tag:blogger.com,1999:blog-7033336220707251714.comments2016-12-13T15:43:43.732+08:00Truly Singaporean Singapore Mathematicslefouquehttp://www.blogger.com/profile/12528621898369349519noreply@blogger.comBlogger27125tag:blogger.com,1999:blog-7033336220707251714.post-88649632819133454982016-12-13T15:43:43.732+08:002016-12-13T15:43:43.732+08:003 x 4.50 is actually 13.50. Great simultaneous-equ...3 x 4.50 is actually 13.50. Great simultaneous-equations riddle.Pilpula Chariftahttps://www.blogger.com/profile/18206257725746191216noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-48624818107947343452016-02-22T14:25:26.562+08:002016-02-22T14:25:26.562+08:00Some very recent research to back-up my point
http...Some very recent research to back-up my point<br />http://www.tandfonline.com/doi/abs/10.1080/10508406.2014.928214?src=recsyslefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-70288718996855399582016-02-09T14:28:45.352+08:002016-02-09T14:28:45.352+08:00In Singapore primary schools, modelling is often u...In Singapore primary schools, modelling is often used, although algebra is also acceptable.lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-8134937350664073352016-02-09T13:59:54.355+08:002016-02-09T13:59:54.355+08:00emma has x no of stickers francis has x no of stic...emma has x no of stickers francis has x no of stickers. emma bought 2*x amount and now have a total of 3*x stickers. francis gave 8 away and have now x-8 stickers. connection is 3x=4(x-8) solve it and you have x=32Unknownhttps://www.blogger.com/profile/09494977366280255065noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-4908160520642668682016-01-30T21:48:11.303+08:002016-01-30T21:48:11.303+08:00Glad you like it. Many of my articles in this blo...Glad you like it. Many of my articles in this blog illustrate the use of heuristics at varous levels, and there are some Olympiad ones too. Type "Olym" in the search box and you should be able to find them.lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-68940316360716371322016-01-30T06:35:01.831+08:002016-01-30T06:35:01.831+08:00This is a very nice list, updating the famous comp...This is a very nice list, updating the famous compilation by George Polya in HOW TO SOLVE IT.<br /><br />In my own experience, it's not so easy to teach a heuristic, as opposed to teaching a specific procedure. My students -- even the very able ones -- have gotten so used to being taught 'facts' and 'procedures' that they are suspicious when I introduce heuristics as something to be learned, perhaps because the exams they take have only questions which can be solved by selecting the right procedures. <br /><br />I mentor/tutor a group of students who are preparing for Olympiad (first level)-style questions, and I assure them that there they will encounter questions which cannot be answered by simply applying a procedure that they have already learned.Doug1943https://www.blogger.com/profile/03833632801624062004noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-28646656413078047812016-01-22T14:59:40.918+08:002016-01-22T14:59:40.918+08:00I fully agree with you. Thats why i refuse to answ...I fully agree with you. Thats why i refuse to answer some questions posted on that Sec and JC Maths F B group.khotl73https://www.blogger.com/profile/05692432997087864184noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-44034736056519921222015-12-01T21:27:12.997+08:002015-12-01T21:27:12.997+08:00Actually, instead of memorising this as a procedur...Actually, instead of memorising this as a procedure to be followed, it would be good if students can figure out the procedure on their own. That is another level of thinking and learning. Can you think of a common mathematical difficulty, and figure out yourself a procedure for solving it in your own words?lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-17665091691430678502015-06-28T10:59:06.802+08:002015-06-28T10:59:06.802+08:00Mathematically, the trick works in general. I jus...Mathematically, the trick works in general. I just used a simple example to illustrate the trick. in Singapore tests questions, pupils don't just get two fractions to compare, they may get a mix of five or six decimals, fractions, mixed numbers and recurring decimals to sort in ascending or descending order.<br />lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-58366236566257922232015-06-28T09:46:00.184+08:002015-06-28T09:46:00.184+08:00A trick that works in part because test-writers ar...A trick that works in part because test-writers are lazy:<br /><br />It's extremely common to ask students to compare fractions of the form (m-1)/m and (n-1)/n (like this one, where m=5 and n=4) and for such problems, the greater of m or n goes with the greater of the two fractions, because they are less than 1 by 1/m and 1/n respectively, and the one that is "less by less" must be greater.