tag:blogger.com,1999:blog-6570061087276796800.comments2015-05-19T13:16:00.430-04:00Out In Left FieldKatharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comBlogger4220125tag:blogger.com,1999:blog-6570061087276796800.post-61609719218046327932015-05-19T13:16:00.430-04:002015-05-19T13:16:00.430-04:00My nephew is in the habit of erasing his mistakes....My nephew is in the habit of erasing his mistakes. I keep telling him to just cross them out and start again, so a teacher can see if you were on the right track. But, he's a neat freak and hates the messy paper.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-13420216340571511782015-05-19T10:22:37.623-04:002015-05-19T10:22:37.623-04:00But does doing a lot of problems increase the prob...But does doing a lot of problems increase the probability of stupid mistakes? Students could get sloppy and/or bored, especially if the teacher then assesses the homework so that conceptual understanding is prioritized over the "stupid" mistakes in assessment. <br /><br />In some long problems, as well, stupid mistakes can turn into significant conceptual errors. My classic example, because i used to do this, is z's that would turn into twos through sloppy handwriting -- a problem gets way easier (or unsolvable) when you remove one of the variables. <br /><br />And, in the end, an answer can be just as wrong when a stupid error (i.e. arithmetic miscalculation, etc.) has been made. <br /><br />bjAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-11640959337648482912015-05-19T10:07:51.455-04:002015-05-19T10:07:51.455-04:00Exactly. That's what I did when I taught math....Exactly. That's what I did when I taught math. Sometimes a student would get stuck early in a problem, but generally know how to solve the problem and would explain that in words. I gave them more partial credit, but not full credit. <br /><br />If they developed the problem through to near the end, but got stuck, I could tell whether it was an understanding issue or a "typo" sort of mistake. Perhaps they missed a minus sign. I could always tell what level of understanding they had. Words are not necessary.<br /><br />I always told my students to show their work. If they didn't, then they would not get partial credit because I could not guess what was going on in their heads. They could do this with words, but the math would get them more partial credit. Words are vague, but the math is not.<br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-80876817433223700122015-05-19T07:25:19.899-04:002015-05-19T07:25:19.899-04:00"Explaining in words is neither sufficient or..."Explaining in words is neither sufficient or necessary. Are you going to flunk a student who gets the correct answers but does not explain them well?"<br /><br />No, but I might <i>not</i> flunk a student who gets the wrong answer (for example, due to a stupid arithmetic mistake) but can explain how to solve the problem. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-25378022166478046412015-05-18T21:41:12.081-04:002015-05-18T21:41:12.081-04:00Giving many problems and demanding wordy answers o...Giving many problems and demanding wordy answers on a test are mutually exclusive. In the time it takes to explain in words one problem, a student could demonstrate their proficiency on several problems with different mathematical concepts. Writing wordy explanations is much slower than giving a student a variety of different questions.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-74777866323873381882015-05-18T21:32:39.704-04:002015-05-18T21:32:39.704-04:00"Or is it possible that the ability to explai..."Or is it possible that the ability to explain one’s answers verbally, while sometimes a sufficient criterion for proving understanding, is not, in fact, a necessary one?"<br /><br />Explaining in words is neither sufficient or necessary. Are you going to flunk a student who gets the correct answers but does not explain them well?<br /><br />"They" want you to explain each problem with words. What does that imply? That is the whole point of giving many problems on a test - to test understanding and flexibility on a wide variety of problems. Doing the problem, showing your work, and getting the correct answer is all that a teacher needs to determine sufficient understanding. The work shows the understanding, not words.<br /><br />Back when I taught math, words might get some partial credit, but I always could tell by examining their math - scribbles and attempts to solve on the paper. If I could see their work and they got the answer correct, then no words were necessary. <br /><br />Nobody can do well in math with just rote understanding. This is a huge fallacy. One can have an inflexible understanding or one with gaps and holes, but there are no words that fix that. It takes more practice and proof by doing and getting the correct answers.<br /><br />Teaching math is all about how words are not enough. Group work in class is all about group words. What individual students need for understanding is to do the homework sets individually and consistently get the correct answer without help from a teacher, tutor, or group.<br /><br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-52049314253050798262015-05-18T11:42:19.231-04:002015-05-18T11:42:19.231-04:00Ha Ha! Auntie Ann, I was just about to suggest a ...Ha Ha! Auntie Ann, I was just about to suggest a similar scenario. That is not to say that once in a while, asking students to describe how they arrived at a math problem answer using sentences might not be appropriate. But only once in a while, because crafting sentences to explain procedures that can be illustrated with mathematical expressions is hugely more time consuming and therefore frustrating. Way to make kids hate math.