tag:blogger.com,1999:blog-8705078887057341738.comments2014-04-22T21:16:53.011-04:00CurmudgeonCurmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger960125tag:blogger.com,1999:blog-8705078887057341738.post-25458062389141237722014-04-22T21:16:53.011-04:002014-04-22T21:16:53.011-04:00Aran, I generally agree with Curmudgeon, but you h...Aran, I generally agree with Curmudgeon, but you have made me think. Yet, I don't think students can get really comfortable with the (very valuable) skills needed to understand statistics or make good choices when buying a house, UNLESS they have some personal ownership of the basic arithmetic and algebra operations, ownership that in my experience young people don't develop unless they can do the operations without a calculator. That's not to say that we shouldn't use calculators once we have that ownership (although I'm careful to keep my hand in with a certain amount of in-my-head and paper/pencil practice).<br /><br />And then there are the students who are going to use serious math later on, and we don't know which students those will turn out to be when they are 14 (though we can make pretty accurate guesses sometimes). Those students may not be mathematicians per se, so much as engineers, accountants, meteorologists, construction managers, radiologists, epidemiologists, supply chain managers, and so forth. They are not necessarily thrilled by the beauty of abstract math, but they have to be very skilled at using mathematical thinking to analyze problems and choose methods for solving them; they are highly oriented towards getting the right answer at the same time.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-10526654311245117622014-04-22T01:09:22.047-04:002014-04-22T01:09:22.047-04:00I'm not talking about making all kids into mat...I'm not talking about making all kids into mathematicians or "city in the clouds" stuff. We need to think very carefully about what we are teaching kids. 90% of what is in the curriculum can be done faster, more efficiently, and more accurately on the smartphone in their pockets. We don't need to teach them mathematical thinking so they can become mathematicians, we need to teach them this so they can use math to reason about statistics they see in the paper or make informed decisions about buying a house. The fact that you say "some day, some of them will get there" implies that you think many of them won't get there. What about these kids? Why are you teaching them? What do you hope they get out of your class? I'm not arguing for "holier-than-thou" math that isn't interesting to them. In fact, I would say that simplifying rational polynomial expressions because they need to do them to solve "all important" limits in calculus is exactly the holier-than-thou math that disinterests them in the first place. Students don't have to try to tackle the Riemann Hypothesis to experience real mathematics. Take the border problem (http://www2.edc.org/cme/showcase/KY/TheBorderProblem.pdf) or this video (https://www.youtube.com/watch?v=Ien-86bXCrI) both of which are by Jo Boaler. These problems are both easily accessible by nearly all students, yet they allow students to explore the concepts deeply. And in both these problems, the right answer is 1) not unique and 2) much less important than the process used to get the answer. If the average person is going to use any of the math we teach them outside of class, it is going to be thinking skills, pattern recognition skills, number sense, or model building. Both experience and research show that they are not going to use the quadratic formula--even if we make them justify it. When was the last time, outside of a math class or an academic setting, that you expanded the product of two binomials? Aranhttp://www.blogger.com/profile/14077578217849158252noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-5709424544945883112014-04-21T18:10:15.879-04:002014-04-21T18:10:15.879-04:00"But when it comes to learning what mathemati..."But when it comes to learning what mathematics really is and learning to truly think mathematically, it's not that the right answer isn't important, it's just that it's irrelevant."<br /><br />And you assume that any more than a small fraction of the students want to focus on math, want to "truly think mathematically" and learn "What mathematics really is"? It's attitudes like that that make your opinion irrelevant to them. <br /><br />Some day, some of them will get there, but they can't just jump directly to your city in the clouds; being so ethereal and holier-than-thou isn't helping to convince them to want to bother.Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-14876239650385019542014-04-20T22:40:45.264-04:002014-04-20T22:40:45.264-04:00I'll agree that to say that the right answer i...I'll agree that to say that the right answer is not important at all sends the wrong message, however I have to disagree with quite a bit of the rest of your post. First, the school board members who say "I've been in business 40 years; every time the right answer matters" are looking at the world through rose colored glasses. Very rarely in business, or really any field, is there a cut and dry "right answer." Answers seem right in hindsight because they work out for the better, and answers seem wrong in hindsight because they don't turn out so great. In the moment, however, those answers are grey and uncertain and what matters is the manner in which a person arrived at them. <br /><br />Beyond that argument, however, I still take issue with your claim that the right answer is step #1. Sure if all we are doing is relatively basic, procedural problems like the ones you posted images