tag:blogger.com,1999:blog-21077063.post7494370541024150333..comments2021-10-09T10:50:55.207+00:00Comments on Donald Clark Plan B: 7 reasons why kids right to have gone apeshit over this GCSE maths questionDonald Clarkhttp://www.blogger.com/profile/00796341486328270474noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-21077063.post-15986514329164951362015-06-13T10:01:53.670+00:002015-06-13T10:01:53.670+00:00The examination question about Hanna's sweets ...The examination question about Hanna's sweets is nonsense. The probability of any of the sweets being orange is 6/n. That applies to all of them, including the first one taken out and the second and any subsequent ones. The probability of the first and second one both being orange is 36/(n x n) and that can never be 1/3 since n is an integer.<br />When the first sweet is removed you don't have to recalculate the probability of those remaining being orange, that probability remains unchanged at 6/n for each of them.<br />If you do want to recalculate after the first one is removed, then the number remaining is n-1, and the number of orange sweets remaining is (6-6/n) and so the probability of the second one being orange is(6-6/n)/(n-1) which simplifies to 6/n.<br /><br />The quadratic equation is also nonsense since it is directly related to the false 1/3.Belindahttps://www.blogger.com/profile/12695138379813942846noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-72642268348304469212015-06-08T10:01:23.413+00:002015-06-08T10:01:23.413+00:00"If 16 year old maths students find this too ..."If 16 year old maths students find this too difficult then where are our future mathematicians, engineers and scientists going to come from?" Sorry Jihn - didn't mean to be offensive." I think it's fine and natural that the majority of 16 year olds find this difficult. I just dont agree tat the GCSE, and algebra, is the solution to the 'maths in the workplace' problem. I've been involved with this issue for many years. We have low numeracy in the workplace, on that we can agree, but this has little to do with algebra. The problem we have is not more students into HE but a decimated vocational system, where functional maths is the the real need.Donald Clarkhttps://www.blogger.com/profile/00796341486328270474noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-8944167080175648392015-06-08T08:08:17.167+00:002015-06-08T08:08:17.167+00:00I do not agree with your reply to my earlier post ...I do not agree with your reply to my earlier post (post 2). I really find it quite offensive, and it is based on a misreading of what I wrote.<br /><br />> Let's bring some maths to that non sequitur. The fact that many found it <br />> difficult does not mean that we'll be short of mathmaticians etc. The <br />> expectation that ALL 16 year olds should know how to solve this problem <br />> is quite simply wrong.<br /><br />I did not say that "ALL 16 year olds should know how to solve this problem",<br />I said that the better ones should be able to do so. For one thing I believe there are two tiers of maths GCSE and this question was on the higher tier.<br /><br />With regards to the twitter storm, I would suggest that the placing of the question three quarters of the way through the paper means that anyone who got this far, and answered most of the previous questions correctly, would have already achieved grades B or C. Weaker students are obviously going to find the latter part of the exam more difficult, but I don't think they would all take to the internet to complain. I therefore feel that complaints are mainly made by those who were on target for an A/A*, but were thrown by a question not following the format of previous exams. <br /><br />I know you shouldn't read too much into individual comments, but can I draw your attention to these two from the Guardian.<br /><br />> Sorry, you lost me at 6/n x 5/n–1.<br />> Its moments like this when I wonder how I got an A in GCSE Maths.<br /><br />That is quite disturbing.<br /><br />> Right. I was in that exam, and that part of the question was no more than <br />> 3 marks. It wasn't a hard question, and it wasn't worth many marks, so this <br />> outrage that seems to have occured is just ridiculous. Surely we should be <br />> talking about the questions which were worth 5 marks and were indredibly <br />> difficult. Take, say, the question about a seed hopper. That was difficult <br />> and took a lot of time to complete. It was worth a lot of marks.<br /><br />Perhaps I shouldn't have mentioned the future mathematical needs of the UK. I think I must have been channelling my inner Gove. Nevertheless, with regards to future supply of STEM undergraduates I refer you to ACME report "Mathematical Needs - Mathematics in the workplace and in Higher Education" from June 2011, which states (page 15)<br /><br />[continued in next post due to word count limitation]JohnGhttps://www.blogger.com/profile/05438907780151254566noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-52594487917913652382015-06-07T22:31:43.418+00:002015-06-07T22:31:43.418+00:00Having used lots of past papers I do get a sense t...Having used lots of past papers I do get a sense that the examiners are detached and don;t understand context (hence the 'sweets' questions). They are also weak in terms of relevance and the structure of test items, as well as instructions. Remember that these exam boards do set questions that are literally impossible to answer - their quality control is awful.Donald Clarkhttps://www.blogger.com/profile/00796341486328270474noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-25039446241645184452015-06-07T22:14:03.316+00:002015-06-07T22:14:03.316+00:00Agree with mixed questions but the fact that so ma...Agree with mixed questions but the fact that so many students complained was interesting. I was trying to unpack that issue, as in my experience this doesn't suggest stupid students but faulty test items. I know that the quadratic is mentioned in b) but one possible point is that the presentation of the question threw them, along with its position in the 25 question sequence. Data from that question and paper in general will be interesting.Donald Clarkhttps://www.blogger.com/profile/00796341486328270474noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-8167651829024741702015-06-07T21:17:11.862+00:002015-06-07T21:17:11.862+00:00This is an A*/A grade question definitely. But I ...This is an A*/A grade question definitely. But I don't think mixed-concept questions should be absent from a GCSE. I would really worry if better students couldn't answer this, especially as you are given the final answer as a 'show that...'. <br /><br />Also, the quadratic does have to be solved, but only in part b which you don't reproduce. I was taught to factorise the numerical figure as a starting point, and once you go 90=10x9 (which you would do first), the answer can only be one thing.<br /><br />And finally, timing questions, leaving questions and coming back to them and so on is part of exam technique.Richardnoreply@blogger.comtag:blogger.com,1999:blog-21077063.post-15028646424969338802015-06-07T20:52:13.642+00:002015-06-07T20:52:13.642+00:00Let's bring some maths to that non sequitur. T...Let's bring some maths to that non sequitur. The fact that many found it difficult does not mean that we'll be short of mathmaticians etc. The expectation that ALL 16 year olds should know how to solve this problem is quite simply wrong.Donald Clarkhttps://www.blogger.com/profile/00796341486328270474noreply@blogger.comtag:blogger.com,1999:blog-21077063.post-7052950339595140692015-06-07T20:38:11.255+00:002015-06-07T20:38:11.255+00:00> Besides, what does it matter that Hannah ate ...> Besides, what does it matter that Hannah ate them?<br /><br />Eating the sweet is a standard cue for "draw without replacement" probability problems in school maths.<br /><br />Back to the main issue...<br /><br />The problem is one which (better) GCSE candidates should be able to do. It just requires the student to connect three concepts which they already know: probability, formulating a mathematical statement from a word problem, and algebraic manipulation. <br /><br />Unfortunately due to "teaching to the test" many will not be able do this. The ability to apply known concepts in an unfamiliar situation is fundamental to problem solving (both in life and in mathematics). If 16 year old maths students find this too difficult then where are our future mathematicians, engineers and scientists going to come from?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-21077063.post-23959213922986876942015-06-07T14:06:13.772+00:002015-06-07T14:06:13.772+00:00Besides, what does it matter that Hannah ate them?...Besides, what does it matter that Hannah <i>ate</i> them?<br /><br />b@BobKLitehttps://www.blogger.com/profile/00473186996974209639noreply@blogger.com