tag:blogger.com,1999:blog-7691251033406320222.post9175897330117614871..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: Math Education: An Inconvenient Truth VideoCatherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger50125tag:blogger.com,1999:blog-7691251033406320222.post-68679140803036639902007-01-22T14:23:00.000-08:002007-01-22T14:23:00.000-08:00I don't know if EM teaches fraction division in 5t...I don't know if EM teaches fraction division in 5th grade. I've looked at everything through the end of the first 5th grade math journal and the most they do is fraction addition and subtraction using clock faces (again). I don't think they get to fraction division at all in 5th grade, but I'm not certain, because we haven't gotten through the year yet.<br /><br />On the other hand, SingaporeMath obsesses over fractions in 5A. If the workbook and textbook aren't sufficient, the home instructor's guide gives lots of suggestions on supplementing the student that doesn't master all operations on fractions by mid-5th grade.LynnGhttps://www.blogger.com/profile/11467061079495021347noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-25629203663513127002007-01-22T11:38:00.000-08:002007-01-22T11:38:00.000-08:00It's a good writing exercise. You are limited to 5...It's a good writing exercise. You are limited to 500 characters.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-88948942300567005452007-01-22T11:36:00.000-08:002007-01-22T11:36:00.000-08:00hmmmm....I wonder who SteveH23 might be?
Hee, Hee...hmmmm....I wonder who SteveH23 might be?<br /><br />Hee, Hee, Hee. I suppose I should do some work today.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-5302921305834140982007-01-22T11:35:00.000-08:002007-01-22T11:35:00.000-08:00I thought the same thing, Catherine. That seems to...I thought the same thing, Catherine. That seems to be our Steve....Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-8509042503135080962007-01-22T11:28:00.000-08:002007-01-22T11:28:00.000-08:00Hey, that was me, Lynn!
I was thinking that again...Hey, that was me, Lynn!<br /><br />I was thinking that again when the forgiving division came up. You could just avoid those pesky ones that you can never remember. It'll all work out.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-66503571923276345312007-01-22T11:17:00.000-08:002007-01-22T11:17:00.000-08:00hmmmm....I wonder who SteveH23 might be?
She's wr...hmmmm....I wonder who SteveH23 might be?<br /><br /><I>She's wrong. Trust me. Don't check out Saxon or Singapore Math. Don't wonder why so many Kumon centers are opening up. Nychold just doesn't understand. Trust me. It's good for little Suzie to write a story about her favorite number. Teachers are experts in math. There is no need for drill-and-kill. Your child will learn to discover everything. Trust me. If your child ends up in the remedial math track in high school, then they are just not good in math. Trust me.</I>Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-50306761835720662582007-01-22T11:14:00.000-08:002007-01-22T11:14:00.000-08:00TRAILBLAZERS doesn't teach fraction division in 5t...TRAILBLAZERS doesn't teach fraction division in 5th grade, which is the final year of the series.<br /><br />It also teaches forgiving division instead of long division. (I hear that our school is supplementing like mad, but TRAILBLAZERS itself does not teach long division.)Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-5255335665974106512007-01-22T10:03:00.000-08:002007-01-22T10:03:00.000-08:00There are a couple of points being lost when I loo...There are a couple of points being lost when I look at the fuzzy comments -- first, after 15 years of fuzzy math, there is absolutely no measure anywhere that demonstrates that it works. The U.S.,(and States and local school districts) have not shown any improvement when fuzzy math is used. How long are we supposed to wait to see results?<br /><br />Second, while I find the algorithms in TERC and EM annoying, someone on KTM once made the insightful comment that the primary effect of the alternate algorithms allows students to avoid ever learning quick recall of basic facts. While the standard algorithm for long division forces a kid to really use those basic facts, partial products and the TERC clusters do not. This would be alright if math weren't so incredibly cumulative.<br /><br />But once you decide to work with fractions, it becomes unmanageable to add, subtract, multiply and divide fractions if you don't have an extremely solid understanding of the basic facts.<br /><br />EM gets around this problem by having no secure goal for fractions in 5th grade. The hardest fraction addition problem we have had so far in 5th grade had denominators that were really "friendly." You won't know what your kid has missed in EM and TERC until you get to middle school or later.LynnGhttps://www.blogger.com/profile/11467061079495021347noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-73284961328012098962007-01-22T08:08:00.000-08:002007-01-22T08:08:00.000-08:00Looking at the video comments again, it seems as t...Looking at the video comments again, it seems as though the fuzzies have called out the troops.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-70981270380838799972007-01-22T07:56:00.000-08:002007-01-22T07:56:00.000-08:00"But it is constructivist through-and-through."
