First Principles.

1. GCSE English and Maths Revision Day. Part 2, MathsHarrow College, 27/4/16johnbald@talktalk.netjohnbald.typepad.com

2. First Principles. Personal organisation – be systematic about time, topics, note-making and review. Time before breakfast counts double. http://www.theguardian.com/teacher-network/2016/apr/19/students-revise-exams-revision-science Know your own strengths and weaknesses. If you can, find a study-buddy. Don’t go past a word you don’t understand.

3. Two key questions: • What is it about this aspect of maths that is making it difficult to understand? • How can we adjust our thinking so that we can handle it?

4. Three recurring difficulties... • Maths begins with common (shared) knowledge – eg counting – but then concentrates it – eg, multiplication tables. To do so, it sometimes creates new words. • As it becomes more removed from everyday life, some ideas take on new meaning. Eg, multiplying by a fraction makes something smaller, dividing it makes it bigger. • Questions in maths often use an imaginary situation, with numbers and words. We need to read the words very carefully in order to find the right mathematical procedure to use.

5. Three specific difficulties... • Students often complete homework conscientiously, but find it difficult to remember what they have learned. • Students do not find it easy to make the best use of online resources, such as My Maths. • Students for whom English is an additional language have particular problems with vocabulary and the wording of questions.

6. Brain cells and connections(from The Learning Brain, Blakemore and Frith, 2005) As we learn, brain cells form connections with each other that build into networks. These connections are strengthened with practice.

7. Brain cell(from Neuroscience and Education, Teaching and Learning Research Project, 2007)

8. Eric Kandel In Search of Memory: the Emergence of a New Science of Mind (NY, 2006). (www.bookfinder.org)

9. How does this affect maths? • Once we understand that we are building and reinforcing neural networks, we can take control of the process. • The way to do this is to make sure that each element is completely clear in our mind – and then practise.

10. My Maths – a route to clarity. • Breaks down each concept into its most basic components, then rebuilds it. • Cartoon-style illustrations – eg dividing a pizza – provide a bridge between the maths and the real world. • Goes slowly at first, and speeds up (Beat the Clock) once the idea has been fully understood.

11. Some ideas on using My Maths • Note down key points in your own words on 8x5 cards, which have room for examples. • Revisit a new topic the day after you’ve studied it. Sleep consolidates learning. • Use and revisit Beat the Clock. • Work with a buddy if possible. • Check past papers for similar questions. • Go back to earlier sections (eg, tables!) if you’re not sure of them.

12. Maths words 1. Vocabulary. • Maths uses words that make sense in its own context. We need to understand them in our own words. • Some words have changed their meaning – common means shared in maths, but in real life usually means “ordinary”. • Some difficult Latin and Greek words have simple meanings. Isosceles - equal legs. • Don’t go past a word you don’t understand.

13. Maths words 1. Vocabulary. • Maths uses words that make sense in its own context. We need to understand them in our own words. • Some words have changed their meaning – common means shared in maths, but in real life usually means “ordinary”. • Some difficult Latin and Greek words have simple meanings. Isosceles - equal legs. • Don’t go past a word you don’t understand.

14. Maths words 2. Questions. • Some foundation questions only require you to know the vocabulary. • Most questions contain a series of steps. You need to extract the steps from the words, then carry them out, and finally answer the question – this means going back to the words.

15. Maths words 2. Questions. • Some foundation questions only require you to know the vocabulary. • Most questions contain a series of steps. You need to extract the steps from the words, then carry them out, and finally answer the question – this means going back to the words.

16. Three Maths Questions • Kerry uses sticky tape to fasten parcels. She uses 15 cm of sticky tape to fasten each parcel. Kerry needs to fasten 25 parcels. She has 300 cm of sticky tape. Does Kerry have enough sticky tape to fasten all the parcels? You must show your working. • Penelope is going to cook a chicken. She uses this rule to find the cooking time. cooking time = 20 minutes for each 0.5 kg + 10 minutes The chicken has a weight of 2 kg. Penelope wants to finish cooking the chicken at 12 30 pm. What time should Penelope start cooking the chicken? • Kevin wants to get the ferry to Ireland. A ferry crossing costs £125 on Saturdays £109 on Mondays Kevin has a voucher for 15% off the cost of a ferry crossing on Mondays. Kevin can go on Saturday without using the voucher or on Monday using the voucher. What is the difference in the cost of the ferry crossing if Kevin goes on Monday rather than on Saturday?

17. An Examiner’s Comments There were too many instances...where working out was set out in such a disorganised way that examiners found it impossible to identify a chosen route of solution by the candidate, in order to award method marks. Equally diagrams and graphs need to be drawn accurately. There were too many examples where candidates were not careful enough in taking readings from graphs. In too many questions candidates failed to read exactly what was being asked for, and instead provided alternative solutions that were either wrong or not required... A significant number of marks were lost by some candidates who failed to show sufficient care. (Higher Paper 1, Summer 2015) Don’t let this be you – take the time to read carefully, and do exactly what it says on the tin – or in the question!