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-9037492649482029882015-05-17T10:43:57.534-04:002015-05-17T10:43:57.534-04:00English class: explain Captain Ahab's obsessio...English class: explain Captain Ahab's obsession with the whale, make sure to use at least one text-to-self and one text-to-text reference, also use math to explain your answer, the math must include diagrams of how it relates to the book.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-63729254084863996952015-05-17T08:06:31.692-04:002015-05-17T08:06:31.692-04:00Is it possible for CCSS to be anything but what li...Is it possible for CCSS to be anything but what lies in the hearts and minds of ed school pedagogues? No. Testing companies, like PARCC, define what CCSS is or is not. It doesn't matter what the SMP says. PARCC says that the highest level of achievement ("distinguished") only means that one is likely to pass a course in college algebra. This highest level of expectations starts in the earliest grades, so CCSS is a non-STEM curriculum by definition no matter what the SMPs say.<br /><br />However, MCPS defines accelerated tracks on their web site. Acceleration opportunities start in grade 4, and in one option, this leads to algebra I in grade 7. Considering that CCSS, at most, expects only pseudo-algebra II content, it's not clear how they prepare these kids for algebra in 7th grade. (They don't.)Whatever they do has to be something not based on anything to do with CCSS. They can use their fuzzy UCARE words, but something else has to happen. <br /><br />They start compacting the material in fourth grade, but the acceleration is based on the same fuzzy content and ideas of K-6 curricula. The only real change is when they get to a real algebra textbook that is far above what CCSS expects. Instead of a proper pre-algebra course, they force kids to suffer through "Investigations in Math." In other words, the only kids who will be on a STEM track are those who get math help at home or with tutors. <br /><br />K-6 math ignorance has not been fixed by CCSS. It is just hidden by acronyms like UCARE. MCPS can make a connection to Calc AP as a junior in high school, but the onus is completely on the students and parents to make the nonlinear transition from K-6 fluff math to the real math textbook high school sequence.<br /><br />CCSS is a one-size-fits-all (algebra II) expectation and anything above that is left up to the students and parents. MCPS can define the paths and students can make it onto those paths, but educators don't (want to) know how kids get on those paths. <br /><br />I went through this exact process with my son. I worked with him on the (stupid) 6th grade Everyday Math material in the summer before 6th grade so that he could take pre-algebra in 6th grade. I know exactly what that nonlinear transition is all about. CCSS fails in that it does not address the transition from the fluff ideas of K-6 to the real world STEM options of the calculus track in high school. When I was in school, I got to calculus with absolutely no help from my parents. This is impossible to do now. <br /><br />SteveHhttp://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-69194765666539492002015-05-16T15:50:36.470-04:002015-05-16T15:50:36.470-04:00The new problems are much wordier and demand wordi...<i>The new problems are much wordier and demand wordier answers. Are they trying to disfavor boys, AS kids and ELL?</i><br /><br />Katharine and I have addressed the issue of requiring students to "explain their answers" rather than simply showing their work in an <a href="http://www.educationnews.org/k-12-schools/math-problems-knowing-doing-and-explaining-your-answer/" rel="nofollow">article at Ed News.</a>Barry Garelickhttp://www.blogger.com/profile/00335707096785705085noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-90846989802693159542015-05-16T15:15:32.715-04:002015-05-16T15:15:32.715-04:00I found that drawing diagrams for the CC problems ...I found that drawing diagrams for the CC problems was far more cumbersome that simply working them numerically because conceptually they were very straightforward. Not so with the Singapore problems which are not straightforward at all unless you draw a diagram.<br /><br />Why couldn't the US simply adopt Primary Mathematics as the "standard" and be done with it?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-40926124435858139022015-05-16T08:05:56.063-04:002015-05-16T08:05:56.063-04:00The new problems are much wordier and demand word...The new problems are much wordier and demand wordier answers. Are they trying to disfavor boys, AS kids and ELL?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-40254150330071703792015-05-15T14:45:03.867-04:002015-05-15T14:45:03.867-04:00LOL, and here I was thinking about how industrious...LOL, and here I was thinking about how industrious Lila must be, baking in such large quantities.kcabnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-82793454271393447662015-05-15T14:07:51.279-04:002015-05-15T14:07:51.279-04:00Thanks for noticing this! The fraction bar did not...Thanks for noticing this! The fraction bar did not go through in the formatting. I've just added it where it was missing.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-15839874307378686812015-05-15T13:55:03.484-04:002015-05-15T13:55:03.484-04:00Are you sure the first set of questions was on fra...Are you sure the first set of questions was on fraction? It seems to be all addition and subtraction to me. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-46257674847313530772015-05-13T19:41:21.349-04:002015-05-13T19:41:21.349-04:00They are not unreasonable if implemented sensibly....They are not unreasonable if implemented sensibly. But requiring lower grade students to critique and analyze the reasoning of others is nonsense, but that's what some are doing. I wrote a series of articles on how the SMP can be implemented sensibly, compared to how they are be implemented in the real world. <br /><br />There's nothing wrong with having students persevere in solving problems, but this has been interpreted as "struggle is good", and giving students problems without much help or guidance and having them "struggle" so that they can learn. There are ways to do this productively, of course. But the "struggle is good" philosophy is one that's been around for a while, and the SMP's are gasoline on the fire of bad math practices that have been around for 20+_years.