This is my first daily update thanks to a commitment to spend 1 hour per day on this project for 100 days
Part of Josie Long's 100 days challenge: http://www.hundreddays.net/
My goal here is to create a website that makes A-Level maths incredibly easy.
Immediate considerations:
How is it best to learn (and therefore teach) maths?
My opinion is that people learn best independently if they have a commitment to do well and if they have access to an expert on the complete syllabus who they have confidence in.
(I may be biased as I get a lot of my income as a private tutor)
It would be interesting to do some further research on best methods of teaching and learning.
My belief is that anybody who embarks on A-Level maths and a good attitude can at least match their GCSE grade.
This is purely anecdotal - I also believe that anyone who can answer a basic ratio question on recipes (i.e. set in a real world situation - here is a recipe for 4 cakes, how do we make 6 cakes?) has sufficient abiliity to pass a GCSE maths (A*-C) if they put in the required effort.
Out of all my many private students, I can only think of one who couldn't answer this question with reasonable prompting (he is now retaking after getting a D...)
and only one of my private students has ever failed to get a C though she could answer that question (got a D but was told by their maths teacher that they would be lucky to get an F and that there was no way they would ever get higher - one of the most satisfied customers I've ever had even though I thought she could have passed: that maths teacher should be struck off)
One problem that I consistently come across is that high school teachers in the UK are often not familiar enough with the A-Level syllabus.
Just this week I have identified
* Teacher teaching material that is not part of the course as though it is urgently important
* Teacher failing to identify consistent mistakes in working and answer (tick! tick! tick!)
* Teacher teaching incorrect material to students (teacher's own notes were wrong)
* Teacher teaching particular complicated requirements for written answers that do not gain any credit according to the exam mark scheme.
* Non-expert mathematicians teaching maths and not really able to answer intelligent questions
* Many, many teachers who fail to inspire confidence in their pupils - particularly bright, ambitious A-level students and including teachers at highly respected independent schools
I've even known cases where teachers have taught the "wrong" syllabus with entirely the wrong content and not realised - either because of an administrative error or because the syllabus had changed without the teacher's realisation.
This possible error is mitigated somewhat by a reasonable series of books covering each exam syllabus. The books are generally good and teachers following them as a guide can be sure to cover most everything - though they are lacking in some detail and particularly in links between different content areas and modules. Motivated self-studiers can potentially do well exclusively by using the books and provided exam materials, but may miss out the underlying ideas of the course and key techniques. Whether or not this provides a good bridge into post-A-level study is debatable? (There are advantages and disadvantages to learning 'by rote', 'for the exam')
With e.g. Edexcel attempting to self-publish course books (so far at least for GCSE), the quality of textbooks may take a step backwards. Their books have a sheen of authenticity but are of poor quality and not good enough for self-study.
What I want to provide is a website where students can be confident that every part of the syllabus is covered fully, in complete detail - identifying what is important, how best to answer a question, possible alternative methods, common problems to be avoided, plenty of worked examples, plenty of potential exam-style questions to try, links between content areas and referring back to previous modules.
The most important thing is to improve student confidence.
(This may be challenging at first when the website needs to build a reputation)
Potentially users can contribute by asking questions, the website is easily updatable if the syllabus changes or if alternative methods are suggested.
The idea is that students can come to be reassured that they have covered everything they need to know.
Problems
Unfortunately a website has the disadvantage (from the students' POV) that there is no immediate interaction
Can provide an on-demand tutor to help (at a cost) - online or in person?
How best to display website on the printed screen?
If the idea is to get across how best to answer an exam question, is this is best done with written examples?
Can a consistent font be used that can draw e.g. an integral sign
(LaTeX standard font is not ideal)
What about questions that require pictures e.g. circle theorems, forces diagrams
Wish to draw these in a consistent and pretty way that can easily be drawn by hand
Is a graphic designer necessary? (Hopefully not)
How do textbooks deal with this problem well/badly?
Asides:
Good name?
It seems natural to link forward to university courses - where do people use maths in their careers/lives? what uni subjects is maths A-Level necessary/useful?
Government goal to get 100,000 pupils taking maths A-level gives a decent sized market. (at the moment ~75,000 full A-level students IIRC)
Which modules to concentrate on?
- C1, C2, S1, M1
- C3, C4, S2, M2
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