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    HowlerKarma #202308 09/29/14 12:49 PM
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    Val Offline OP
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    Originally Posted by HowlerKarma
    I do think that some things about modern pedagogy in mathematics COULD be very good. It is mystifying to me why it isn't a better state of affairs there, honestly. Because what was done in 1970 wasn't terribly effective for a huge segment of students who had learning challenges or differences, and the pedagogy exists (in spades) to reach that segment now.
    frown

    Yes, it's very strange. Stranger still is the idea that if any of these books are trying to reach that segment of students, they're probably making things a lot harder for them. That mishmash of random ideas I mentioned is primarily responsible for that problem. And there's more; the school's book also uses terms with exponents casually in the absence of any instruction about them. That kind of thing must be crazy frustrating for students (who probably blame themselves for not understanding any of it).

    The pre-algebra book foisted on my second son last year was even worse than the one I described. Chapter 2 (!) had students solving thorny inequalities with variables. The book was full of out-of-place stuff that required a huge amount of background knowledge that hadn't been taught yet. The students were just given recipes to follow.

    Originally Posted by Dude
    DD9 picked out ... [an] earth sciences textbook. She flipped it open to a random page, and as I looked over the disjointed mass of colors, images, and text boxes, I was prompted to say, "It looks like somebody barfed all over the page."

    Yes, the problem definitely isn't restricted to math books. It's pretty much everywhere. Multiply-nested text boxes, indeed. eek

    bluemagic #202337 09/29/14 06:27 PM
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    Originally Posted by bluemagic
    A few years back I complained because the "planner" our school was asking our children to buy was like this. It was crazy, they want to teach our kids to USE the planner but it's impossible to find the page you want. And the page is so busy it's hard to figure out where to write, and then you only get a tiny amount of space. The thing was 3X bigger than it needs to be. It had all this extraneous stuff about schools and even ads. So the kids they are most desperate to get to use it can't even function with it because it's simply too busy.

    Thankfully someone listened because the planner this year is a lot smaller and more streamlines.

    6th grade I had to go make a planner for my son that worked better than the stupid one they made...now her uses his calendar on his phone in 9th grade. I said I was going to market my better planner.

    HowlerKarma #202343 09/29/14 08:17 PM
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    Originally Posted by HowlerKarma
    Well, I've seen a lot of different math textbooks in the pre-algebra through calculus sequence over the past six years or so.

    I have to say that I have nothing much to add to Val's detailed and (IMO) accurate assessment on the previous page. Just one thing, perhaps-- that I suspect that the distracting content is intended to make such textbooks less threatening/intimidating to those children who have math phobia. Unfortunately, they also teach very little in the way of mathematics and numeracy, but they do not frighten students with walls of text or pages filled with derivations.

    {sigh} tired

    I do think that some things about modern pedagogy in mathematics COULD be very good. It is mystifying to me why it isn't a better state of affairs there, honestly. Because what was done in 1970 wasn't terribly effective for a huge segment of students who had learning challenges or differences, and the pedagogy exists (in spades) to reach that segment now. Technology alone makes some things possible that used to be excruciatingly slow and laborious to implement. I have no idea why we've thrown the baby out along with the bathwater here, however.

    frown

    OK... I'll put away my 60's Dolciani Structure Method books for another day wink But, I dispute that anything we might know about pedagogy has actually made it into most modern books. Plenty of old books are better than anything I've seen today for both high and average ability students.

    The best book I've seen for either very young or math phobic folks is Harold Jacobs' "Elementary Algebra". It feels like it is written by a smarter version of your goofy 8th grade math teacher. It has clever engaging examples. It has relevant picture, cartoons, and diagrams widely interspersed. It is written by an actual mathematician. It is recommended by some of the previous Epsilon Camp staff. It is more rigorous than most current texts but somewhat lighter than AoPS, Foerester, or Dolciani... and it has a copyright of 1979.

    My copy of Jacobs' Geometry is from '74. The '86 edition is also fabulous. The 2003 3rd edition is more discovery and light on proofs for some peoples tastes.

    The Jacobs' books are designed to be both rigorous and approachable. There doesn't have to be a tradeoff. Regardless of student ability, I would pick these books from the 70's over any research based, committee designed, standard public school text commonly in use today.

    Val #202346 09/29/14 08:29 PM
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    Man, I know that Jacobs text of which you speak. I LOVE that book. I learned geometry from the 1974 imprint. Love-love-love.

    {sigh}

    What mystifies me is that a few decades' worth of research should have made for a landscape filled with examples like it-- and it hasn't for the reasons that Val illustrates so amply (both in her original post and in the one above).

    Spiraling is a complete disaster in the hands of a publishing industry that doesn't actually pay Subject-Expert AUTHORS to write textbooks. I'm convinced that the people assembling such a dog's breakfast genuinely fail to appreciate that they haven't taught the students some of the things they're presenting out of order.

    crazy Nutty as Christmas fruitcake, but there it is.



    Schrödinger's cat walks into a bar. And doesn't.
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    Originally Posted by Val
    I've been studying algebra and other math books for a couple years now, and I've concluded that it's no wonder so many students are mathematically incompetent. How could they be anything else, given the material?

    I found this article interesting, A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein . He discusses the role colleges of education have played in promoting progressivism in mathematics education. It's one explanation of why math textbooks are so bad.

