tag:blogger.com,1999:blog-6570061087276796800.comments2014-11-18T18:00:27.408-05:00Out In Left FieldKatharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comBlogger3952125tag:blogger.com,1999:blog-6570061087276796800.post-54004146135966035762014-11-18T18:00:27.408-05:002014-11-18T18:00:27.408-05:00I could have!
(But it's still a miracle ---- ...I could have!<br /><br />(But it's still a miracle ---- !)<br /><br />CatherineCatherine Johnsonhttp://www.blogger.com/profile/06902723049206581931noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-61588831077731788472014-11-16T16:00:38.937-05:002014-11-16T16:00:38.937-05:00Good point, Anonymous. The Principle of Conservati...Good point, Anonymous. The Principle of Conservation (http://en.wikipedia.org/wiki/Conservation_(psychology)#Solid_quantity) is probably more applicable here than object permanence. Though it develops substantially later than object permanence, it's in place substantially earlier than 8th grade.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-31351791379025723862014-11-16T04:32:04.246-05:002014-11-16T04:32:04.246-05:00Object permanence doesn't make children grasp ...Object permanence doesn't make children grasp that a cup of water in a tall, thin glass is the same amount of water as in a short, wide glass, even if you pour it back and forth from one to another. That's something children figure out around kindergarten or so.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-82493892661325934532014-11-15T07:10:00.780-05:002014-11-15T07:10:00.780-05:00You might provide students with an example that...You might provide students with an example that's prepared in advance, for addressing this question, with solution (5+5/7, 2-2/7). One in which guessing the solution is highly unlikely.concernedhttp://www.blogger.com/profile/14374789062880735051noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-48501768630662280722014-11-14T11:49:03.220-05:002014-11-14T11:49:03.220-05:00So much for deeper understanding. They don't w...So much for deeper understanding. They don't want students to explain why they are equal, they want them to spew back memorized knowledge.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-31166262945390920352014-11-14T10:51:54.633-05:002014-11-14T10:51:54.633-05:00I don't recall hearing of this Cavalieri guy, ...I don't recall hearing of this Cavalieri guy, but I know how to roll quarters, so I'd get it right.C Thttp://www.blogger.com/profile/01178189190498225759noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-15617164665131362732014-11-12T15:00:47.892-05:002014-11-12T15:00:47.892-05:00@Auntie Ann
When I used to teach word problems in...@Auntie Ann<br /><br />When I used to teach word problems in Beginning Algebra I would tell students, "You may be able to solve these word problems without equations, but I'm not so much interested in the answers as I am in the writing of the equations. If I were only interested in answers the questions would be A LOT harder. And if you're interested in just answers, go take an engineering class because they're mostly interested in answers - but your answers better be right!"<br /><br />And the equations are a great way to convince someone else that your answers are right!eddie sacroboscohttp://www.blogger.com/profile/05542999467489867201noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-46035956738664400012014-11-11T15:16:48.807-05:002014-11-11T15:16:48.807-05:00Guess and check is only an acceptable way to reach...Guess and check is only an acceptable way to reach an answer if the possible options are VERY limited. Adults use it all the time (in our heads) when there are only 2 or 3 possible answers. So you can introduce it to children on that basis, using a few examples that show that this is an OK method ONLY if it gets you to the answer very quickly.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-42472256837814302572014-11-11T14:36:38.547-05:002014-11-11T14:36:38.547-05:00Answer: I believe it is important for students to ...Answer: I believe it is important for students to work real-world problems, and the real world doesn't come with an answer key to check against. An engineer often has no way to check their calculations. If an aircraft engineer is wrong, the plane crashes. People in the real world who use math have to have a reliable method for attaining the answer. <br /><br />They also will be fired if they spend all day guessing and checking instead of reaching a quick and reliable answer.<br /><br />Guess-and-check is simply not a real-world method.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-52024411865362056342014-11-11T13:30:50.010-05:002014-11-11T13:30:50.010-05:00Thanks for the smiley, Ze'ev. And not to torp...Thanks for the smiley, Ze'ev. And not to torpedo my own work, but it occurs to me that the interviewer could say "And what do you think of 'guess and check' as a reasoning strategy?" Oops. Guess I better seek employment in a car wash!Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-993584373202342002014-11-11T13:20:35.249-05:002014-11-11T13:20:35.249-05:00"This experience would serve me well, I thoug..."This experience would serve me well, I thought. If I ever got to interview for a teaching job and I was asked to describe how I would work within the Common Core standards, I could say “Getting the right answer isn’t enough; students have to show their reasoning” or some such language."