tag:blogger.com,1999:blog-2036014053389751696.comments2022-05-16T08:19:23.211+01:00Colin Foster's Mathematics Education BlogColin Fosterhttp://www.blogger.com/profile/12463017049484632672noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-2036014053389751696.post-88601069618995592992022-05-16T08:19:23.211+01:002022-05-16T08:19:23.211+01:00(Please note that the comment above was from Mike ...(Please note that the comment above was from Mike Ollerton - for some reason the system labelled it 'Anonymous'.)Colin Fosterhttps://www.blogger.com/profile/12463017049484632672noreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-10375249180133918812022-05-15T16:43:39.808+01:002022-05-15T16:43:39.808+01:00There are many interesting ideas here, none of whi...There are many interesting ideas here, none of which I would disagree with. This sounds like something of a double negative, however, I want to suggest other tasks, as positive additions to these you have suggested within an interconnected framework. I suggest multiplication and division need connecting just as multiples, divisors and factors need connecting. I thing x2, x4 and x8 need connecting, as does halves, quarters and eighths need connecting. I 100% agree squaring and square numbers are very important constructs and coming to recognise how square number have odd amounts of factors. How times tables and sequences are connected and how even numbers are connected to odd numbers. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-22542467403155923872022-05-12T12:25:19.020+01:002022-05-12T12:25:19.020+01:00I think there are some arguments for going up to 1...I think there are some arguments for going up to 12, to do with 12 having lots of factors, so there's some structure you see beyond 10 which you wouldn't otherwise. There's also an argument for going past 10 just so that people don't see 10 as a hard stop (like going past 1 when working with fractions). And also for telling the time it's quite important to know 12 x 5 = 60. But I agree the need is less than it was.<br /><br />(Sorry about the 'invalid URL' - I'll look into that!)Colin Fosterhttps://www.blogger.com/profile/12463017049484632672noreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-23418290978632722912022-05-12T12:13:20.158+01:002022-05-12T12:13:20.158+01:00Why 11 and 12? Don't we need to go only to 10?...Why 11 and 12? Don't we need to go only to 10? 11 and 12 come from the old days when there were 12 pennies in a shilling, etc, surely.<br /><br />WR (it wouldn't let me set up a Name/URL: it said 'invalid URL', which is not true.)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-40535279306919683962022-05-11T08:56:43.761+01:002022-05-11T08:56:43.761+01:00We talk to our primary student teachers alot about...We talk to our primary student teachers alot about bringing context, language and representations together to help expose structure. 'Interference' contexts crop up in their planning quite often in a bid to make the learning 'engaging for children'. This post will definitely stimulate a lot of discussion.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-32189248729288797162022-05-02T17:32:22.349+01:002022-05-02T17:32:22.349+01:00Thanks for this blog Colin - good fodder for our d...Thanks for this blog Colin - good fodder for our department meeting!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-66318082531215574402022-04-27T14:21:05.199+01:002022-04-27T14:21:05.199+01:00Thanks very much. Yes, I guess so, although, with ...Thanks very much. Yes, I guess so, although, with 48 + 7, I think I'd eventually want to get to 'knowing' the '8+7' bit, or mentally partitioning the 7 into 2 and 5, rather than going '49, 50, 51, ...'.Colin Fosterhttps://www.blogger.com/profile/12463017049484632672noreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-18290834767453996032022-04-27T14:14:02.676+01:002022-04-27T14:14:02.676+01:00I'm thinking about "fading" by discu...I'm thinking about "fading" by discussing the relative efficiency of the new method. In the example of "counting on", if you use larger numbers it is easy to see that a tens and ones approach will be quicker and more accurate, but having that conversation is the important bit. 48 + 37 is more efficient using tens and ones but counting on probably works better for 48 + 7. <br />Thanks Colin, I'm going to enjoy these. Suenoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-8323781805829130472022-04-19T13:23:50.709+01:002022-04-19T13:23:50.709+01:00This article got me thinking about the ‘procept’ -...This article got me thinking about the ‘procept’ - an amalgam of three components: a "process" which produces a mathematical "object" and a "symbol" which is used to represent either process or object. <br />As well as the fact that more able mathematicians often do qualitatively different mathematics from the less ableAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-89475734368090122572022-04-17T08:15:14.841+01:002022-04-17T08:15:14.841+01:00Thank you, as a relatively new Year 4 teacher l fo...Thank you, as a relatively new Year 4 teacher l found this article really useful.Mike Walkerhttps://www.blogger.com/profile/11188519232895043139noreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-75361025924360046042022-04-14T09:27:36.306+01:002022-04-14T09:27:36.306+01:00These reflections apply to advanced mathematics to...These reflections apply to advanced mathematics too. If the ABC Conjecture is true then the proof of Fermat's Last Theorem condenses to a page or so. Anonymoushttps://www.blogger.com/profile/00414541795067932225noreply@blogger.com