of, then the right answer is important. But only because there really isn't much else in the problem that could be more important. The problem is that even if we encourage students to justify their answers or force them explain why rules they applied work, they're not explaining them because they need or want to, but because it's part of the game. We know the answer, and they know we know the answer. This song and dance doesn't encourage them to engage fully with the material. In fact it often encourages them to engage just enough to satisfy their teacher that they didn't get lucky. Or in some causes, the students think "this game is silly, and I'm not even going to play" and then they don't engage at all. <br /><br />The issue, at least as I see it, is that the problems that you use as your examples are just exercises (and these problems constitute the vast majority of what students see in K-12 math). If we don't ever give students a chance to engage in real problems--problems where there multiple right answers or multiple productive approaches--then we are hiding mathematics from them. Expanding (a+b)(x+y) is not math. Explaining why (a+b)(x+y) is also not math. Mathematicians do not publish papers on how well they can repeat back a result that their teacher explained to them once. Certainly, many fields (physics, business, etc.) make great use of the results of math, but we cannot confuse an ability to fluently calculate using procedures in applied situations with learning math.<br /><br />Learning these procedures, learning to get the right answer, and learning to know when you didn't get the right answer are admittedly important parts of being able to be successful in mathematics. But when it comes to learning what mathematics really is and learning to truly think mathematically, it's not that the right answer isn't important, it's just that it's irrelevant.Aranhttp://www.blogger.com/profile/14077578217849158252noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-8270875879159331892014-04-14T16:02:14.270-04:002014-04-14T16:02:14.270-04:00Trade fairs are so vieux jeu. These are both hors...Trade fairs are so vieux jeu. These are both horse & buggy presentations compared to your average YouTube presentation.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-40388333774199678112014-04-14T12:15:42.009-04:002014-04-14T12:15:42.009-04:00This is a great post. At the heart of what you'...This is a great post. At the heart of what you're getting at, as I interpret it, is that "21st century education" hasn't shifted, it has expanded. In the old days, transmissive classroom style learning was the only way to teach...now it's just one of many options available. Unfortunately, many want to ascribe some sort of inherent evilness to that particular style, rather than deciding educational design based on situation. Glenhttp://apointofcontact.netnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-40202907405481034172014-04-13T16:47:03.151-04:002014-04-13T16:47:03.151-04:00I love what you do at Desmos, because it's und...I love what you do at Desmos, because it's undeniably obvious that all you want to do is connect with educators and make math education better. No company can "sell" that. (I think Simon Sinek had a famous book onthat idea...) <br />As a dedicated, thoughtful, reflective teacher, it's frustrating to me to see TI run a booth like this. I have a background in accounting, so I took a look at their 10-K. 4% of their revenue in 2013 came from calculators.. Their statements to their investors explicitly says that their "investments [in the calculator segment] are minimal and growth expectations are much lower." It's like they have this strangle-hold on a market that they their corporation cares very little about. Most people know them for calculators, so they can use that name recognition to extend their outdated, expensive handhelds. Here's a good example of this: They haven't updated the TI-83 in maybe a decade. They did a decent update to the TI-84 and came out with a color version. The calculators don't function differently overall, but the 84 has many more features now (fractions, superscript, log base changing, stats wizards and so on). Yet they keep selling it next to the 84, for $20 less. When you are talking about a $100 calculator, $20 is a big chunk of change making it more attractive to students and parents. Maybe I'm wrong, but do other companies continue to sell their (more) obsolete products right along side their current line? <br />As far as the CEO is concerned, I'm sure if a concerned teacher went to him to complain about frustrations, his response would be, "We still sell calculators?"<br />Again, love everything Desmos comes out with. You've made a great product and connected a lot of educators to one another. Thank you for all you do to help us. mathybeagle.comhttp://mathybeagle.com/noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-87900848759104885432014-04-13T16:07:49.819-04:002014-04-13T16:07:49.819-04:00A lot to unpack here. I want to weigh in here with...A lot to unpack here. I want to weigh in here with a few thoughts. First, there were a ton of big booths and Texas Instrument's seemed, by far, to be the most trafficked. Texas Instruments is the foil that people see when they look at Desmos for one main reason: it has been *extremely* successful -- at sales, at marketing, at partnerships, and even at pedagogy, design, and technology. I learned to program on my TI-83 and loved it. Much as it's fun to denigrate a large faceless company that in many ways is holding onto the past, I think all of us at Desmos recognize how much we have to learn from them still.