought of asking about something she doesn’t understand while everyone is watching sends shivers down her spine. And there are many more students like Laura; it is extremely common for A Level Maths students feel like this. They shouldn’t; we as teachers are here to help. However, the fact remains that some students don’t like to ask questions in class. And as a result they end up slowly falling behind.

My Approach as a Tutor

In my experience, these traits very common. So common, in fact, that I have written an article on how an A Level maths tutor can help students who have fallen behind. In this situation, the key to getting a student back on track is to thoroughly assess at the earliest opportunity. But the word” assess” can induce a lot of anxiety. The first thought that comes to mind is the idea of having to do a paper in timed conditions, a situation that would leave a student who is struggling feeling useless and exposed. But it need not be that way; assessment can be gentler. Assessment can be performed concurrently with teaching.

Over the years, I have found that assessment for the purpose of determining gaps in knowledge is better done during lessons using past paper questions; the approach involves concurrently discovering gaps in knowledge and supporting the student in filling those gaps. I have found this to be far more effective in the initial stages than simply setting a student off with a past paper and constantly reminding them their knowledge has gaps. The latter would be demoralising and serve no real purpose.

Once these initial gaps in knowledge are filled, I have found it particularly productive to then try to teach students slightly ahead of their class teaching schedule, getting them, say, one week ahead of what they will be learning in class so that they have the ground knowledge and confidence to ask (and answer!) questions in class.

Example Student #2: Overconfident After GCSEs and Doesn’t Practise

Simon (again, hypothetical) is a student who performed brilliantly in his GCSEs. An all round top grade student. However, a couple of terms into A Level Maths his grades from school seem to be slipping. Simon says that it is just a blip and that he feels he is doing well, but as a parent you are not so sure. This is yet another common scenario. Many students who have a natural ability up to about the GCSE level often find that as soon as a bit of extra work is required outside of lessons, things start to fall apart.

My Approach as a Tutor

This is yet another very common scenario, with these traits most commonly being found in boys who achieved highly at GCSE. Early intervention is the key to restoring confidence and instilling a strong work ethic that will carry them successfully through A Level. With this type of student it is imperative that the gaps in knowledge are diagnosed and that a programme of work is drawn up early on to help the student. But generating a (potentially long) list of knowledge gaps is not enough.

On its own, to simply tell a student that they are behind and can be overwhelming and demotivating. The best approach is to drip feed the students the gaps in knowledge and simultaneously plug the gaps so as not to knock the student’s confidence.

Once the gaps are filled and the student is back on track, a slightly different approach is then needed. As an experienced A Level Maths tutor, at this point I would ensure that the student actually starts to get ahead of the game, teaching them the content that they are about to study in class to give them a head start will put them in a position in which they ooze confidence, but by this stage the confidence is justified.

Example Student #3: High Achiever but Terrified of Exams and Underperforms in Tests

This particular type of student is also very common. The pressure of exam situations always gets to them and they underperform as a result. They are a top student: they ask questions; they do the homework; they take detailed notes and spend time rewriting them out neatly; they make beautiful concise revision cards to bolster their study. But it is with these final two points where the problem lies. The student spends a lot of time doing many many things other than the thing they find most difficult: exam questions.

My Approach as a Tutor

In my time as a classroom teacher and tutor of A Level Maths and Further Maths, I find that a gentle approach to try to wean students off spending their time producing (admittedly beautiful) archives of lesson notes and fantastic revision cards. With A Level Maths and Further Maths, any classroom teacher or private tutor will tell you that to do well, the key is practice practice practice of exam questions. To change the working habits of a hardworking and diligent high achiever could be made into a battle, but it is important not to approach it this way. I have found that the confidence of such high achieving students is easily shattered and to tell them that they have been doing everything wrong up to this point would be a mistake.

My approach in this situation would be to have the student to discover for themselves that there is a better way of working by gently nudging them in the right direction.