W..."But it is constructivist through-and-through."<br /><br />We shouldn't be talking about pedagogy or opinion when the problem is about basic competence. Talking about constructivism gives them way too much credence.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-91042605432200407922007-01-22T06:54:00.000-08:002007-01-22T06:54:00.000-08:00What we're experiencing, which I'm going to have t...What we're experiencing, which I'm going to have to start writing about, is a horrifically bad "traditional" course that I <I>think</I> is horrifically bad because of the constructivist ideology all of our new young teachers have absorbed in ed school.<br /><br />Ms. K teaches everything "from the top" - i.e. all skills and concepts are "embedded" in a whole mess of other skills and concepts.<br /><br />This month the kids were asked to set up and solve their FIRST equations with variables on both sides:<br /><br />* ON A TEST<br /><br />* IN A COMPLICATED VERTICAL, COMPLEMENTARY & SUPPLEMENTARY LINE DRAWING <br /><br />They had spent no classtime learning how to set up these equations; they had spent no classtime to my knowledge learning how to solve these equations; they'd had a few days at most on vertical, complementary, and supplementary angles.<br /><br />All of this stuff - all of it - was "taught" as one big mush.<br /><br />I've come to believe that the constructivist ideology of ed schools is horrifically damaging to older kids for these reasons:<br /><br />1. new teachers have NO idea how to break a concept down into its component parts<br /><br />2. new teachers have NO idea that they SHOULD break a concept or skill down into its component parts <br /><br />3. new teachers have NO idea that "understanding" is distinct from "being able to do it on a test" <br /><br />4. new teachers have NO idea that learning for all living creatures happens through a process of spaced repetition which, in math, translates to distributed practice<br /><br />The constructivst ideology of young teachers explains why the math chair thinks it's fine to tell us that "if students need distributed practice parents can find worksheets online."<br /><br />She doesn't think distributed practice matters.<br /><br />She thinks conceptual understanding matters, and she thinks once you've put material on the board conceptual understanding has occurred.<br /><br />The way to assess whether conceptual understanding has occurred is to give students an extremely difficult, timed test with multiple problems all of which require the student to use multiple concepts and skills to solve.<br /><br />If a student fails the test, that is taken to be a sign that the student needs "extra help," which means that the student comes in before school and has the concepts explained to him again by the teacher, one-on-one.<br /><br />Everything is taught via "explanation"; if explanation fails, more explanation is assumed to be the remedy.<br /><br />If more explanation fails, the student is assumed to be incapable of learning the material and is moved to an easier course in which less material is "covered,"<br /><br />This gets back to the question of whether there are any "real" constructivist classrooms in the country.<br /><br />If you looked at Ms. K's class you would call it traditional. The textbook is traditional (harks back to the first New Math, in fact); the lecture format is traditional.<br /><br />But it is constructivist through-and-through.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-78445457773697005772007-01-21T19:46:00.000-08:002007-01-21T19:46:00.000-08:00Adele,
Thanks so much for sharing your experiences...Adele,<br />Thanks so much for sharing your experiences. You are saying that at least by the time their child has been having trouble with the crazy TERC-like math, the video would make it very clear to any parent what's going wrong.<br /><br />I'd been thinking about the case of parents watching the video before their child had been exposed to the program and perhaps not realizing the seriousness of the situation before it was too late to do anything.Mehttps://www.blogger.com/profile/05080767128939690601noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-62544799570845278192007-01-21T19:11:00.000-08:002007-01-21T19:11:00.000-08:00"... but because it was all so clear to me -- he c..."... but because it was all so clear to me -- he couldn't do math because HE DIDN'T KNOW HOW TO - "<br /><br />This is not about which algorithm is best to teach. It's about competence, both curricular and teaching. It's nice to have students take responsibility for their learning. They just shouldn't have to take responsibility for the teacher's teaching.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-44189401333280401142007-01-21T07:26:00.000-08:002007-01-21T07:26:00.000-08:00I still can't fathom how Google searches, even tho...I still can't fathom how Google searches, even though I am pleased with the result.<br /><br />A blog search for "math" has me in second place after linda moran, out of nearly two million candidates:<br /><br />1,983,256 posts matching math - showing 1 through 10<br /><br />Meteorologist critiques TERC and Everyday Math<br />3 hours ago by lindamoran - References<br />As a parent and math teacher, after ten months of studying the "Math Wars" upside and down, inside and out, I have to admit, I've come out pro-reform math. But the wrinkles yet to be ironed out of this revolutionary new approach to math ...<br /><br />Teens and Tweens - http://www.lindamoran.net/blog_teen/<br /><br />Fuzzy math video<br />17 hours ago by Instructivist - References<br />Math video.<br /><br />Instructivist - http://instructivist.blogspot.com/index.html<br /><br />In her latest post, linda moran, after much scrutiny, comes out on the side of the fuzzies, even though serious wrinkles still need to be worked out, she admits.<br /><br />I wondering if the "wrinkles" couldn't be so fundamental that they are the program itself, its essence. The analogy with Communism comes up again.<br /><br />In any event, she promises to write in greater detail about this shift.Instructivisthttps://www.blogger.com/profile/01652458042291988959noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-68570878640212111612007-01-21T07:10:00.000-08:002007-01-21T07:10:00.000-08:00I gotta get back to KUMON.
