Maths » GCSE
How to prepare for your first lesson
Know your student
Effective tutoring starts from the first time you meet. The first time you meet your student, make sure you ask lots of questions and find out as much as possible about their current attainment and attitude towards maths. What do/don't they like to do in lessons? Do they dislike maths or do they just find it difficult? Do they have mathematics anxiety?
Structure your lessons
Try to think back to when you were at school. Lessons were monotonous if you were just talked at; students need variety! Maths can be particularly dull if you are just working through exercises, so don't spend too long on any one type of activity. For example, introduce a topic and cover the theory, then have a go at some simple practice questions to cement the technique. Next, have a go at some harder questions, perhaps word problems or questions involving some extra steps. Finally, allow your student to work through some exam questions. As a plenary, ask them to summarise what they have learnt on a new page. I like to draw a box on the whiteboard, and then task them with fitting everything they’ve learned into it - a real challenge for those who like to write volumes of notes!
Make sure your student is making progress
What can your student do at the end of the lesson that they couldn't do at the start? It doesn't have to be a huge leap forwards, but your student will need to see improvement to stay motivated. If possible, establish a ‘learning objective’ at the beginning of your lesson, so that you and your student have a tangible goal to work towards.
What can your student do at the end of the lesson that they couldn't do at the start? It doesn't have to be a huge leap forwards, but your student will need to see improvement to stay motivated.
Resources
My go-to bank for resources is TES. Many of the resources are available for free and are in formats that you can edit, so you can tailor them to suit you and your student. It is essential that you take time to check and adapt the resources - downloading them saves time but there can be mistakes and you should have your own set of solutions prepared.
Tutoring online means you don’t want to have to be switching between pages to view questions and answers. The most usable resources have gaps after the questions where you and your student can work. For example, these worksheets are ideal for practicing solving equations, with a variety of activities at a range of levels.
Once your student starts revising for the exam itself, past papers are your golden resource. They are available online (make sure you look up the correct exam board) and most will have mark schemes too. I would suggest that you don’t attempt papers in their entirety too early; just pick key questions that reflect the typical way a topic is examined. Save whole past papers for closer to the exam date once all topics have been revised individually. The most efficient way to cover whole papers is to ask students to complete the paper in their own time, and use the lesson itself to mark the paper together, stopping to spend time on the questions they struggled with. I would normally ask my student to scan in and send me the completed paper in advance of the lesson. That way I can have a look through it before we mark it together (I usually print and annotate a copy so that I have a reminder of the points I want to make), and I can be sure that there won’t be any issues uploading it to the Online Lesson Space.
1. Maths anxiety is a recognised emotional reaction to being faced with a mathematics problem. For more information, The Nuffield Foundation are currently conducting some research into it and have an excellent explanation of the effects of it here.
FAQs
The hardest part of tutoring maths is understanding why students often find it so difficult - some overwhelmingly so. Our job is to help them achieve as best they can by making the syllabus accessible and taking as much time as is needed to cover and review material. Be wary of asking anything too challenging too soon, but have a wide range of materials ready which cover a broad range of ability levels, and be flexible with which ones you use and for how long. Step up the difficulty gradually and explain what you have added that makes this question slightly more complex than the last.
The hardest part of tutoring maths is understanding why students often find it so difficult - some overwhelmingly so.
Sometimes the student will just say or write down a correct answer with no explanation. In this case, don't stop there: insist that they explain their logic to you. It might be that they are using a 'trick' method or skipping steps, which will work for the easy questions but will fall apart when the questions get harder. It is essential that the method they learn will work for all questions, not just the easy ones.
It is also worth noting that most students, even the weaker ones, will have areas of the syllabus that they find much more manageable than others. Therefore it’s important to have some higher-level materials available. The last thing you want to do is to restrict your student to simple questions when they are capable of tackling more advanced problems.
What is changing in maths?
Maths exam specifications have been updated, and students will be tested on the new syllabus this summer (June 2017). Starting from this summer, English and Maths GCSEs will be graded with the new 9-1 system. 9 is the highest, but fewer of these will be awarded than the number of A*s awarded in previous years. An old C grade is roughly equivalent to a 4 in the new system. Exam boards have updated their specifications, but past papers will still be relevant, as it is likely that each exam board will set questions in a similar style to before.