Example Student #4: Failed to Progress onto the Second Year of the A Level Maths Course

Dan struggled throughout his first year and never really seemed to get to grips with the jump between GCSE and A Level. A few weeks before the end of year tests Dan realised the mess he was in and worked harder than he’d ever worked before. But it was too late and it was not enough. He has been told that he didn’t get enough marks on his end of year test to progress to the second year, so if he wants to continue with maths he has no option but to repeat the year.

My Approach as a Tutor

With students in this scenario it is important that a tutor gets in there straight away before the student loses hope. Clearly the student’s confidence is bruised, but a good A Level Maths tutor will know that this situation can be turned round and made into a positive. In this situation, as a tutor I would capitalise on the improved work ethic that Dan exhibited towards the exam period and help him use this to his advantage. Dan has spent all of the last year feeling like he is bottom of the class but he will still have taken in a lot of the mathematics that was taught to him even if it is not currently fluent or instantly recallable, but there will be an underlying base knowledge. And provided a tutor works with Dan to keep him slightly ahead of the schedule of what he is going to be taught in class, he can go from like he felt last year (bottom of the class and behind) to feeling on top of the material and able to hold his own, achieving well in homework and class tests.

Conclusion

In order to be an effective tutor of A Level Maths and Further Maths, some degree of flexibility is required in order to adapt to the individual needs of a student. Not on that, but you need to bear in mind that the needs of the student can evolve over time. As a tutor, I am well aware that I need to keep my finger on the pulse and not just focus on the mathematics, but also look for the emerging signs and changes within student body language and demeanour to indicate whether a given approach needs to be modified. Being able to spot these signs early on comes only with experience.

I am passionate about helping all students (not just my own tutees) succeed in their A Level Maths and Further Maths studies. For this reason I have created hundreds of tutorial videos covering the entirety of the A Level Maths sylllabus which are freely accessible on my YouTube channel. So even if you decide not to go with me as your tutor, you can still benefit from my teaching for free.

You can visit my YouTube Channel by clicking here.

My Academic and Professional Background

I am a fully qualified teacher of mathematics holding a PGCE and Qualified Teacher Status in the UK. My degree is in Mathematics and Computer Science and I hold a Master’s degree in Applied Mathematics in which I was awarded a “distinction” grade.

My classroom teaching background is in sixth form colleges where it was my full-time job to teach A Level Maths and Further Maths. You can view my certificates below.

In order for the sessions to be truly interactive, the student needs to have access to the technology that will make this possible. Many students have such technology without even realising it!

1. A good, stable internet connection is essential to ensure that the session runs smoothly. Uninterrupted dialogue is essential to ensure that learning takes place.
2. A tablet (e.g. iPad, MS Surface or Touchscreen Laptop) with stylus or a graphics tablet attached to your computer is used in conjunction with cutting-edge and simple-to-use whiteboard software which enables me to see what you are writing in real-time, allowing me to demonstrate, explain and mark your work as you produce it.

You may by this point still have reservations about the effectiveness of online tuition so to ease these anxieties and give you a full picture of how online tuition works, I have written an article on this very topic entitled “Online vs In-Person A Level Maths Tuition”.  

And that’s everything! As long as you have access to both of the above then online tuition is as interactive, personal and effective as in-person tuition, as you can see from the video below.

You will have noticed that my rates are higher than those of many other tutors. These rates reflect my many years of experience in teaching A Level Maths and Further Maths both in the classroom and through online tutoring, my qualifications and, more importantly, the results my students achieve through a partnership of both mine and their hard work and dedication. Each lesson includes:

• • • An hour of one-to-one tuition from me, John Armstrong, the creator of ALevelMathsRevision.com, an experienced teacher of A Level Maths and Further Maths with exam board marking experience;
    • Expert advice on exam technique and how to “target the marks” in an exam situation on a topic-by-topic basis;
    • Tailor-made resources to complete as homework that complement the learning process and further embed any newly learned material.

If you want to book a lesson or are unsure about whether one-to-one tuition is for you, please get in touch using the contact form below to organise an interactive online demonstration of how interactive, engaging and effective one-to-one tuition can be.