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    If you haven't read this NYT article about the Japanese method, and it's relationship to historical US pedagogical methods, you might find it worth the time:

    http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0


    ...pronounced like the long vowel and first letter of the alphabet...
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    My daughter's honors calculus course is using some of the Matsuyama-Takahashi-Lampert methods discussed in that article.

    I'm thrilled for her-- it's exactly what she needs to really light up with a subject. That Socratically-oriented approach is so powerful. smile

    I'm just not sure how a textbook fits into that framework.

    Eta my favorite quotes from that article:

    Quote
    Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. “Remember,” Lampert says, “American teachers are only a subset of Americans.” As graduates of American schools, they are no more likely to display numeracy than the rest of us. “I’m just not a math person,” Lampert says her education students would say with an apologetic shrug.

    I've frequently been APPALLED at the level of preparedness in the subject that my DD's teachers have themselves confessed to her (or me)-- while lovely and caring people by and large, there is something very wrong with a high school geometry instructor who "doesn't really understand calculus." eek


    Quote
    With the Common Core, teachers are once more being asked to unlearn an old approach and learn an entirely new one, essentially on their own. Training is still weak and infrequent, and principals — who are no more skilled at math than their teachers — remain unprepared to offer support. Textbooks, once again, have received only surface adjustments, despite the shiny Common Core labels that decorate their covers. “To have a vendor say their product is Common Core is close to meaningless,” says Phil Daro, an author of the math standards.

    Indeed... smirk


    Quote
    He listened carefully for what Japanese teachers call children’s twitters — mumbled nuggets of inchoate thoughts that teachers can mold into the fully formed concept they are trying to teach. And he worked hard on bansho, the term Japanese teachers use to describe the art of blackboard writing that helps students visualize the flow of ideas from problem to solution to broader mathematical principles.

    YES, YES, YES-- this is the kind of dynamic classroom that isn't exactly "flipped" (though I suspect that it is the engine that drives success in flipped classrooms by keeping students actively engaged) and is highly successful for pretty much ANY discipline, and even moreso in STEM where students must master their own internal set of concepts in order to build a framework of real understanding and not just memorization.



    I'm wondering if anyone has read Elizabeth Green's book, which was the basis of that NYT Magazine write up?




    Last edited by HowlerKarma; 09/30/14 01:27 PM.

    Schrödinger's cat walks into a bar. And doesn't.
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    Val Offline OP
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    Originally Posted by HowlerKarma
    Spiraling is a complete disaster in the hands of a publishing industry that doesn't actually pay Subject-Expert AUTHORS to write textbooks. I'm convinced that the people assembling such a dog's breakfast genuinely fail to appreciate that they haven't taught the students some of the things they're presenting out of order.

    Yes, exactly. The Brown/Dolciani books "spiral," but in a very different way than the current circus of books. Brown/Dolciani stay focused on one theme at a time. They present information, provide problems of increasing difficulty...and then, at the end of each section, they give 15-ish mixed review problems that are there to remind you about the stuff you learned last week.

    I ask myself how the spiral idea originated. Maybe someone out there was thinking about mixed review exercises and decided that if 10 milligrams of spiraling worked well to cure forgetfulness, then, boy howdy! --- maybe we should try 10 full grams of the stuff! Dunno.

    I tried a web search, but only found this kind of stuff:

    Originally Posted by Spiral people
    The spiral also builds meaning as children learn to use and understand at a higher cognitive level.

    Originally Posted by The EM crowd
    In a spiral curriculum, learning is spread out over time rather than being concentrated in shorter periods. In a spiral curriculum, material is revisited repeatedly over months and across grades. Different terms are used to describe such an approach, including “distributed” and “spaced.”

    The “spacing effect” – the learning boost from distributing rather than massing learning and practice – has been repeatedly found by researchers for more than 100 years. Findings about distributed learning are among the most robust in the learning sciences....


    In other words, our curriculum has a florid case of ADHD. It can't sit still and it can't focus.


    Some people even say it seems "spaced out."




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    Originally Posted by aeh
    If you haven't read this NYT article about the Japanese method, and it's relationship to historical US pedagogical methods, you might find it worth the time:

    http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0
    That article is titled "Why Do Americans Stink at Math?", but I have not seen evidence that this is the case when accounting for demographics. East Asians do well on international math comparisons, but children of East Asian parents in the U.S. also do well in math.

    Joanne Jacobs http://www.joannejacobs.com/2014/09/japanese-learn-math-in-cram-schools/ linked to a blog post by a Japanese writer Big Doubts on the NY Times Article: "Why Do Americans Stink at Math?" who pointed out that a large fraction of Japanese children attend afterschool (juku) programs, so to the extent that the Japanese are good at math, we don't know if the schooling or the afterschooling should get the credit. And if the afterschooling used the same teaching methods as the schooling, parents would be less likely to pay for it.

    Val #202422 09/30/14 03:34 PM
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    I have added the Spivak and Jacobs books to my wishlist to keep track of for future reference. smile

    This whole subject is why I still have my old textbooks, and why I buy old textbooks at yard sales and library sales -- I figure they're only getting worse, so we can always go back and refer to the old ones if the new ones are incomprehensible. And, indeed, we do refer to the Algebra and Geometry ones when DS's e-school materials leave us scratching our heads.

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