<br /><br />It's such a quick formula for producing a question with a known result that I've also seen many testwriters writing comparisons for larger (2 digit, usually greater than 20) denominators use a common integer as the subtrahend, and do the same thing to produce an apparently difficult problem that you can solve instantly if you know the trick: e.g. set common subtrahend to 4, m to 68 and n to 69, and ask students to compare 64/68 and 65/69. (for extra evil, reduce the first fraction, so that the final question is 16/17 versus 65/69, but most testwriters have to produce so many problems in such a short time that they don't hide things that well).<br /><br />John Barneshttps://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-11530554318232337452015-06-09T20:11:42.044+08:002015-06-09T20:11:42.044+08:00I just used Microsoft Excel. I think nowadays you...I just used Microsoft Excel. I think nowadays you can use Google Sheet for online collaboration for this type of thing.<br />lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-30442022066854493032015-06-09T14:38:41.115+08:002015-06-09T14:38:41.115+08:00what is the diagram software you have used to crea...what is the diagram software you have used to create this bar chart? It is <a href="http://creately.com" rel="nofollow">creately</a> online diagramming application that supports real-time collaboration?Shalin Siriwardhanahttps://www.blogger.com/profile/11700813966165068507noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-79538528730734265522015-05-26T19:49:12.254+08:002015-05-26T19:49:12.254+08:00The tactic illustrated here can be used for all ar...The tactic illustrated here can be used for all arithmetic sequences i.e. those with equal spacing between numbers e.g. 2, 5, 8, 11, 14. the sum total formula always has the pattern 1/2 × something × something.<br /><br />actually it is not meant to be memorised at the primary school level. maths is about observing patterns. if the pupil just memorises, and relies entirely on calculator and does not learn to observe patterns, s/he will find it hard to attain a high achievement in maths, especially in later years.<br />lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-14760679060034922592012-09-29T00:38:00.264+08:002012-09-29T00:38:00.264+08:00thanks for the tip.
thanks for the tip.<br />lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-13835682997624551872012-09-29T00:36:46.417+08:002012-09-29T00:36:46.417+08:00I agree!
Unfortunately, most schools in most coun...I agree!<br /><br />Unfortunately, most schools in most countries (except possibly Finland) still test and teach according to specific skills and content. Besides Curriculum Design, viable Alternative Assessments seems to be a big issue.<br /><br />If I had my way, I'd probably give the students an "unseen" pure or applied maths problem, lock them in a room for 3 days, but provide all the reference books, Internet access and pizza ... see what they can come up with by deriving their own formulas and/or solving the problem.<br /><br />Another idea I have is to get the teacher plus one or two external referees to follow the students through their mathematics learning journey to see to what extent each student has manifested or improved upon a set of intellectual dispositions (e.g. rigour, creativity, perseverance, pattern seeking, ... etc.). acquistion of skills and content becomes just a by-product of these. is this idea too expensive to implement?<br /><br />what do you think?lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-31721144884189161702012-08-02T15:45:29.127+08:002012-08-02T15:45:29.127+08:00I would look at John Mighton's JUMP Math (non-...I would look at John Mighton's JUMP Math (non-profit out of Toronto Canada) that engages students' in conceptual and procedural mastery and importantly identity and relevance. The third party studies done on his work especially in underprivileged schools are amazing. His philosophy and methodology map very well to this framework. Especially interesting is his book "The End Of Ignorance".lsaariohttps://www.blogger.com/profile/09751550028250078420noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-39343431102506806812012-05-10T03:29:00.408+08:002012-05-10T03:29:00.408+08:00"Rule 1: Life is not fair -- get used to it!&..."Rule 1: Life is not fair -- get used to it!"<br />Bill Gates<br /><br />"Be the change you want to see in the world."<br />Mahatma Gandhilefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-16225738457497128022012-04-12T05:46:27.720+08:002012-04-12T05:46:27.720+08:00Seymour Papert has an appropriate quote, shared to...Seymour Papert has an appropriate quote, shared today on the Daily Papert, which may answer your question Laura.<br /><br />“Being a mathematician is no more definable as “knowing” a set of of mathematical facts than being a poet is definable as knowing a set of linguistic facts. Some modern math ed reformers will give this statement a too easy assent with the comment: Yes, they must understand, not merely know. But this misses the capital point that being a mathematician, again like being a poet, or a composer or an engineer, means doing, rather than knowing or understanding.” Seymour Papert, 1970<br /><br />In other words, if we want students to learn how to think like a mathematician, they have to do what a mathematician does, which is to construct ideas from existing ideas, to do mathematics. Learning skills or concepts in itself should not be the primary goal - learning ways of thinking should be.Davidhttps://www.blogger.com/profile/08098221991466148258noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-66182408715763183592012-02-22T00:43:05.224+08:002012-02-22T00:43:05.224+08:00thanks for the comment. two days ago, i was just ...thanks for the comment. two days ago, i was just tutoring a student (from a top Singapore school) whose teacher set 8 homework questions similar to <br /> sketch the graph of |x^2 - 2x - 1| for -1 < x < 4<br />i was wondering: why did the teacher set so many similar questions to torture the student. [yes, Singapore students (are made to) work very hard.]