<br /><br />Nice! :-)<br /><br />But why to insist on equations? Aren't pictures, "visual fractions," and "area models" good enough? We need no stinkin' equations in Common Core! Another :-)Ze'ev Wurmannoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-74869827298382126622014-11-11T00:51:00.691-05:002014-11-11T00:51:00.691-05:00I must have an earlier edition (_A School Algebra_...I must have an earlier edition (_A School Algebra_ by Wentworth, 1895). I have been going through it lately to outline it in preparation for creating an online introductory algebra class. I've been comparing some of its problems to the remedial algebra I've seen as a tutor, and I am amazed at the depth and complexity of the problems from the older text. Why can't they make textbooks like that anymore? Instead, modern publishers insist on dressing up their pig with two-inch margins and four-color printing. Have to justify the triple-digit price somehow, I guess ~Niels Henrik Abelhttp://www.blogger.com/profile/00554447042962336254noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-8643794982006736622014-11-10T21:32:32.672-05:002014-11-10T21:32:32.672-05:00My third child is now 14. He took Algebra 1 in 7th...My third child is now 14. He took Algebra 1 in 7th grade and Geometry in 8th grade. He is now in Algebra 2 as a freshman. He is riding a wave of the last fortunate kids to be able to take these classes in earlier grades. I highly doubt that a 10th grader is going to be able to or even be allowed to take two math classes at one time. That seems really unfair, especially if the children are completely capable of completing the course. Here in CA, the standards are being dumbed down by CCSS.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-37324231865114695372014-11-10T15:33:17.432-05:002014-11-10T15:33:17.432-05:00I really appreciate these Math Problems Of The Wee...I really appreciate these Math Problems Of The Week postings. Could you please continue naming the source textbook (EngageNY in this case) in the post title? Different publishers are producing vastly different materials, all labeled "Common Core aligned" or "CC inspired". It's really helpful to distinguish the paths that different publishers are taking rather than lumping them all together.jmayhttp://www.blogger.com/profile/09989627957781277972noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-65153760788544464182014-11-10T00:49:08.318-05:002014-11-10T00:49:08.318-05:00I have a copy and it's nice and straightforwar...I have a copy and it's nice and straightforward.<br /><br />Does she actually work from the book? Ours is in good shape, but I wonder how well it would hold up to full use.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-12578184118199620662014-11-09T13:46:09.529-05:002014-11-09T13:46:09.529-05:00It's the Wentworth's "New School Alge...It's the Wentworth's "New School Algebra" that I've used in many of the math comparison problems. Great book, published in 1919!Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-82137847075461292942014-11-09T08:14:20.142-05:002014-11-09T08:14:20.142-05:00The good engineering schools (and the good college...The good engineering schools (and the good colleges in general) expect you to take Calculus AB or BC as a senior.<br /><br />If you want to major in science or math, some of the schools don't even accept the AP Calc credits- they just use them for placement.<br /><br />But if you can't place into a decent math course as a freshman, there's no way you'll complete an STEM degree in a timely manner, especially with all the prerequisites.<br /><br />When you don't offer decent math, you shut doors for the kids. It's one things if the kids and parents decide math isn't important-- but the administration should not be shutting doors on its own.Deirdre Mundyhttp://www.blogger.com/profile/14357363160387734552noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-9738183632636948832014-11-08T12:57:21.006-05:002014-11-08T12:57:21.006-05:00What curriculum has she been using?What curriculum has she been using?C Thttp://www.blogger.com/profile/01178189190498225759noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-31624867384837708462014-11-05T09:28:26.118-05:002014-11-05T09:28:26.118-05:00Additionally, we are seeing that 8th Algebra is th...Additionally, we are seeing that 8th Algebra is the only section where the Regent's Exam is not being gamed. Students who take the course in 9th do not receive the real deal. They will be taught to use the calculator to find answers, instead of the mathematical techniques to find solutions. And they will be penalized if they don't use these gaming techniques and actually use the mathematical techniques they learned in their online/Kumon/someotherprovider Algebra class.lgmnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-85377860908686610062014-11-04T21:57:09.668-05:002014-11-04T21:57:09.668-05:00The problem is that many schools are ignoring what...The problem is that many schools are ignoring what parents want by making changes that make the pathway to calculus in high school more difficult. Nobody is talking about whether calculus in high school is "the end all be all". Students have always had a choice to not go into algebra in 8th grade. However, many students are or could be ready if only K-6 schools used better math curricula. The Common Core did not deal with this issue and now many educators are trying to create the impression that algebra in 8th grade is some sort of exceptional math brain standard. No. When I was in 8th grade in the 60's we had maybe 30% of the students taking the course, and that was without any help at home from parents.