On 27 April Michael Scoles drew our attention to the BBC webpage: http://news.bbc.co.uk/2/hi/uk_news/education/6589301.stm
Jim Clarke responded: > Do we know what percentage of Chinese students get the right answer? When I took the General Certificate of Education (GCE) "Advanced Level" (pre-university) mathematics exam in the UK in the 1950s this kind of three-dimensional geometry was part of the syllabus and problems of the order of the one given on the BBC webpage were to be expected in the exam. This remained the case through the 1960s when I first started teaching the subject. (I still have a booklet called "Advanced Level Pure Mathematics: A Revision Course" in which there are numerous problems comparable in standard to the Chinese one. It was published in 1971.) Briefly, though I recall there had been a decline earlier, mathematics standards in the UK really started to tumble after the replacement in 1986 of the GCE "Ordinary Level" (taken at age 16) by the GCSE (General Certificate of Secondary Education), which was taken by all school students (whereas previously those with less ability in mathematics didn't take "Ordinary Level" GCE, they took a different exam more appropriate to their abilities). Incidentally, three dimensional problems can seem to be more difficult than they actually are if one is unused to them, and unsure how to approach them in a way which breaks the parts down to their simplest form, e.g., by extracting sections out of the main diagram and drawing them separately. For instance, unless my memory of doing such problems several decades ago has let me down, the solution to part (i) is as follows: BD is perpendicular to AC Therefore BE is perpendicular to AC Since BE is perpendicular to any other line in the plane A1AC, it follows that BD is perpendicular to A1C With regard to the question on the BBC webpage from a "test used in a 'well known and respected' English university to assess the strength of incoming science undergraduates' maths skills", I trust that all but a tiny minority of the students would have had absolutely no trouble with it. At least I hope and pray that is the case. :) Allen Esterson Former lecturer, Science Department Southwark College, London http://www.esterson.org/ --- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