<br /><br />guess what? good news! Wolfram Alpha can do the job for the student<br />see here http://bit.ly/A9xdC5<br /><br />the bad news: when the student grows up, he/she would find it hard to get a job if Wolfram Alpha can do it. so why are educators still focusing on teaching and testing the top of the pyramid? note: i'm not saying the top of the pyramid is not important. mathematics has a long history of how knowledge is discovered and difficulties conquered, of interesting personalities (men and women mathematicians) ... and a lot of culture ... students are missing out on all these, even in Singapore. our current students need to be able to discover, research, think critically, solve problems using maths (and other disciplines) to address issues of the day e.g. energy, environment, over-population, ... etc. and of course, as part of their jobs they can use calculators and software (like Wolfram Alpha, MS Excel, ... etc.) to help them. Hopefully, computers won't be advanced enough to do human language processing and critical thinking, otherwise I fear for our human race. Nevertheless, some big companies are trying ...lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-90092609122923692152012-02-22T00:26:36.754+08:002012-02-22T00:26:36.754+08:00Oh, I probably should add that I am in the United ...Oh, I probably should add that I am in the United States. (and that last sentence above should read, "...or simply use it..."Laura Whttps://www.blogger.com/profile/17579160512689867301noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-377346557113084792012-02-22T00:23:15.655+08:002012-02-22T00:23:15.655+08:00I am interested in the very top of the pyramid. W...I am interested in the very top of the pyramid. What I see happening in the schools (I am a substitute teacher, so I am in a LOT of schools) is that teachers attempt to teach the concepts, but this isn't very successful, so, instead, they really focus simply on teaching the skills. The good students learn the skills well (and the poor students, poorly, or not at all), but they don't learn much about the concepts, because the beauty of the concepts and their relationships with other concepts is hardly touched on at all. <br /><br />On the other hand, I am not convinced that everyone needs to understand the real mathematics behind the concepts. Most people do need the some simple concepts and simple skills. Whether they need to understand the mathematics or simply used it is a question I am still debating with myself.Laura Whttps://www.blogger.com/profile/17579160512689867301noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-68256934574357302272012-02-11T04:58:48.891+08:002012-02-11T04:58:48.891+08:00i haven't had time to explain everything yet, ...i haven't had time to explain everything yet, because i write only when i have the time / energy. however, the idea is to increase awareness in society and get everybody to start thinking / talking about it. when most people in society are in the same mind, then there is a chance for political / societal change. if not, any "change" is likely to be superficial, at best.lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-46559216768637477662012-02-11T03:00:21.769+08:002012-02-11T03:00:21.769+08:00magnificent points altogether, you simply received...<b>magnificent points altogether, you simply received brand new|a new} reader. What might you recommend in regards to your post that you just made some days ago? Any certain?</b><br><a href="https://sites.google.com/a/shopfor.goodorderbuy.q69x.net/where-to-buy-dustpans-sweeping-homegarden-on-sale/save-on-casabella-56364-dustbucan" rel="nofollow">Casabella 56364 Dustbucan</a>Nicolas D.Woodmanhttps://www.blogger.com/profile/17472338927930834121noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-19447177015121460172012-02-09T17:32:17.584+08:002012-02-09T17:32:17.584+08:00No worries! Same here!No worries! Same here!Winston Hohttps://www.blogger.com/profile/16103708849399765289noreply@blogger.comtag:blogger.com,1999:blog-7033336220707251714.post-90183669150722912342012-02-03T04:32:09.628+08:002012-02-03T04:32:09.628+08:00thanks for your reflections. if this thing is rea...thanks for your reflections. if this thing is really implemented, we'd probably need to overhaul the exams / assessment system. sorry, i didn't have time to explain everything yet. i write only when i have spare time. :-)lefouquehttps://www.blogger.com/profile/12528621898369349519noreply@blogger.com