I told Christopher the...I gotta get back to KUMON.<br /><br />I told Christopher the other day that I think he's going to be going back to KUMON and he pitched a fit.<br /><br />I'm going to stay away from the KUMON topic today.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-4236177003980388952007-01-21T07:09:00.000-08:002007-01-21T07:09:00.000-08:00When Christopher and I took the KUMON placement te...When Christopher and I took the KUMON placement test he placed into 2nd grade and I placed into 4th.<br /><br />So you shouldn't feel too bad.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-63739825175934660552007-01-21T07:08:00.001-08:002007-01-21T07:08:00.001-08:00Adele, if you're around - what book did you buy?Adele, if you're around - what book did you buy?Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-16168995783678918192007-01-21T07:08:00.000-08:002007-01-21T07:08:00.000-08:00The progressive methods also vary from the standar...<I>The progressive methods also vary from the standard ones in a very disadvantegous way -- they require a lot more spatial organization.</I><br /><br />THAT'S IT!<br /><br />Every time I see one of these problems I feel overloaded and bewildered, but I could never put my finger on the reason. I assumed my problem was just that the algorithm is unfamiliar.<br /><br />But you're right: the demands on spatial organization are <I>enormous</I>.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-25130963322600208312007-01-21T07:07:00.000-08:002007-01-21T07:07:00.000-08:00The great thing about Math Dad is that he's even m...The great thing about Math Dad is that he's even more ferocious than I am. <br /><br />Ed talked to a parent who knows him; the parent kept saying, "He has a strong personality. He has a very strong personality."<br /><br />I like that in a man.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-17655473846584868602007-01-21T07:06:00.000-08:002007-01-21T07:06:00.000-08:00our evenings at home became a grinding routine of ...<B>our evenings at home became a grinding routine of math tutoring</B><br /><br />Hi Adele!<br /><br />I for one am looking forward to a grinding Sunday of math tutoring.<br /><br />Christopher is down to a D- or thereabouts in Ms. K's class & has to make up a test tomorrow, so today promises to be a horror.<br /><br />On one of her recent tests, possibly the one Christopher is making up, she included a problem requiring the kids to:<br /><br />WRITE AN EQUATION WITH VARIABLES ON BOTH SIDES IN ORDER TO FIND THE MEASURES OF A COMPLICATED SET OF ADJACENT, VERTICAL, SUPPLEMENTARY, AND COMPLEMENTARY ANGLES<br /><br />The Math dad emailed Ms. K pointing out that she had never taught the kids how to set up or solve an equation with variables on both sides.<br /><br />She replied that she had taught it last year. <br /><br />This is the new mantra; the math chair told us the same thing about the test Christopher got his 60 on. The reason Ms. K was justified in giving the kids a small, complicated, hard-to-read drawing of a submarine to find the volume of was that "she taught it last year."<br /><br />She did indeed teach how to find the volume of a cylinder last year, or, rather, Ed taught the subject. The class (Ed) spent perhaps 5 days on the subject and iirc she never returned the final test they took which I presume Christopher and many of his friends bombed.<br /><br />Not a problem for the math chair.<br /><br />"She taught it last year."<br /><br />Math dad knows every single topic Ms. K has taught inside out; he knows when she taught it, too. <br /><br />He told her, "Maybe you're thinking of last year's 7th grade class. You probably taught it to them."Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-88968137795907227982007-01-21T06:56:00.000-08:002007-01-21T06:56:00.000-08:00correction
Rory says M.J. McDermott created the v...<B>correction</B><br /><br />Rory says M.J. McDermott created the video in connection with the Where's the Math folks.<br /><br />I'm trying to think where I got the idea she did it on her own....it's possible I read that on Linda Moran's TERC listserv.<br /><br />I'll check later on.Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-28836029251229554272007-01-21T06:52:00.000-08:002007-01-21T06:52:00.000-08:00"Take any one of them in the video and think about..."Take any one of them in the video and think about how much "peripheral" calculation was required - numbers were stored to the right and the left of the central problem and then have to be regrouped in order to present the answer.<br /><br />This is a superb point!<br /><br />It also occurred to me, while watching the TERC method, that this cumbersome method makes heavy demands on the pathetically limited working memory people have. Remember the magical number seven, give and take?<br /><br />Inevitably, such "peripheral" calculations provide a rich opportunity for error. Can you imagine a kid, possibly struggling with organizational issues, having to keep track of all these ancillary calculations?Instructivisthttps://www.blogger.com/profile/01652458042291988959noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-71717979811391905742007-01-21T03:33:00.000-08:002007-01-21T03:33:00.000-08:00This all makes me think of the great “Taught my do...This all makes me think of the great “Taught my dog to whistle” image.