<br />Barry Garelickhttp://www.blogger.com/profile/00335707096785705085noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-20315240190083233382015-05-13T10:09:12.993-04:002015-05-13T10:09:12.993-04:00Barry, I found the Practice Standards here: http:/...Barry, I found the Practice Standards here: http://www.corestandards.org/Math/Practice/<br /><br />(With the exception of 3, they don't seem unreasonable to me.)<br /><br />I thought I would see "Students should be able to solve problems in more than one way," but I didn't find that particular phrase on the page I linked to. Do you know where it comes from?Hainishnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-57739546038741827832015-05-13T01:39:14.233-04:002015-05-13T01:39:14.233-04:00While CCSS is being used to advance the constructi...While CCSS is being used to advance the constructivist and other faddish trends, they are not entirely without blame. They lend themselves to such interpretations, particularly through the Standards of Mathematical Practice which are the old and recast NCTM Process Standards.Barry Garelickhttp://www.blogger.com/profile/00335707096785705085noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-65499370179159249282015-05-11T14:16:44.634-04:002015-05-11T14:16:44.634-04:00Are we to understand that this BS is the result of...Are we to understand that this BS is the result of collaboration, persistence, critical thinking, and creative thinking?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-52605053424597858832015-05-11T13:20:15.162-04:002015-05-11T13:20:15.162-04:00I agree with everything you've written here, B...I agree with everything you've written here, BUT I think it's a bit unfair to pin the problems on CCSS, which is being used as a Trojan horse to get to do the kid of teaching these people wanted all along. If anything, having common standards solves a massive coordination problem -- they can be fixed for many states at once, instead of piecemeal.Hainishnoreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-25025565157004069962015-05-10T17:58:23.625-04:002015-05-10T17:58:23.625-04:00FedUpMom, That is a fascinating movie--and, yes, v...FedUpMom, That is a fascinating movie--and, yes, very comparable to what's going on with FC. If I recall, the dad sanctioned the documentary in the hope that it would vindicate them, but it seems to do the opposite.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-11226592732981743562015-05-09T08:49:26.348-04:002015-05-09T08:49:26.348-04:00The PARCC problem has an even greater difficulty: ...The PARCC problem has an even greater difficulty: A a student who is truly thinking critically might waste time puzzling over the following issues: <br /><br />1) The problem specifies the number of seats in each vehicle type, not the number of passengers it can carry. Does the correct answer presume that you have added a driver for each vehicle when calculating the total number of people transported?<br /><br />2) If you need to make room for drivers, are the teachers driving a vehicle? So is the number of people in the vehicles equal to 69 students plus 3 teachers plus a driver for each vehicle, or three less than that total since the teachers could double as drivers. <br /><br />Admittedly, the three "correct" answers all exceed any the total number of students, teachers, and drivers, but how much valuable time might be wasted by a student who thinks about this issue?<br /><br />In addition, there is a third issue:<br /><br />Who is driving the vehicles? The problem only mentions three adults (i.e., the three teachers), but no combination of vehicles can accommodate all the teachers and students with only three vehicles. So a student who is thinking critically might well conclude that it is impossible for all the students to be taken on the field trip.Stevenhttp://www.blogger.com/profile/05538580578315800416noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-39901800229850255902015-05-08T22:03:16.421-04:002015-05-08T22:03:16.421-04:00This discussion reminds me of a movie called "...This discussion reminds me of a movie called "My Kid Could Paint That", about a little girl who paints sophisticated abstract paintings -- or does she? It's a similar story about people projecting their own fantasies and desires into a powerless child.FedUpMomhttp://www.blogger.com/profile/00951858601020687242noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-38714975435224791332015-05-07T13:11:27.541-04:002015-05-07T13:11:27.541-04:00The two are also fundamentally not equivalent in d...The two are also fundamentally not equivalent in different way. You could have a kid do about 5 different problems, showing different skills and knowledge in the time it would take them to do the PARCC problem. <br /><br />A better assessment of the strengths of the two tests would be to show the number of problems a child can reasonably do in a set amount of time from each, and see how many skills the child has to master to do well on those problems.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-6570061087276796800.post-59801211505909555682015-05-06T11:44:20.993-04:002015-05-06T11:44:20.993-04:00These things make me so sad. It diverts parents to...These things make me so sad. It diverts parents to trying useless things, wasting time and money on approaches that can never work. They also delay the day when parents accept their child as they really are, and work with that reality to give their kid everything they can.Auntie Annhttp://www.blogger.com/profile/05777983027361603449noreply@blogger.com