tag:blogger.com,1999:blog-7691251033406320222.post7917715846930886675..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: The times table and the number lineCatherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-7691251033406320222.post-84545946924783567272012-02-17T05:50:26.688-08:002012-02-17T05:50:26.688-08:00And then hang the poster above your computer!And then hang the poster above your computer!FedUpMomhttps://www.blogger.com/profile/00951858601020687242noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-28495149468617854742012-02-17T05:28:52.280-08:002012-02-17T05:28:52.280-08:00Catherine, your assignment is to write "gist&...Catherine, your assignment is to write "gist" 100 times in different colored markers on a large poster.FedUpMomhttps://www.blogger.com/profile/00951858601020687242noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-11181163336162142832012-02-16T21:17:57.523-08:002012-02-16T21:17:57.523-08:00Huh -- I realize this is a very old post. (I was s...Huh -- I realize this is a very old post. (I was specifically looking for it to pass along to a friend) -- but this time when I read it, it was immediately obvious to me why you made the 6x7=43 error -- you were conflating the 6x7 fact with 6+7. I don't know why I didn't see that the first time through.TerriWhttps://www.blogger.com/profile/18200629750466604443noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-17450884859290105232011-08-27T12:07:34.108-07:002011-08-27T12:07:34.108-07:00I have a BS in math and a PhD in computer science,...<i>I have a BS in math and a PhD in computer science, and I still don't know all of my multiplication factoids.</i><br /><br />OK, Bonnie proves the point!<br /><br />Our brains aren't built to memorize the math facts. You can do it (and I'm in favor of kids doing it), but human (and animal) memory is built to remember jist, not precise detail.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-10667864582918145162011-08-27T12:05:23.539-07:002011-08-27T12:05:23.539-07:00In regards to Catherine's mistake of 6x7=43, i...<i>In regards to Catherine's mistake of 6x7=43, if one of my kids gave that answer, I'd ask if it made sense for a multiple of an even number to be odd.</i><br /><br />Yes, and let me tell you I was darned embarrassed when I realized I'd spent my entire adult life without realizing that.<br /><br />I wish to heck our schools would just go ahead and adopt Singapore Math universally. I was reading the study about elementary school teachers being math-phobic -- well, how likely is it that a math-phobic grade school teacher is going to alert her students to the fact that multiples of even numbers are always even?Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-35171368963752766612011-08-27T12:02:12.534-07:002011-08-27T12:02:12.534-07:00'Come,
come, gentlemen, it can't be both,&...<i>'Come,<br />come, gentlemen, it can't be both,' Kummer exclaimed. 'It must be one or the other.</i><br /><br />Oh, I love that!!Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-26216797054904429222011-08-27T11:14:02.331-07:002011-08-27T11:14:02.331-07:00I met a classmate of my son's who had the enti...I met a classmate of my son's who had the entire multiplication table memorized at age 6, in first grade. He was happy to whip them all off. He had an older sibling that was using recitation to memorize and had overhead her enough to get it down. Fantatic auditory memory. This enabled the lad to play many games on the school server that didn't require actually understanding what multiplication was. <br /><br />In later years, he had trouble. Because he memorized before he understood, it was difficult to discipline himself to think through the why explanations and internalize the associative, commutative, and distributive properties in third and forth grade, rather than jump to the 'answer'. He did not make it 8th grade algebra.lgmnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-75198158162698156702011-08-22T05:49:50.235-07:002011-08-22T05:49:50.235-07:00I have a BS in math and a PhD in computer science,...I have a BS in math and a PhD in computer science, and I still don't know all of my multiplication factoids. I think it is far more important to be able to visualize multiplication, so you know when to use it to solve a problem. I know way too many college students who don't have a firm grasp of the concept of multiplication, though I suspect they could spout their times table factoids with ease.