<br /><br />http://www.kitchentablemath.net/twiki/bin/view/Kitchen/TaughtMyDogToWhistle<br /><br />“I said I taught him, but I didn’t say he learned.”Texhttps://www.blogger.com/profile/12015376722906862434noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-15052896770195042532007-01-21T03:21:00.000-08:002007-01-21T03:21:00.000-08:00So many excellent comments that concisely communic...So many excellent comments that concisely communicate the issues!<br /><br />From Adele:<br />“We're enchanted with the idea that children will somehow derive the higher meaning in numbers and we shouldn't clutter up their mind with repetitive exercises. Tell that to the piano student, the dance student, the tennis player, the golf player, the French student and so on and so on and so on....frankly, I just don't know how on earth we got to where we are.”<br /><br />I think about how this can resonate with many parents whose kids are not so involved in math.Texhttps://www.blogger.com/profile/12015376722906862434noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-39560175110333539422007-01-20T21:36:00.000-08:002007-01-20T21:36:00.000-08:00I am one of those parents who (as you say) did not...I am one of those parents who (as you say) did not feel comfortable with the standard math algorithms and this is what I have to say. <br /><br />My son struggled with math continuously from 3rd through 8th grade. He received "intervention" services in the form of teacher consultation, support classes, etc. for those years at our school district. I cannot imagine what the cost of this was over those several years to taxpayers but one can assume it was significant. In addition to the support he received at school, our evenings at home became a grinding routine of math tutoring. I was never a good math student. The best I could do was stay a little ahead, try to do the worksheets with him and then wait for the bad grades to come home (and they did). Through all this effort and expense, he never did better than a C on any report card and was consistently demoralized and/or angry. At 10:30 PM one night, I loaded myself into the car and ran down to Borders Books in dire frustration because the methodology to accomplish the homework he had that night could not be found ANYWHERE in the textbook. There I purchased a simple guide on how to do basic math. There were no pictures, no stories of "what would happen if you wanted to make a kidney shaped swimming pool .." etc., etc., etc. There were simple instructions for each type of problem followed by exercises.<br /><br />This was a turning point for us as I realized that we (him AND I) were not inadequate, we were simply NOT BEING TAUGHT. <br /><br />The video fails to mention this -- the schools are all teaching this "progressive" math program but, as mentioned earlier, the end result is that a large majority of kids ARE NOT LEARNING ANYTHING AT ALL. Yet, the homework is designed around getting ready for the standardized tests and the tests themselves assume they have learned the standard methods so...what gives? Are they supposed to be doing this magical sort of learning whereby you just "get exposure" to math concepts and...voila! You can do it! The progressive methods also vary from the standard ones in a very disadvantegous way -- they require a lot more spatial organization. Take any one of them in the video and think about how much "peripheral" calculation was required - numbers were stored to the right and the left of the central problem and then have to be regrouped in order to present the answer. How on earth is this better? Furthermore, the reformed approach assumes time is not an issue so they've created revisions with no thought to how long it takes to complete a problem. Last I checked, every major test these students will take from APs to SATs, ACT, etc. are time-based, meaning they are graded by accuracy within time limitations. Contrary to the methods shown in the video, TIME IS OF THE ESSENCE. <br /><br />The simple book from Borders starting making all the difference. With this realization, I took him over to a Kumon Center. They gave him a simple assessment test. I treated this warily thinking this was just part of the "sell." He was in 8th grade at this point and his assessment was 3rd grade level. I cried that day -- not because of his deficiencies but because it was all so clear to me -- he couldn't do math because HE DIDN'T KNOW HOW TO - as stupid as this sounds, this was a revolutionary concept in our family at that time and certainly not one ever expressed to me by an educator. <br /><br />I have often thought of the current style of math instruction as a system in which we want to create skillful experts but for some reason, we don't want to let them know what tools they can use to hone their skills. We're enchanted with the idea that children will somehow derive the higher meaning in numbers and we shouldn't clutter up their mind with repetitive exercises. Tell that to the piano student, the dance student, the tennis player, the golf player, the French student and so on and so on and so on....frankly, I just don't know how on earth we got to where we are. I am so sorry for the lengthy post but heck, I feel better!Adelehttps://www.blogger.com/profile/00090079040370964085noreply@blogger.com