tag:blogger.com,1999:blog-6570061087276796800.comments2014-11-27T10:49:59.912-05:00Out In Left FieldKatharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comBlogger3965125tag:blogger.com,1999:blog-6570061087276796800.post-47729522883105886062014-11-27T10:49:59.912-05:002014-11-27T10:49:59.912-05:00Arg! "Even more ridiculous is the idea"...Arg! "Even more ridiculous is the idea"? There's that "red is the color" word order again!<br /><br />One traditional way to get around this awkwardness is the expletive "it's", as in "It's even more ridiculous to cook the turkey in a bag." That sounds a lot better to me. FedUpMomhttp://www.blogger.com/profile/00951858601020687242noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-33984834463223672562014-11-26T20:52:33.356-05:002014-11-26T20:52:33.356-05:00Oops, I did that wrong. Let me try this again:
&q...Oops, I did that wrong. Let me try this again:<br /><br />"Stuffing comes out dense and it is quite difficult to properly cook a turkey when a it is overstuffed."<br />Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-66436639855140110182014-11-26T19:07:18.836-05:002014-11-26T19:07:18.836-05:00Stuffing comes out dense and it is quite difficult...Stuffing comes out dense and it is quite difficult to properly cook when a turkey is overstuffed.Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-36062157813191767152014-11-26T12:07:15.313-05:002014-11-26T12:07:15.313-05:00Exercise 1 is throwing me because it seem to imply...Exercise 1 is throwing me because it seem to imply that the idea of brining is, itself, ridiculous (which I don't think is a common perception). Given that brining is ridiculous, I'd edit to:<br /><br />Some people think that soaking a turkey in brine overnight makes it tastier. Even more ridiculous is the idea of cooking the turkey in a bag.Hainishnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-61793485698131433582014-11-26T08:00:25.971-05:002014-11-26T08:00:25.971-05:00C T--yes, the pattern in English matches the verb-...C T--yes, the pattern in English matches the verb-second pattern of inversion in German. I'd guess it reflects shared DNA of Germanic languages.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-29552844220761689822014-11-26T07:57:16.486-05:002014-11-26T07:57:16.486-05:00Thanks for your submissions! Keep'm coming. I&...Thanks for your submissions! Keep'm coming. I'll post answers on T-day.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-91557865864536945662014-11-26T01:27:02.249-05:002014-11-26T01:27:02.249-05:001. Cooking turkey in a bag is a ridiculous idea.
...1. Cooking turkey in a bag is a ridiculous idea.<br /><br />2. Properly cooking the turkey is difficult when it is overstuffed.Adelaide Duponthttp://www.blogger.com/profile/01490123934889071074noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-12708859853031135062014-11-25T18:19:03.450-05:002014-11-25T18:19:03.450-05:00Inversion is common in German. Is that where the E...Inversion is common in German. Is that where the English version comes from?C Thttp://www.blogger.com/profile/01178189190498225759noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-15703194796600184802014-11-24T21:56:55.161-05:002014-11-24T21:56:55.161-05:00Conceptual understanding is just that - conceptual...Conceptual understanding is just that - conceptual. Too many educators mistake it for proper mathematical understanding. Conceptual is at the level of motivating why you are learning the material in the first place. It's at the pie chart level, and that simple kind of understanding of fractions provides no support for understanding rational fractions. Many teachers say that the toughest math class in high school is Algebra II because that's when those conceptual understandings fall apart. Understanding should be built on identities, not pies or bars.<br /><br />Some students need more motivation than others, but it is neither necessary or sufficient for real understanding. That is built from doing and understanding nightly individual problem sets.<br /><br />As for testing, how can standardized tests ever test conceptual understanding or problem solving in the sense of applying mathematical ability to new problems - ones not covered in all of the problem variations encountered in homework?<br /><br />What are teachers, potted plants? Are they incapable of making those judgments even with seeing the kids every day? What is the purpose of yearly standardized tests? Are they used because we can't trust teachers or are they used just as a safety net? If they are used as a safety net, then it would be much simpler to just test the basics - results that can give specific things to correct. As it is now with NCLB, our schools get vague scores on "problem solving" and no other details on why the results aren't as good this year. Shouldn't they already know what the problems are?<br /><br />Why on earth would anyone expect a problem solving yearly standardized test be part of a critical thinking feedback teaching loop?<br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-18403338236756898652014-11-24T20:40:23.573-05:002014-11-24T20:40:23.573-05:00Your point being what?Your point being what?Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-53058574693628655772014-11-24T09:52:28.374-05:002014-11-24T09:52:28.374-05:00From a recent Atlantic article: "Tougher asse...From a recent <a href="http://www.theatlantic.com/education/archive/2014/11/should-the-us-make-standardized-tests-harder/383084/2/" rel="nofollow">Atlantic article</a>: "Tougher assessments tend to avoid multiple-choice questions, relying on open-ended prompts that challenge a student to gather evidence from a supplied text or use narratives to express a mathematical concept."<br /><br />Hainishnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-67672837343722489732014-11-23T17:02:50.613-05:002014-11-23T17:02:50.613-05:00Anonymous: Depends what you mean by conceptual und...Anonymous: Depends what you mean by conceptual understanding. A problem that asks for how many 2/3 oz servings are in 1 3/4 oz of yogurt requires that a student recognize that the problem is solved by division as well as a procedural knowledge of how to do fractional division. If the student cannot explain why the "invert and multiply" rule works but shows he understands what the problem is asking and how to solve it, does that mean he/she lacks conceptual understanding?<br /><br />I agree with Katharine that McCallum and others should be making more public statements about what CC math standards require and what they do not. After I wrote my first article offering alternative interpretations of CC math standards (in Heartlander), McCallum showed some interest and even <a href="http://commoncoretools.me/2014/08/07/drawings-in-the-common-core/" rel="nofollow">blogged about it.<br /><br /></a> He even acknowledged that the standard algorithm for multidigit addition and subtraction can be taught in grades earlier than 4th--the grade in which that algorithm is mentioned in the CC standards: "By the way, the standard algorithms for addition and subtraction are “strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.” The standards do not forbid them being introduced in Grade 2—nor do they require that."Barry Garelickhttp://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-23656560559232750772014-11-23T15:55:14.313-05:002014-11-23T15:55:14.313-05:00What I don't understand is why, instead of hav...What I don't understand is why, instead of having students verbally show that they understand, can't they design problems that can't be solved unless the student has conceptual understanding? The Singapore math books are full of such problems--and interestingly, back when they were first developed, a huge number of the students using them were English language learners.Anonymousnoreply@blogger.comtag: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.com