<br /><br />But to push back -- we had neither a big budget nor a sales agenda. Our goal at NCTM was to have as many conversations with teachers as we could. We wanted to answer questions, to ask our own, to get feedback on our new work, and to chat with the folks who have been supporting us over the last couple of years. <br /><br />I wouldn't want a classroom to look like our booth. But I'd sure love if more exhibitors treated the exhibit floor as a place to learn rather than to sell. I'd love if teachers felt comfortable coming over to TI, Casio, or Pearson to complain to the CEO/CTO about frustrations, or to chat about implicit graphing with the engineer who built it. I'd rather live in that world. Not just because the exhibit floor wouldn't feel like a soul-sucking shark-tank of sales pitches, but because every organization would put out better products as a result.Elihttp://www.blogger.com/profile/04186309206490709215noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-80212915377278327632014-04-13T16:05:12.728-04:002014-04-13T16:05:12.728-04:00This comment has been removed by the author.Elihttp://www.blogger.com/profile/04186309206490709215noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-53037200170825799732014-03-30T19:49:18.556-04:002014-03-30T19:49:18.556-04:00Also--and this is something I pointed out on Twitt...Also--and this is something I pointed out on Twitter--most of those tests are fee-based. If you fail the test and have to retake the test, OF COURSE they'll let you re-take it. It means more money for them.Tomhttp://www.blogger.com/profile/15379096331960338241noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-89663361510591419242014-03-29T09:11:44.415-04:002014-03-29T09:11:44.415-04:00Curmudgeon, what do you think about this: mental ...Curmudgeon, what do you think about this: mental math, short cuts, re-arranging numbers in your head, etc., are very important skills. Anyone who is proficient at the basic operations also still uses the more idiosyncratic ways all the time. BUT, each person ends up using the tricks that work best for them, and they develop a menu of tricks and methods over time, with no threat of failure if any particular trick just doesn't do it for them. To my mind, requiring young children to use complicated tricks in order to solve problems and to write about them, for crying out loud, is a terrible pedagogical mistake.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-69390280356624465052014-03-26T22:26:20.822-04:002014-03-26T22:26:20.822-04:00Yes, math is subject that sustain a lifetime. I ad...Yes, math is subject that sustain a lifetime. I admit back when I was in school, had a hate-hate-hate relationship with math but when the time came that I had to be on my own, I realized that math should have been one of the subjects I should have paid more attention. Layce of Mymathdone.comlayciegracehttp://www.blogger.com/profile/08495019603000697996noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-58047369514406081252014-03-14T10:59:11.462-04:002014-03-14T10:59:11.462-04:00I love your common sense approach. I love your common sense approach. Lsquaredhttp://www.blogger.com/profile/00858524638866166691noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-45139322918436639012014-03-07T16:28:01.279-05:002014-03-07T16:28:01.279-05:00I feel as if I have read, though I cannot tell you...I feel as if I have read, though I cannot tell you where, that literally if the family's income increases due to better jobs that student performance also increases.<br /><br />I also don't see how the funding has been equalized when you hear about Chicago public schools having something like 60 students in high school classes. If the children really need the extra help and support surely the smaller class sizes would be best? It's what private schools strive to do. I agree that the funding may be there, and simply mismanaged (lord knows that I see how much my school spends on needless professional development meetings that would be better utilized by simply having more staff). <br /><br />While I ultimately agree that the things parents do at home certainly have the largest impact on the child, that the culture of poverty isn't something that is always easily overcome, even if the child is exceptionally smart. I work with very underprivileged children who have ultimately given up because they simply can't get their work done at home (online school) because someone is always interrupting them with requests to baby-sit or run an errand or attend to some trifling need of the parent. That the television is not turned off or the noise level reduced when the student is trying to work because that would interrupt everyone else in the house. <br /><br />I recently became acquainted with a young mother in poverty through a friend, and she just simply has no idea of what she is doing as a mother, or a model of how to become a good one. Her 1 month old baby sits in front of the TV, she thinks this is cute that the baby is "watching" The Little Mermaid. She would have greatly benefited from some kind of program that checks in on new mothers in poverty and given tips about ways to interact with the child in a developmentally appropriate way. She will probably never have access to give the baby enriching experiences or visit a public library because there isn't one she can access with no vehicle. <br /><br />I don't know what all of that is to say, except that I'm not sure that it's all about motivation or that some dogged determination leads everyone to the top. Sure it leads some, but I doubt that is the norm. We just hear those stories more frequently than the story of the person who kept trying but remained at a low level due to being passed over for various reasons.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-22089968467821243192014-03-05T10:15:12.976-05:002014-03-05T10:15:12.976-05:00I cannot tell you how thoroughly I enjoyed this po...I cannot tell you how thoroughly I enjoyed this post. It made me laugh so hard. THANK YOU!Stacy S.noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-10343719028515321202014-03-01T06:38:39.604-05:002014-03-01T06:38:39.604-05:00Conclusion: DON'T DO ME... MATH!Conclusion: DON'T DO ME... MATH!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-28241559810858053202014-02-13T07:02:49.667-05:002014-02-13T07:02:49.667-05:00BODMAS
