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Are you sure you've posted in the right place? Here's a link to our subject forum which should help get you more responses if you post there. Just quoting in Fox Corner so she can move the thread if needed
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A level maths is getting to know your basic toolkit, geometric proofs is not your basic toolkit.
Original post by l'etranger
A level maths is getting to know your basic toolkit, geometric proofs is not your basic toolkit.
That's not true actually. Geometry can in some ways be seen as very simple, after all back many years ago this is how people would learn mathematics, there is not much need for any other tools before you learn geometry so it is very basic (does not mean it is easy in any way necessarily).
Original post by B_9710
That's not true actually. Geometry can in some ways be seen as very simple, after all back many years ago this is how people would learn mathematics, there is not much need for any other tools before you learn geometry so it is very basic (does not mean it is easy in any way necessarily).
I agree that it can be very fundamental, the first proofs were geometric in fact. This all said, calculus, binomial expansion, the quadratic formula and a solid foundation of algebra as the bread and butter of mathematics.
Original post by l'etranger
I agree that it can be very fundamental, the first proofs were geometric in fact. This all said, calculus, binomial expansion, the quadratic formula and a solid foundation of algebra as the bread and butter of mathematics.
Yeah I guess learning algebra opens up a lot of doors for topics elsewhere in maths.
It's a well known fact that the mathematics O Level from the 1950s and 60s was much more difficult and challenging than the GCSE is. What hasn't been given the attention that it really deserves by education analysts and curriculum reformers was the large quantity of Euclidean geometry found in the O Level course from the 1950s and 60s. Look at exam papers from the era and note how many questions involve Euclidean geometry in one way or another then compare them with GCSE papers from recent years. It's not clear why the O Level course from the 1950s and 60s placed so much emphasis on Euclidean geometry. Was it a course influenced by the mathematics topics taught to students in posh public schools during the early 20th century with a syllabus designed to be familiar to teachers and students at these type of schools rather than one to meet the needs and requirements of society and industry in a post war era? At the same time the O Level course did not include statistics and probability. These topics were only included in the late 1970s.
The mathematics A Level from the 1950s and 60s contrasted very sharply with the O Level from the same time in that it contained virtually no real geometry. Like the modern A Level course, the pure syllabus consisted almost entirely of algebra, calculus, and trigonometry. There was not even an optional paper covering Euclidean, Riemannian, or 3D geometry like there was for statistics and mechanics.
Therefore geometry comprised a large fraction of the secondary school level mathematics syllabus in the 1950s and 60s – possibly at the expense of more useful topics for students who have no desire to study mathematics beyond O Level – but as a topic it effectively dead ended as it did not feature in the A Level course and would only again be studied at university level. Ideally, it would have been more sensible to have moved the more advanced topics in Euclidean geometry – like tricky proofs – from the O Level course to the A Level course then replaced them with potentially more useful topics – like statistics and probability.
In the transition from the mathematics O Level course from the 1950s and 60s to the modern day GCSE, geometry has been 'axed' more than any other topic has. It is debatable whether this was a good move or not but very few people appear to have mentioned whether geometry should be included in the A Level course.
The mathematics A Level from the 1950s and 60s contrasted very sharply with the O Level from the same time in that it contained virtually no real geometry. Like the modern A Level course, the pure syllabus consisted almost entirely of algebra, calculus, and trigonometry. There was not even an optional paper covering Euclidean, Riemannian, or 3D geometry like there was for statistics and mechanics.
Therefore geometry comprised a large fraction of the secondary school level mathematics syllabus in the 1950s and 60s – possibly at the expense of more useful topics for students who have no desire to study mathematics beyond O Level – but as a topic it effectively dead ended as it did not feature in the A Level course and would only again be studied at university level. Ideally, it would have been more sensible to have moved the more advanced topics in Euclidean geometry – like tricky proofs – from the O Level course to the A Level course then replaced them with potentially more useful topics – like statistics and probability.
In the transition from the mathematics O Level course from the 1950s and 60s to the modern day GCSE, geometry has been 'axed' more than any other topic has. It is debatable whether this was a good move or not but very few people appear to have mentioned whether geometry should be included in the A Level course.
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