tag:blogger.com,1999:blog-6570061087276796800.comments2014-10-23T00:42:19.792-04:00Out In Left FieldKatharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comBlogger3909125tag:blogger.com,1999:blog-6570061087276796800.post-20821895479341817642014-10-23T00:42:19.792-04:002014-10-23T00:42:19.792-04:00One issue is that increasingly I find teachers mea...One issue is that increasingly I find teachers mean "Math in Focus" when they say "Singapore Math," not what the Primary Mathematics, which is what homeschoolers usually mean. Math in Focus is based on a second Singapore curriculum, intended for weaker students, called My Friends are Here, and is slower and more like typical US textbooks.<br /><br />The Common Core-aligned Math in Focus books actually say Singapore Math on the cover, which is part of the confusion.ChemProfhttp://www.blogger.com/profile/01720659176087492651noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-80565113395377390562014-10-22T20:15:24.086-04:002014-10-22T20:15:24.086-04:00"By "continually rave about how wonderfu..."By "continually rave about how wonderful Singapore math is" I assume you mean "periodically post comparisons between Singapore Math and other math programs"?"<br /><br />loll!<br /><br />though I must say, comparing Singapore Math to other math programs is tantamount to raving about how wonderful Singapore Math is ----- !<br /><br />(from me, Catherine)Catherine Johnsonhttp://www.blogger.com/profile/06902723049206581931noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-56062893826093315082014-10-22T13:44:36.399-04:002014-10-22T13:44:36.399-04:00Last year, a friend of ours pulled her kids out of...Last year, a friend of ours pulled her kids out of our private school the day her third grader reported that the teacher chewed out his entire class for doing so poorly on their standardized tests. She now homeschools. <br /><br />Of course, the teachers and the school seemed to solely blame the kids...the 8-year-old kids, not the adults who have held those kids' education in their hands for at least three years.<br /><br />And, until last year, it was an Everyday Math school.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-62640315044521297372014-10-22T13:28:21.223-04:002014-10-22T13:28:21.223-04:00What I find incredible is that schools blame the s...What I find incredible is that schools blame the students (they just need more engagement) and they depend on state tests(now things will be different!), as if they have little control over what they teach and how they test in class. As for a feedback loop, do they really wait until once a year to make corrections to what and how they teach? One parent-teacher meeting I was in talked about how the state test results showed a lower score for "problem solving". Their solution? Focus more on problem solving.<br /><br />How can state tests properly judge understanding or critical thinking? What is the role of teachers who see students daily? Are they potted plants?<br /><br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-22383619057835127692014-10-21T17:47:28.001-04:002014-10-21T17:47:28.001-04:00A kid might be able to do the 5-2n problem without...A kid might be able to do the 5-2n problem without factoring. If they start with setting the two expressions equal to each other, then multiplying both sides by 6 to get rid of the fractions, they could see that there is clearly a 5-2n on each side. Then they'd have to avoid the pitfall of:<br /><br />5-2n = 6p(5-2n)...get rid of the two 5-2n's, and, voila!: 0=6p<br /><br />If they can get through that to 1=6p, they should have it without needing to factor.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-37780301039274404252014-10-21T16:03:20.760-04:002014-10-21T16:03:20.760-04:00gas...,
I think you have it completely backward.
