tag:blogger.com,1999:blog-7718462793516968883.post4911955191062627352..comments2024-02-19T23:16:40.042-05:00Comments on MadMath: Never-Ending AmazementDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-7718462793516968883.post-8386931430124553632012-09-17T12:06:44.024-04:002012-09-17T12:06:44.024-04:00Powerful comments.Powerful comments.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-36259865711653323622012-09-12T12:29:46.787-04:002012-09-12T12:29:46.787-04:00You basically have to teach this yourself to your ...You basically have to teach this yourself to your kids. Sorry, but public schools, and even private ones, are not going to do it. <br /><br />This is the one single thing that I wish more parents knew.Gregory Matoushttps://www.blogger.com/profile/02695669454780832427noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-81303120028349691702012-09-11T11:43:27.847-04:002012-09-11T11:43:27.847-04:00I'm deeply troubled that this stuff isn't ...I'm deeply troubled that this stuff isn't explained thoroughly, tested for, stragglers weeded out, and taken for an everyday common thing by grade 3 of elementary school. Alas, looking how my daughter is being taught "math" so far up to grade 3 of elementary school, I stopped being amazed at anything. It's a miracle I'm not drinking myself silly every time I see what they "teach" my daughter.---https://www.blogger.com/profile/02360963065007021231noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-52340570055752566202010-07-12T11:47:33.634-04:002010-07-12T11:47:33.634-04:00@Gareth: as Delta points out, shopping is all posi...@Gareth: as Delta points out, shopping is all positive numbers, who knows what crazy stuff happens when you try and bring in negative numbers. Do people worry about whether "savings" are applied as each item goes through the checkout, or all at the end? I bet some people do.<br /><br />@tialaramex: While I agree in general with your broader point, there _are_ valid reasons for asking "89 + 47". For example: assessing ability for abstract reasoning.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-56827275931013460222010-04-08T20:03:42.527-04:002010-04-08T20:03:42.527-04:00I do think a lot of my students are so messed up o...I do think a lot of my students are so messed up over negative numbers, that they just assume nothing is predictable or consistent once negatives go into the mix. It's always the first proposed counterexample to commutativity.<br /><br />I must confess that there was a stage at a very young age when I could do numerical arithmetic in school just fine, but was completely helpless at adding Monopoly money (I remembering running from the room and pestering my dad over and over). For me, it was partly having just learned about timekeeping base-60 and assuming that "real world" stuff had to then always be different from "school numbers".Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-19200524774959945532010-04-04T10:13:10.846-04:002010-04-04T10:13:10.846-04:00Gareth, they probably imagine that any commutativi...Gareth, they probably imagine that any commutativity problem would apply to "special" cases, and their shopping isn't special. Notice that their failed counter-examples were special cases.<br /><br />The reason why a lot of early testing was changed to ask questions about real stuff was that the same question asked in this way got better answers from low-achievers. They thought they couldn't do addition, but actually they could, they just didn't know it. The high-achievers breeze past the fluff, so it's Win-win unless your objective is to make students fail tests.<br /><br />89 + 47 looks like hard arithmetic, which the weak student falsely believes they can't do. But 89 cents in one pocket and 47 cents in the other, how much do you have? - is an everyday problem they know how to answer. Their approach may take a minute of silent counting when it ought (at say age 12) to be instant, but it's a lot better than "I don't know".<br /><br />We see this in other subjects too. If a confident student advances the opinion that Romeo's feelings for Juliet are no more sincere than his quickly forgotten love of Rosaline they may press on even if the rest of the class don't see this possibility (maybe they're all hopeless romantics like me). But a weaker student may give up, believing they got it wrong, when really it's not settled and you just wanted evidence that they've understood the material.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-21512694331327073952010-03-30T07:43:18.393-04:002010-03-30T07:43:18.393-04:00That's awesome. But I can't help wondering...That's awesome. But I can't help wondering ... if you really weren't sure whether addition were commutative, wouldn't you be really anxious every time you went shopping? You'd be thinking, could it make a difference to how much I'm going to pay if I put the bread through the till first, or the milk?Gareth Reeshttps://www.blogger.com/profile/15405124248006286547noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-68723007311503878952010-03-29T22:18:22.205-04:002010-03-29T22:18:22.205-04:00As a tutor of mostly High School students, I often...As a tutor of mostly High School students, I often find that revisiting concepts introduced many years before is very worthwhile. Students may have passed the test back then, but they did not understand the concept in a fundamental way. <br /><br />I believe that revisiting key concepts months or years later in a conceptual (vs procedural) way, and helping students make similar/different connections (+ and * are commutative, - and / are not, etc.) is incredibly important to their confidence and interest in the subject.<br /><br />Thank you for sharing your experience!<br /><br />http://mathmaine.wordpress.comAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-4301964866255058622010-03-29T13:46:00.394-04:002010-03-29T13:46:00.394-04:00"Usually a class can read the teacher, and wi..."Usually a class can read the teacher, and will prefer to give the answer the teacher wants."<br /><br />Exactly. I wonder if something about the way you asked it made them think you were expecting a "no". I think it's good to do that sometimes -- use a tone that implies the wrong answer so that they have to think instead of just giving the answer "the teacher wants".Tylerhttps://www.blogger.com/profile/03197090819217016934noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-49874874694409969932010-03-29T13:16:59.098-04:002010-03-29T13:16:59.098-04:00I am impressed that they were honest enough to kee...I am impressed that they were honest enough to keep saying 'no'. Usually a class can read the teacher, and will prefer to give the answer the teacher wants. (Great article on clever Hans, <a href="http://researchinpractice.wordpress.com/2009/10/24/required-reading-for-math-teachers-i/" rel="nofollow">here</a>.)<br /><br />It sounds to me like you've helped them to feel really safe. I'm so glad I read this, because I do fly past commutative and associative properties, assuming students will know those cold.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com