The new specifications have more content and are more demanding than before, so begin by reading the updated syllabus. Make sure that you have it clear in your mind what they do (and just as importantly don't!) need to know; what is given to them on a formula sheet and what they need to learn by heart.
The next step is to look through some past papers; get a feel for how students should be able to apply their knowledge. Work out what the key areas are for weaker students, and which areas are aimed at those students seeking that A* grade.
There is a new content area which affects all exam boards, called ‘ratio, proportion and rates of change’. Many of the specification points in this area are not new, but they used to be covered in other parts of the syllabus. This, along with the ‘number’ content area, now make up half of the examinable material for the foundation tier papers.
There are three Assessment Objectives:
AO1- Applying standard techniques (this makes up 50% of the foundation tier marks and 40% of higher tier);
AO2- Reasoning, interpreting and communicating (this incorporates the old ‘Quality of Written Communication’ marks that used to be awarded; 25% of foundation tier marks will be assessed in this way, 30% of higher tier);
AO3- Solving non-routine problems (25% of foundation tier marks will be assessed in this way, 30% of higher tier; there is more focus on this method of assessment across both tiers than there has been previously).
Make sure you read the specification before you start tutoring. The OCR specification can be found here. Some topics, such as venn diagrams, have been added to both foundation and higher tiers; some topics, such as trigonometric ratios, which were previously higher tier only, have been added to foundation tier; some topics, such as finding approximate numerical solutions to equations using iteration, have been added to higher tier only.
There is a new content area which affects all exam boards, called ‘ratio, proportion and rates of change’. Many of the specification points in this area are not new, but they used to be covered in other parts of the syllabus. This, along with the ‘number’ content area, now make up half of the examinable material for the foundation tier papers.
There are three Assessment Objectives:
AO1- Applying standard techniques (this makes up 50% of the foundation tier marks and 40% of higher tier);
AO2- Reasoning, interpreting and communicating (this incorporates the old ‘Quality of Written Communication’ marks that used to be awarded; 25% of foundation tier marks will be assessed in this way, 30% of higher tier);
AO3- Solving non-routine problems (25% of foundation tier marks will be assessed in this way, 30% of higher tier; there is more focus on this method of assessment across both tiers than there has been previously).
Make sure you read the specification before you start tutoring. AQA have summarised the changes to the GCSE here, and Luke Graham (@bettermaths) has broken down the changes here. Some topics, such as calculating pressure in numerical and algebraic contexts, have been added to both foundation and higher tiers; some topics, such as calculating exactly with multiples of π, which were previously higher tier only, have been added to foundation tier; some topics, such as finding approximate numerical solutions to equations using iteration, have been added to higher tier only.
Edexcel have published their new specification and a particularly helpful ‘what’s new’ document here.
There is a new content area which affects all exam boards, called ‘ratio, proportion and rates of change’. Many of the specification points in this area are not new, but they used to be covered in other parts of the syllabus. This, along with the ‘number’ content area, now make up half of the examinable material for the foundation tier papers.
There are three Assessment Objectives:
AO1- Applying standard techniques (this makes up 50% of the foundation tier marks and 40% of higher tier);
AO2- Reasoning, interpreting and communicating (this incorporates the old ‘Quality of Written Communication’ marks that used to be awarded; 25% of foundation tier marks will be assessed in this way, 30% of higher tier);
AO3- Solving non-routine problems (25% of foundation tier marks will be assessed in this way, 30% of higher tier; there is more focus on this method of assessment across both tiers than there has been previously).
Make sure you read the specification before you start tutoring. Some topics, such as knowing the exact values of sinθ and cosθ for θ=0°, 30°, 45°, 60° and 90°, have been added to both foundation and higher tiers; some topics, such as standard form, which were previously higher tier only, have been added to foundation tier; some topics, such as inverse and composite functions, have been added to higher tier only.
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james@mytutor.co.uk