...gas...,<br /><br />I think you have it completely backward.<br /><br />K-12 schools are about offering instruction at levels that are achievable by every student that gets good instruction, not about selecting the elite few that can go beyond their instruction and actually apply what they learned to new problems of the type they have not seen before.<br /><br />If that were the criterion, 99.9% of teachers would fail immediately. Why do you think they have to attend all those interminable "professional development" hours if they could "apply their prior knowledge to new problems"? After all, they supposedly already know the math, or the literature, from their college days. All that is left is to "apply it to new problems."<br /><br />In fact, not only would essentially all the teachers fail on the spot, but most population would. Only at the PhD level one is expected to apply knowledge to truly novel situations. And how many PhDs do we have? Less than 2% of the population.<br /><br />Consequently, all those "new problems" <b>cannot be new or novel</b> otherwise everyone would fail. Instead, Smarter Balanced will offer <b>pretend novel problems.</b> Those students that were drilled on those "novel" problem (hence making them rote) will easily succeed. The unlucky ones whose teachers actually believe the ed-school crap they are fed, that <i>"student need to struggle on the test and apply prior knowledge to new problems"</i> will simply fail on those questions.<br /><br />Talk about incentives for teaching to the test. Or about the damage ignorant highfalutin educrats can inflict.Ze'ev Wurmannoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-8164089629269258942014-10-21T11:26:41.698-04:002014-10-21T11:26:41.698-04:00I'm confused by "What I find inauthentic ...I'm confused by "What I find inauthentic is judging seventh and eighth graders’ math ability based on how well they are able to apply prior knowledge to new problems."<br /><br />Ability to apply prior knowledge to new problems is precisely what should be measured for students—the problem is that very few exams do that, and "teaching to the test" makes it even harder. A math test should not be a test of memory, but of ability to apply what their math skills to new problems.<br /><br />I agree with your statement "I do have a problem when part of this is learning how to write explanations that will pass muster according to scoring rubrics." Elementary educators and test writers alike often have very strange ideas about what they will accept as an explanation. Good math explanation is a skill that few ever develop, and rubrics are almost useless in judging explanations. For math tests to be about math and not about writing skills, the scoring should be based solely on ability to do the math, at least until students have been taught proof techniques in high school, when some formulaic explanations can be requested.gasstationwithoutpumpshttp://gasstationwithoutpumps.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-56779871904447604832014-10-20T22:04:56.006-04:002014-10-20T22:04:56.006-04:00There is a brief review in 3B for the third and US...There is a brief review in 3B for the third and US edition, But mostly to look at what to do when a number is close to a ten, like 48, somewhat of a new strategy. So it is not accurate to say no mental math. Plus, mental math strategies are taught in other contexts (money and measurement. But in grades 2 and 3, mental math chapters comes after the standard algorithm. But making a ten or subtracting from a ten is important in grade 1, to lead up to that algorithm. It is just that in the US, they don't have that understanding by third grade. Hence the more extensive review. <br /><br />And, in these grades, the standard algorithm is taught with place-value discs, in a way to foster "deep understanding" of it. Mental math is good for certain situations, numbers close to ten or hundred, adding and subtracting money that ends in 0 and 5 (in 2B they are allowed decimal notation for money, in Common core not until grade 4). Adding and subtracting measurement in the metric system. Nice little strategies that help speed computation.<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-36235704612004106502014-10-20T20:34:40.182-04:002014-10-20T20:34:40.182-04:00Thanks for this explanation, Anonymous@1:18 PM. It...Thanks for this explanation, Anonymous@1:18 PM. It's notable that making tens is at this point simply a mental math strategy (not a "deep understanding" strategy), and that the closer you get to the original Singapore math, the less review there is of it in 3rd grade (down to zero review in 3rd grade in the original).Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-13864271551955752292014-10-20T13:18:50.763-04:002014-10-20T13:18:50.763-04:00On pages 28 and 29 of the Primary Mathematics 3A W...On pages 28 and 29 of the Primary Mathematics 3A Workbook Common Core edition, there are some problems for making 10. These involve 2-digit plus 1 digit, e.g. 55 + 7, or 2-digit + 2-digit, e.g. 58 + 34, by making a ten with a number close to a ten (the 58). These two pages are almost identical to pages 26 and 27 of the 2008 Standards edition. They go with a chapter in the textbook specifically titled Mental Calculation, which does do a brief review of making tens or adding tens first and then ones when adding 1 digit to 2 digits, or 2 digit numbers. <br /><br />In the original third edition, to which the US edition is closest, this review was in 3B, not 3A, was even briefer, and was immediately followed by some mental math strategies for multiplication and division of tens and hundreds. <br /><br />Note that students have already learned to add and subtract 2-digit numbers both mentally and with the standard algorithm way before 3A, plus they have added and subtracted 3-digit numbers in 2A, extensively, using the standard algorithm, in all three editions. <br /><br />The original third edition had no review of this at all. It had a section on sum and difference, an introduction to bar model, and problems involving addition and subtraction of 3-digit numbers, without any strategies, even standard algorithm, as its review of second grade. Then it jumped into adding and subtracting 4-digit numbers using the standard algorithm. No mental math with 1- and 2-digit numbers in 3A originally. They already knew this, presumably.