{"id":153,"date":"2007-03-29T12:47:55","date_gmt":"2007-03-29T12:47:55","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=153"},"modified":"2020-03-14T19:29:30","modified_gmt":"2020-03-14T19:29:30","slug":"dumbing-down","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=153","title":{"rendered":"Dumbing Down"},"content":{"rendered":"

There’s a fascinating post at The Unapologetic Mathematician<\/a>\u00c2\u00a0called Math and science testing in public\u00c2\u00a0schools<\/a>\u00c2\u00a0which says that, because many students are failing the current maths and science tests, Washington state is proposing that they should be replaced by easier end of\u00c2\u00a0course tests:<\/p>\n

I went to public schools in Maryland, where we had similar exams. Those students sharing my cynical bent referred to them as the \u00e2\u20ac\u0153functional idiot tests\u00e2\u20ac\u009d. I really do mean that it mostly tested respiratory function. I passed two of them by filling in pseudorandom bubbles and never actually opening the test booklet.<\/em><\/p><\/blockquote>\n

This picture of dumbing down will be familiar to British readers. This quote from the same post<\/p>\n

This is exactly what Washington state is about to do. The important thing is evidently not to teach mathematics or science to its students. It\u00e2\u20ac\u2122s to draw the target after we know where they land \u00e2\u20ac\u201d give them a test we know they can pass.<\/em><\/p><\/blockquote>\n

echoes some of the controversy over new GCSE Science exams to be taken by 16 year olds Critics attack new science GCSE<\/a>. I have never met any mathematics teacher who isn’t convinced that mathematics in the UK has been dumbed down quite considerably. The one attempt in 2000 to redress this problem ended in miserable failure and so the slide downwards has continued.<\/p>\n

But there’s another issue here. In\u00c2\u00a0Britain, over at least the last 100 years or more, there has been an attempt to democratise education in the sense that, where only elites\u00c2\u00a0stayed on at school beyond the age of 14\u00c2\u00a0in the early 20th century, there are proposals to raise the school leaving age to 18 and ensure that 50% of the population go on to higher education.\u00c2\u00a0It means that studying mathematics is compulsory at least until the age of 16.<\/p>\n

This is good but the effect has been to simplify the syllabus substantially to allow more students to succeed. Examination questions set in the early twentieth century on complicated algebraic manipulation or a\u00c2\u00a0question\u00c2\u00a0on inversion<\/a> (see <\/a>*<\/a> below) set in 1962 could not be set now. So the question that needs to be asked is<\/p>\n

Is it possible to teach mathematics to a larger range of students without compromising on the level taught?<\/em><\/p><\/blockquote>\n

Alexandre Borovik’s book Mathematics under the Microscope<\/a>\u00c2\u00a0in the section 4.6 Mental arithmetic and the method of Radzivilovsky<\/strong>\u00c2\u00a0details\u00c2\u00a0a radical approach by “a brilliant and idiosyncratic mathematics teacher, Vladimir Radzivilovsky” who<\/p>\n

systematically builds bridges between various mental presentations of order and number in his pupils\u00e2\u20ac\u2122 heads<\/em><\/p><\/blockquote>\n

and<\/p>\n

Radzivilovsky\u00e2\u20ac\u2122s success is measured by the fact that, among his former students, he can name dozens of professional mathematicians, physicists and computer scientists<\/em><\/p><\/blockquote>\n

There must be\u00c2\u00a0others who have ideas about teaching mathematics to a wide range of students\u00c2\u00a0whilst still maintaining standards.<\/p>\n

<\/a>*<\/a> Here is an inversion question taken from a University of London A level Paper III Summer 1962:<\/p>\n

Prove that the inverse of the point (\\alpha,\\beta) with respect to the circle x^2+y^2=r^2 is<\/p>\n

\\left(\\dfrac{r^2\\alpha}{\\alpha ^2 + \\beta ^2}, \\dfrac{r^2\\beta}{\\alpha ^2 + \\beta ^2}\\right)<\/p>\n

Find the equations of the inverses of the circles<\/p>\n

S_1,\\ x^2+y^2-2x=0 and S_2,\\ x^2+y^2+4x+y-4=0,<\/p>\n

with respect to the circle x^2+y^2=r^2.<\/p>\n

Deduce<\/em> that S_1 and S_2 intersect at right angles.<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"

There’s a fascinating post at The Unapologetic Mathematician\u00c2\u00a0called Math and science testing in public\u00c2\u00a0schools\u00c2\u00a0which says that, because many students are failing the current maths and science tests, Washington state is proposing that they should be replaced by easier end of\u00c2\u00a0course tests: I went to public schools in Maryland, where we had similar exams. Those students […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-153","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/153","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=153"}],"version-history":[{"count":1,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/153\/revisions"}],"predecessor-version":[{"id":292,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/153\/revisions\/292"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}