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Hi, I am fascinated by the way the teaching of mathematics has evolved over the years, and would like to make use of past teaching and examining materials to attempt to recreate a structured syllabus which turns back the clock on the progressive "dumbing down" that we have been, and continue to be, subjected to in recent years. For example, I recall thinking, back in 1986-88 when I was revising for my A levels, how simple the questions in the exams that I took then had become compared with questions that had appeared in past papers (I used to have books of past papers going back to around 1968, and during my revision I think I must have attempted pretty much every question on the further maths papers - I wish now that I had kept both the question papers and my solutions). It was also clear that, despite the actual syllabus not having changed a great deal over the period, the questions themselves had become much easier over time. The pre-1970 questions were relatively challenging from a problem-solving perspective and expected/required significant stamina and dexterity in algebraic manipulation, whereas the 1980s questions tended to be much shorter and straightforward and generally required less forethought to solve. To give you an idea of the difference, the average time it would take me to solve a 1980s question was around 3-4 minutes as compared with around 20-25 minutes per question on the pre-1970s papers. I also recall that the syllabus was chopped considerably the year after I took my A levels. (This was also true of the O level syllabus, which was subsequently merged with CSEs to be replaced by GCSEs). The general decline seems to have continued ever since then. I now teach A level mathematics on a voluntary basis on weekends, and I have to say that I am rather dismayed by the types of questions asked in today's exam papers, where almost no problem-solving ability is required and the questions are so "dumbed-down" that students need only directly apply a standard set of basic techniques which they will have memorised in advance. There is very little to distinguish the extremely bright from the merely competent, but more importantly, students are no longer being taught 'mathematics' as I understand it, but rather, how to pass a specific mathematics exam where the questions to be asked are so straightforward as to be effectively known in advance. [If students find today's A levels challenging, it is because they are so much less well prepared for them than they would have been in the past, and find themselves struggling to learn much more far too late in the day]. It concerns me that my own children (I have three sons, aged 11, 10 and 6) are quite possibly going to be come out of school with top grades yet only a relatively superficial understanding of the subject matter. Coming back to the original question, I have gathered a collection of older mathematics textbooks, particularly those by C V Durell et al from the late 1920s onwards. These were dense thoughtful texts and well-planned graduated examples and numerous exercises and drills that were designed not only to ensure that the basics were clearly understood, but also to challenge the very brightest. I do not think that it would be an exaggeration to say that the standard of today's A levels seem to be roughly comparable to the basic knowledge an average 13 or 14-year old might have expected to have back in those days. I realise that obtaining a decent education was much more of a privilege in the distant past. However in making it more accessible it seems also to have been watered down considerably. I do not believe that children are fundamentally any less capable or intelligent than they were in the past. However it is clear that they are not being suffficiently pushed or challenged and end up achieving (and worse, expected to achieve) much less than they would have been back then. Not only are students less well prepared, so of course are the teachers that teach them, leading to something of a vicious circle. Not that any of us would like to admit as such, but those old enough to remember, or those bothering to look at past textbooks or exam papers in an objective way, will find it difficult, I would hope, to reach any other conclusion. I believe that each student should be given the opportunity to achieve his/her potential, and that this should not be a function of any particular syllabus put together by the government or an examinations board with any agenda which may not be geared to what is best for the students themselves. By examining how mathematics was taught in the past as well, it should be possible to rearrange topics in a structure which allows students to progress each according to their own ability. The better students should be comfortably able to take their A levels in further mathematics at 13 or 14 and should not be discouraged in any way from doing so. Neitehr should they be hindered in progressing beyong that if they are capable. It should be noted that facility in algebraic manipulation and elementary calculus is a prerequisite for properly understanding physics and other sciences, and I see no reason why our children should be deprived of such an understanding when they are fully capable of achieving it. I am not sure that this actually answers your question, but I hope it explains to some extent where I am coming from. Best wishes, Sabbir. P.S. Thanks for the links, though I am looking more specifically for the bound sets of papers that used to be widely available.
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