<br /><br />Which is why, when US schools adopted Primary Mathematics way back when, they would have had to go back to 2A.<br /><br />So, now in the Standards edition and the Common Core edition, for the US, review of mental math strategies is in 3A. And the section on sum and difference and introduction to bar models no longer includes 3-digit numbers. Only 2-digit numbers. They can focus on the concepts in that chapter rather than having to add and subtract 3-digit numbers which they might not know how to do yet, if they came from a US math second grade. Then there is a review of adding and subtracting 3-digit numbers using the standard algorithm, under the guise of estimation in the Standards edition (something not in the US edition at all) and called Looking Back in the Common Core edition. <br /><br />It is interesting that in the Primary Mathematics this is called mental math. Which to me means doing it in your head, without paper and pencil. And the strategy is introduced in 1A concretely, then pictorially, but then they should be able to do it abstractly and can use that strategy in their heads, as they learn the facts. That is, to easily think 10 + 5 when seeing 8 + 7. Mentally.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-51716807787933234322014-10-20T10:57:16.133-04:002014-10-20T10:57:16.133-04:00There have always been third graders who didn'...There have always been third graders who didn't figure out how to use the 'make a ten' number bonds before third grade started. In the past, they were put into a small group and given direct instruction at their level of need. Now, everyone in the class is held hostage and not allowed to continue their math instruction until their classmates 'catch up'. That is the real issue. Low expectations for those who are relegated to thumb twiddling while they wait. Of course, if the parents pull them and send them to private school they are called 'elitist'.lgmnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-76749159359566852052014-10-20T07:49:02.481-04:002014-10-20T07:49:02.481-04:00On page 27 of my edition (2008), there are a total...On page 27 of my edition (2008), there are a total 8 problems in which making tens is presented as an option. The directions are simply "add." On p. 29 there are two subtraction problems that have the same graphical "look" as "make 100s", but that don't involve making hundreds. Here the directions are simply "subtract." <br /><br />As Barry points out above and in his Ed News piece, Singapore Math introduces making 10s in 1st grade. By 3rd grade it is old hat. The point Barry and I are both making is that that in Singapore Math, unlike in U.S. Reform Math, the making tens methods (and other ad hoc methods) do not eclipse (or take substantial instructional time away from) the standard algorithms, which, by 3rd grade, are solidly in place in the curriculum.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-52953829360813717012014-10-19T23:09:30.033-04:002014-10-19T23:09:30.033-04:00Third grade Singapore Math workbook pages 28-29, m...Third grade Singapore Math workbook pages 28-29, making tens. Third grade Singapore Math workbook page 30, making hundreds.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-81813932720976352822014-10-19T17:22:57.533-04:002014-10-19T17:22:57.533-04:00Hi, Anonymous,
By "continually rave about h...Hi, Anonymous, <br /><br />By "continually rave about how wonderful Singapore math is" I assume you mean "periodically post comparisons between Singapore Math and other math programs"?<br /><br />"I wish you would actually crack open a Singapore Math book."<br /><br />It would be hard to post those Singapore Math comparison problems without cracking open a Singapore Math book.<br /><br />"Decomposing numbers and making tens comes straight out of Singapore Math."<br /><br />As Barry points out above, and in his piece on Ed News, decomposing numbers predates by many decades U.S. imports of Singapore Math. The issue here isn't that it shouldn't be done, but that it shouldn't eclipse standard algorithms-- or delay more advanced math.<br /><br />"I teach 3rd grade and we begin the year reviewing making tens and then go on to expand it to making hundreds."<br /><br />Singapore grade 3 workbooks (Primary Mathematics 3, Standards Edition) contain no making tens or making hundreds problems. Arithmetic in these books begins at a much higher level than that.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-3050311158979096532014-10-19T14:43:51.148-04:002014-10-19T14:43:51.148-04:00Actually, Singapore Math introduces making tens in...Actually, Singapore Math introduces making tens in first grade. The difference is that students are also expected to memorize math facts, and for two digit and more numbers, Singapore also introduces the standard algorithm for multi-digit addition and subtraction in 2nd grade. That algorithm is not delayed until 4th grade as many schools are doing in the name of Common Core. Because the standard algorith appears in the 4th grade CC standard, the popular interpretation of CC is to delay teaching it until 4th grade. In fact, there is nothing prohibiting teaching it earlier such as in 1st or 2nd grade--something that William McCallum and Jason Zimba (lead writers of the CC math standards) have said, though not in wide public venues.