<br /><br />Back when kids had to tie shoes because there were no other options, they did learn, and much earlier than today. I cannot remember a single kid in my first grade class who could not tie his or her shoes.Bonniehttps://www.blogger.com/profile/08364766877630085946noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-44086702333310840012011-08-21T14:46:25.132-07:002011-08-21T14:46:25.132-07:00In regards to Catherine's mistake of 6x7=43, i...In regards to Catherine's mistake of 6x7=43, if one of my kids gave that answer, I'd ask if it made sense for a multiple of an even number to be odd. <br /><br />Sometimes it feels like my primary task in homeschooling math is to get my kids to actually double-check their answers to see if they make sense. Here's an example from last week.<br /><br /><i>"Mrs. Ward bought 840 eggs. She sold them in trays of 12 eggs each. How much money did she receive if the selling price per tray was $3?"</i><br /><br />My DD divided 84 not 840 by 12 and wound up with an answer that was off by a factor of ten. If she'd stopped to think for a moment, she'd have realized that the answer should be somewhere in the ballpark of $240 (800/10 * 3).Crimson Wifehttps://www.blogger.com/profile/03254830856234479999noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-18778993183110794042011-08-21T12:31:12.051-07:002011-08-21T12:31:12.051-07:00Oh, and what's the explanation for why childre...<i>Oh, and what's the explanation for why children are so poor at approximation or understanding of quantities?</i><br /><br />My thought exactly, especially having in mind my recent student (8 years old, normal intelligence) who could not identify simple quantities without counting each time? For example, if shown a picture of 1 thing, a picture of 4 things and a picture of 30 things (all the same item), he could not tell you which was the picture of 4 without manually counting. He could not even look at the picture of 1 and stay, that's not 4. He had to count the 1 to arrive at that conclusion. <br /><br />If "all children are born with a quantity representation which provides the core meaning of numerical quantity", what can be the explanation?palisadeskhttps://www.blogger.com/profile/13700503881038569921noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-12992014065436974622011-08-21T10:35:44.935-07:002011-08-21T10:35:44.935-07:00And for those people for whom it was easy to memor...And for those people for whom it was easy to memorize the times tables, what's the explanation then?<br /><br />Oh, and what's the explanation for why children are so poor at approximation or understanding of quantities?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-81839388072667325622011-08-21T08:33:50.294-07:002011-08-21T08:33:50.294-07:00@SteveH
My son couldn't tie shoes either; he j...@SteveH<br />My son couldn't tie shoes either; he just made a big knot and slipped them on and off. When he was around six or seven, though, we explained to him the topology of square knots, and why the ends of the laces were doubled back for the second part of the knot.<br />Then he could do it, but decided it was too much trouble (and now, nearly 40, wears sandals with Velcro most of the year).<br />--Linda SeebachLinda Seebachhttps://www.blogger.com/profile/06426741820143208210noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-48888614931265317222011-08-21T06:15:15.852-07:002011-08-21T06:15:15.852-07:00My hypothesis is that shoe tying qualifies as a bi...My hypothesis is that shoe tying qualifies as a biologically determined category of<br />knowledge. My son always tied his shoes once when we bought them, and never tied them again. We struggled to get him to untie his shoes before taking them off, but it was hopeless. We complained that he was ruining his shoes, but he always outgrew them before real damage showed up. When he did tie his shoes, it always took him longer than 7 seconds per shoe. He can play the piano and he can do Jacob Ladder in 3 seconds, so that must imply that there is something genetic about shoe tying.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-47127872719242760452011-08-20T16:50:41.138-07:002011-08-20T16:50:41.138-07:00And the classic Ernst Kummer story:
"Ernst E...And the classic Ernst Kummer story:<br /><br />"Ernst Eduard Kummer (1810-1893), a German algebraist, was rather poor at arithmetic. Whenever he had occasion to do simple arithmetic in class, he would get his students to help him. Once he had to find 7 x 9. 'Seven times nine,' he began, 'Seven times nine is er -- ah --- ah -- seven times nine is. . . .' 'Sixty-one,' a student suggested. Kummer wrote 61 on the board. 'Sir,' said another student, 'it should be sixty-nine.' 'Come,<br />come, gentlemen, it can't be both,' Kummer exclaimed. 'It must be one or the other.<br /><br /><br />http://jcdverha.home.xs4all.nl/scijokes/10.html#Kummer_1<br /><br />-Mark RouloAnonymousnoreply@blogger.com