<br /><br />Barry is not hinting. He is openly stating that in terms of math, many schools do not care about what parents want. (BTW, this is not Barry's opinion.) In our town, we parents had to fight to get any sort of decent math pathway in 8th grade that led to geometry in 9th grade, but now there is the same talk that algebra in 8th grade is some sort of special thing and they might limit who can take the course. It couldn't possibly be a problem with math in K-6.<br /><br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-27733876053165865142014-11-04T16:46:54.256-05:002014-11-04T16:46:54.256-05:00I do not think taking Calculus in 12th grade is th...I do not think taking Calculus in 12th grade is the end all be all. What happened to taking proper Calc 101 and 102 as a college freshman? Don't the engineering schools still require Engineering Calculus any way? Isn't the college Calculus more rigorous? I am not a teacher. I am a parent. And I'm getting a hint in here from Barry of something I am hugely tired of: some how parents are not allowed to have an opinion about their child's education? We're supposed to not care, not comment? It's obnoxious and I'm hugely tired of it. ESPECIALLY because these days parents are being asked to spend an hour a day teaching their kids and making them practice, since at school they dabbled in the concept or dispensed with class altogether to go to a fundraiser assembly or other such nonsense.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-25317897312593865342014-11-03T12:45:01.813-05:002014-11-03T12:45:01.813-05:00We have not experienced peer tutoring demands at a...We have not experienced peer tutoring demands at all since full inclusion began. Apparently the IEPs require professional staff to deliver instruction as well as remediation and re-teach.<br /><br />High school NHS members are expected to tutor students that are struggling and want peer help, but that is formally arranged and supervised. It is also never a classmate, always someone that is in a different cohort..lgmnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-90502660679090467912014-11-03T11:27:37.836-05:002014-11-03T11:27:37.836-05:00Group work is also a way to take advantage of the ...Group work is also a way to take advantage of the direct instruction that some students are getting at home from their frustrated parents. The kids being taught at home or at Kumon pass along what they've been taught to the others. The teachers get to pretend it's constructivist.<br /><br />The problem is the social: no one wants to listen to the smart-a$$ kid know-it-all. It just adds to the social problems.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-27559500352879720892014-11-03T10:14:41.302-05:002014-11-03T10:14:41.302-05:00The idea that future employers might expect employ...The idea that future employers might expect employees to show up on time, dress/groom themselves appropriately, listen to instructions, follow specific procedures and express themselves clearly and politely seems not to be considered. Back in the dinosaur era (50s), we were constantly told (from first grade; no k), that school was our job and preparation for being able to get paying jobs (part-time in school and full-time after graduation; few went to college)later. Kids who didn't make that standard couldn't even get babysitting or lawn-mowing jobs. <br /><br />As for groupwork, I see it as easier for the teacher and enabling the pretense that "all" are learning (a vital pretense in the mandated full-inclusion classroom). The idea that kids with severe cognitive handicaps, autistic kids, emotionally disturbed/unsocialized kids,kids with learning disabilities, spoiled brats, thugs, bullies, decently socialized "average" kids and highly-performing to really gifted kids can all learn the same material, presented the same way, in the same amount of time, in the same classroom is an impossible fantasy, as is the idea that any significant number of teachers can "differentiate instruction" decently.momof4noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-89843870106540209792014-11-03T09:04:54.297-05:002014-11-03T09:04:54.297-05:00Katherine, how much of this groupwork is being pus...Katherine, how much of this groupwork is being pushed because of the belief that it will help inner city youth get to graduation by making them contributors to the classroom via active discussion, rather than feeling that the teacher is 'dominating' them by asking for quiet while delivering a mini-lecture or asking that one person at a time be heard in discussion? The Atlantic article by Lucy Graves "The Economic Impact of School Suspensions" on 10/26/14 seems to assert that school has to change away from the model where one respects the teacher and other students to one where the learner has to discover in order to get past that 'domination' idea. lgmnoreply@blogger.com