<br /><br />The use of number bonds to solve elementary addition and subtraction equations is not limited only to Singapore’s math textbooks. It has also been used extensively in U.S. textbooks, such as my third grade arithmetic book (Arithmetic we Need by Busell, Brownell and Sauble; 1955).<br /><br />See also <a href="http://news.heartland.org/newspaper-article/2014/08/06/common-sense-approach-common-core-math-standards" rel="nofollow">here</a>.Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-27545308707964272102014-10-19T11:50:32.812-04:002014-10-19T11:50:32.812-04:00You continually rave about how wonderful Singapore...You continually rave about how wonderful Singapore math is. I wish you would actually crack open a Singapore Math book. Decomposing numbers and making tens comes straight out of Singapore Math. I teach 3rd grade and we begin the year reviewing making tens and then go on to expand it to making hundreds. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-80192726523800928262014-10-19T11:11:53.172-04:002014-10-19T11:11:53.172-04:00This is something I've been working on a littl...This is something I've been working on a little. I think the problem for me is the lack of tests. As recent studies have shown, tests and studying for tests, is a very good way to learn. With tutoring, everything is always a bit low-key and low-pressure. Without a test, it's hard to make the student sit down with the materials and really absorb and come to terms with the math. Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-30444500284385082352014-10-19T09:00:01.115-04:002014-10-19T09:00:01.115-04:00It depends on the tutor. I'm sure you're a...It depends on the tutor. I'm sure you're a great one!<br /><br />Where I've seen problems is specifically with tutoring of older, accelerated kids in upper-level math courses, where the entire course is the tutoring itself. I should have been clearer about that.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-59317463492766639762014-10-17T16:32:15.310-04:002014-10-17T16:32:15.310-04:00I find it very hard to agree with these statements...I find it very hard to agree with these statements. I have tutored Math semiprofessionally at many levels for almost two decades, and at every moment I was very keenly aware of what my kids do and don’t know. Tutoring is not at all just a peasant “intelligent” talk about the subjects – very far from it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-24035547923483371242014-10-17T11:36:22.184-04:002014-10-17T11:36:22.184-04:00The school I grew up in had a cloak room attached ...The school I grew up in had a cloak room attached to every classroom for hanging up coats and taking off boots. I doubt schools are being built that way anymore, which means the mess of recess either ends up all over the hall or in the classroom.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-38219972356289893902014-10-17T09:12:27.379-04:002014-10-17T09:12:27.379-04:00I talked to a young German woman today who is work...I talked to a young German woman today who is working in the US as an au pair for a homeschooling family this year.<br /><br />She said she considered coming to the US as an exchange student in high school, but would have been held back a year once she returned to school in Germany. It made more sense to take the year off after abitur.<br /><br />The suckitude of US public schools vs European schools is not amenable to a quick fix that can be delivered by a school committee, an expensive curriculum plan, or a for-profit charter scheme.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-33170207523288742992014-10-16T09:06:54.992-04:002014-10-16T09:06:54.992-04:00I also agree the US Students should go out in all ...I also agree the US Students should go out in all but torrential rain/hurricane weather for recess, but when I brought it up at the PTA I was laughed out of the room. The issue is the significant number of parents/caregivers who will not provide their children with appropriate clothing. Unlike yesteryear, when kids would layer up and had a pair of rainboots/snowboots with growing room, and grandma would knit them gloves & hat, it is considered elitist to expect them to go outside with anything less than the wealthiest child is wearing...so if the donors aren't providing North Face etc. then equity demands that we provide a recess that all can participate in. <br />I kid you not.lgmnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-67091194283811750112014-10-16T02:52:51.178-04:002014-10-16T02:52:51.178-04:00He also doesn't mention that Finnish teaching ...He also doesn't mention that Finnish teaching methods are for the most part very traditional. Teacher talk, textbooks, students working individually. Here's a link to a "study" from last year on Finnish methods of teaching maths, published in an academic journal. It concludes that because such teaching methods are (apparently a priori) "wrong", they cannot have any influence on Finnish attainment in maths, which must "therefore" be down to cultural factors only!<br />http://www.diva-portal.org/smash/get/diva2:647275/FULLTEXT01.pdfChrisNnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-89471237556138316342014-10-10T00:25:25.600-04:002014-10-10T00:25:25.600-04:00(I didn't know calculators were allowed until ...(I didn't know calculators were allowed until I was finished with the problem, so I was trying to come up with an integer result which wouldn't take a lot of time to work out the arithmetic.) Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-86668708932705287042014-10-09T22:36:08.505-04:002014-10-09T22:36:08.505-04:00Guess and check is justified by the math reformers...Guess and check is justified by the math reformers as getting students to analyze and work with "patterns". Which ignores the fact that there are other more efficient patterns that one can master through fundamental procedures and facts as Ze'ev has demonstrated.Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.com