Improve your algebra skills for A-level

mathematics

As an A-level mathematics tutor, I notice that a large number of students beginning their A-level studies have remarkably poor algebra skills. This hard core of students (usually boys) are unable to manipulate fractions, confidently rearrange formulae, work with negative numbers or perform the necessary basic skills to progress in the subject. They repeatedly ask the same questions and try to learn methods by rote because they don’t have the skills to do otherwise. Teaching them can be very frustrating because the same issues are revisited again and again and little progress can be made until they learn basic skills which should have been learned at GCSE.

I should add that this is a minority of students but nevertheless a significant minority. If you recognise yourself in this category, do yourself a big favour and learn to walk before you try to run. Mathematics is a hierarchical subject and progression is made on the basis of having mastered prior skills.

What to look for in a tutor

I have been tutoring privately since 2013 and teaching mathematics and physics since 1996. I have tutored well in excess of 100 students since I started and have covered all manner of syllabi in both subjects. I have taught GCSE, IGCSE, A-level, Pre-U, International Baccalaureate as well as AP Calculus AB (the American syllabus).

In my experience, the most important factor which is overlooked is the tutor’s subject knowledge. A close second is the tutor’s enthusiasm and ability to motivate the student. If I am not totally familiar with a syllabus, all the information that I need is available online. But if I don’t understand the topics covered, it is not going to be much use even if I know the syllabus inside out. All maths and physics syllabi share a large amount of common material. You can be sure that 80% of the material is the same.

Teaching Advanced Placement Calculus

Ap Calculus

In 2019 I taught online a student taking Advanced Placement Calculus AB and used the free Khan Academy resources available here. I must say that it is a lovely resource as it keeps a running track of the student’s weaknesses and strengths topic by topic and even by subtopic.

Online tuition

More and more tutors are providing online tuition these days. I use a digital pen and an interactive whiteboard. Notes that I write are displayed on a shared screen and the student can also interact via this learning space. Documents in jpeg or pdf format may easily be uploaded. All that is needed is a stable internet connection at both ends. There are so many resources on the internet to enhance any lesson. I give about 50% of my lessons online and it is very convenient. Lesson notes may be retrieved at any time.

One factor in choosing online tuition is the lack of availability of good local tutors, if the student lives in a remote area or if you simply want convenience.

I currently tutor students regularly in the UK and overseas. I believe that it is going to be the future of learning. There are even schemes to introduce online teaching to poorer families by teaching several students at once. The cost is then shared equally, allowing parents who could never afford private tuition to be able to do so. Just imagine if a scheme could be rolled out like this in the developing world. Five or so poor kids from a South African township meet up at their local church or community centre and log on to computers or even just mobile devices. They have an interactive learning experience with a teacher in the UK and it costs them almost nothing because the relatively low cost per student is subsidised by the organisation they are meeting at.

Museums near London for kids who like science

For any kids into their science, the National Museum of Computing at Bletchley Park in Bedfordshire is a must. It has a replica of the Bombe built by Alan Turing during the war years to crack the Enigma Code. It also hosts a rebuilt Colossus, the first electronic computer. It also has a vast range of computer memory devices from car readers to one of the first disc drives. You can call and arrange a guided tour – which is recommended.

The National Maritime Museum has some of John Harrison’s prototype clocks used to solve the longitude problem. This is well worth a visit and is free.ย Harrison H1 blog.jpg

The Observatory Science Centre at Herstmonceux Castle, the former site of the Greenwich Observatory, hosts courses on astronomy, permanent exhibits on science themes and much more.

Dungeness B Visitor Centre is where you can arrange a visit to a nuclear reactor. What’s more, it is free.

Dungeness B Reactor

 

Resources for A-level maths revision

Here are some of my preferred A-level maths revision websites.

http://m4ths.com/teach-yourself-a-level-maths.html

This site is run by retired maths teacher Steve Blades and contains links to a great deal of instructional videos that offer a lot of detailed help on all areas of the syllabus.

https://www.savemyexams.co.uk/a-level/

Save My Exams offers help on maths and the three sciences in not just A-level but pre-U, GCSE and IGCSE exams and is syllabus specific.

https://www.physicsandmathstutor.com/maths-revision/

This site offers syllabus specific support and has solution banks and past papers.

https://www.biochemtuition.com/

Despite its name, this site has extensive support as well as copies of text books (copyright alert!)

https://www.examsolutions.net/

This website is highly rated by my students. It has instructional videos on examination past papers for mathematics A-level. It covers Edexcel, AQA, OCR and MEI syllabuses.

GCSE maths resources

Many students going back to school in year 10 and 11 quickly realise that they are not prepared for the demands of the course – especially in mathematics. It is a demanding subject and requires discipline and a lot of practice, practice and more practice. It is essential to get into good habits early. I have some resources to recommend as well as some tips.

Don’t neglect to work on your arithmetic, both mental and written. An inability to work quickly and carefully with the basic operations of arithmetic trip up many students. They get muddled and trip up before they even start. To help, I recommend doing online practice wit a website such as www.arithmetic.zetamac.com.

Review the fundamentals before starting to try examination questions. There is no point trying examination questions until you understand the fundamentals. You will find two kinds of questions in your text book and on websites. There are ‘consolidation’ or ‘confidence-building’ exercises and actual exam type questions. If you find that your school provided text book might lack exercises in some topics. In which case, you will need to supplement your revision with some good online resources. Three of my favourite resources are below.

GCSE Maths takeaway

GCSE Higher Level Worksheets

Just Maths

Poor understanding of maths vocabulary can hinder learning. I recommend reviewing GCSE maths vocabulary as a part of revision.

Ti-nspire graphing calculator resources

The Texas Instrument Ti nSpire is an advanced graphical display calculator able to do complex algebra.

I use the Texas Instrument Ti-nspire pictures, which is a computer algebra system graphing calculator. Some great resources for this calculator are listed below.

http://www.johnhanna.us/TI-nspire.htm

https://learnit.hoonuit.com/2410

 

Year 8 and year 9 physics resource

In 2009 and 2010, I created a Google Sites website for the Key Stage 3 students that I was teaching. I hadn’t looked at the site since 2010 but then yesterday, I took a look. You might find it useful as it links to many resources.

Year 9 physics site

Year 8 physics site

 

My favourite resources for tutoring maths and physics

Here are a few of my preferred resources.

Desmos Graphing Calculator is a web-based calculator. It is very versatile and can plot functions in Cartesian, polar and parametric form. It is very intuitive. You can switch simply between degrees and radians and it is web based so there is no need to download any software.

 

 

 

 

Mr Barton GCSE Maths Takawayย is a GCSE site of course with a lot of resources arranged conveniently by topic. It is a free resource and very popular.

Exam Solutionsย offers video instruction (short video clips) which are tailored to specific syllabuses. For those students who really need to see it done in real time rather than learn from the book, this is excellent. Many of my students have said that they like this website.

I tutor the International Baccalaureate Diploma in maths and physics. An excellent WordPress site isย IB Physics Notes. It is very detailed and offers detailed revision material on all parts of the syllabus broken down by topic.

I also recommendย Hyperphysicsย because it offers a clickable concept map showing all topics within Physics. It’s great for revision too.

Also thoroughly recommended is the inspirational siteย Physics Footnotes. This offers a large range of explanatory video clips that bring to life the principles in Physics.