6-1*0+2/2
6-1*0+(2/2)
6-(1*0)+1
6-0+1
7BODMAS<br /> 6-1*0+2/2<br />6-1*0+(2/2)<br />6-(1*0)+1<br />6-0+1<br />7Lucky Hlatshwayohttp://www.blogger.com/profile/07197787460321708476noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-69164113965343468822014-02-10T09:22:30.085-05:002014-02-10T09:22:30.085-05:001/4 brick weighs 3/4 libs, so the whole brick will...1/4 brick weighs 3/4 libs, so the whole brick will weight 3/4 lbs * 4 = 3 lbscamilohttp://www.blogger.com/profile/05761909883894227174noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-1621882415269687152014-02-09T12:06:05.662-05:002014-02-09T12:06:05.662-05:00Differentiation works better on the motivation sid...Differentiation works better on the motivation side of learning than the cognitive side. For example, if students can choose their own research paper topics, they are more motivated. But it doesn't work if some of the students already know how to research a topic and are able to produce a 15-page paper, while others don't know research skills and can only sustain a piece of writing for 3 pages.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-27300122364889996672014-02-02T09:38:09.889-05:002014-02-02T09:38:09.889-05:00Wanting to invent all your own methods and materia...Wanting to invent all your own methods and materials amounts to proclaiming that the successful teachers that preceded you have nothing to contribute to your practice. It's HIGHLY arrogant for a beginning teacher to say this, or for her/his professors to hold that opinion. And it also amounts to saying that alignment between grade levels is useless, and that your desire to invent everything over again trumps the students' need to have access to a tested curriculum. <br /><br />Of course, experienced teachers start with solid curricula (hopefully with the cooperation of their school districts) and then add their personal expertise and knowledge of what has worked well in the past. <br /><br />I would have sunk like a stone as a first grade teacher without a highly structured reading program with good materials. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-56297118094740491712014-01-30T22:24:23.067-05:002014-01-30T22:24:23.067-05:00I did notice that only the left to right order of ...I did notice that only the left to right order of MD and AS were called "truly" arbitrary, so maybe the entire PEMDAS order wasn't being called arbitrary.<br /><br />But in that case, I think the left to right rule is to minimize student errors. Even if they don't know that subtraction and division are "really" addition and multiplication (so PEMDAS is really PEMA), they still have some freedom when working with something like 8-2+1. It's entirely valid to do the addition first, as long as you know to actually do -2+1 = -1, and still end up with the correct answer of 8-1=7.<br /><br />PEMDAS itself isn't the problem. The problem is teachers who don't quite get it, think it's a stupid rule handed down from above, and get angry at a straw man--or rather, a straw Aunt Sally.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-53811881265762484072014-01-30T21:23:41.566-05:002014-01-30T21:23:41.566-05:00I used to think that PEMDAS was "arbitrary&qu...I used to think that PEMDAS was "arbitrary" as well, but try writing a polynomial, say 500-16t^2 for the height of some dropped object after t seconds, using another order. Let's try PASMDE: it's 500-(16(t^2)), if I haven't managed to confuse even myself with my new ordering (or "SAR" to the inexplicably angry math teachers out there)...the point is that there is actually some thought behind the order.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-18499363477936500132014-01-30T08:34:34.679-05:002014-01-30T08:34:34.679-05:00These people who wrote this problem clearly haven&...These people who wrote this problem clearly haven't got a clue. The whole idea of forcing an algebraic problem onto a geometrical situation is hopelessly wrong headed. The other way round, ie finding an algebraic representation of a geometrical problem - that IS math.Howard Phillipshttp://www.blogger.com/profile/18297158336334346872noreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-61087742961835125872014-01-30T08:21:19.153-05:002014-01-30T08:21:19.153-05:00Well, heck! why bother with the periodic table of...Well, heck! why bother with the periodic table of elements? there are other ways to represent those atoms. And why go into Linnaean taxonomy? I think mice look sort of like armadilloes, they must be part of the same genus. Cripes!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8705078887057341738.post-46535558605748772362014-01-30T08:15:20.770-05:002014-01-30T08:15:20.770-05:00The bad news is that even some foreign language de...The bad news is that even some foreign language departments believe in the "embedded" approach. My son dropped HS Japanese because, as he complained, the teacher "isn't teaching us the structure of the language." Anonymousnoreply@blogger.com