Skip to main content

The NY Times has had a series running on math and science education.  There was a comment in a response about expecting students to learn algebra without knowing "times tables.

Now, in my experience, this whole "times table" thing has always been a rote memorization experience designed to torture elementary school students.  That is an example of what is totally wrong with teaching mathematics, or maths as they say in the rest of the world as their isn't just one.  In 50 years of working with subjects mathematical I don't think I've ever remembered those "times tables" that we chanted in what I think was a 2nd grade or 3rd grade classroom.

Students need to learn what these abstract concepts like 7 x 3 mean and develop their own heuristic skill set to work the problems.  But then, even that is the real critical missing piece in learning classical Algebra.  The really important missing skill in mastering Algebra is fractions.  I've taught a little Algebra and wrestling with fractions is the real hurdle for most students because in Algebra, those damn fractions come at you from every direction.

Your Email has been sent.
You must add at least one tag to this diary before publishing it.

Add keywords that describe this diary. Separate multiple keywords with commas.
Tagging tips - Search For Tags - Browse For Tags


More Tagging tips:

A tag is a way to search for this diary. If someone is searching for "Barack Obama," is this a diary they'd be trying to find?

Use a person's full name, without any title. Senator Obama may become President Obama, and Michelle Obama might run for office.

If your diary covers an election or elected official, use election tags, which are generally the state abbreviation followed by the office. CA-01 is the first district House seat. CA-Sen covers both senate races. NY-GOV covers the New York governor's race.

Tags do not compound: that is, "education reform" is a completely different tag from "education". A tag like "reform" alone is probably not meaningful.

Consider if one or more of these tags fits your diary: Civil Rights, Community, Congress, Culture, Economy, Education, Elections, Energy, Environment, Health Care, International, Labor, Law, Media, Meta, National Security, Science, Transportation, or White House. If your diary is specific to a state, consider adding the state (California, Texas, etc). Keep in mind, though, that there are many wonderful and important diaries that don't fit in any of these tags. Don't worry if yours doesn't.

You can add a private note to this diary when hotlisting it:
Are you sure you want to remove this diary from your hotlist?
Are you sure you want to remove your recommendation? You can only recommend a diary once, so you will not be able to re-recommend it afterwards.
Rescue this diary, and add a note:
Are you sure you want to remove this diary from Rescue?
Choose where to republish this diary. The diary will be added to the queue for that group. Publish it from the queue to make it appear.

You must be a member of a group to use this feature.

Add a quick update to your diary without changing the diary itself:
Are you sure you want to remove this diary?
(The diary will be removed from the site and returned to your drafts for further editing.)
(The diary will be removed.)
Are you sure you want to save these changes to the published diary?

Comment Preferences

  •  I don't see how math computation is possible... (18+ / 0-)

    ...without memorization of times tables. They pushed it up to "nines" in my school, but Catholic schools pushed it as far as fourteens in the past...

    As far as fractions go, they essentially ARE algebra, they just don't tell anyone, and each step in solving them builds the the next step, which means any student who doesn't "get" one of the steps is suddenly and irreparably behind...

    Now, ya wanna talk "idiocy in education" try this: the morons who constructed my high school's math lesson plans insisted that we MEMORIZE LOG TABLES....I went from "A's" to "F's" overnight!

    "Ronald Reagan is DEAD! His policies live on but we're doing something about THAT!"

    by leftykook on Tue Dec 10, 2013 at 06:44:44 AM PST

  •  I think of times tables as like scales. (18+ / 0-)

    If you're going to play music well, it takes a lot of practice until the scales are burned into your muscle memory.  At that point, they become tools to use rather than obstacles to overcome.  Times tables strike me as pretty similar.  

    •  right, how else would they be learned? (10+ / 0-)

      In effect, we learned arithmetic the same way--through rote practice--but we had a smaller set of digit pairs to memorize (starting with 0 through 9).

      I think multiplication tables provide a fundamental building block towards other math skills like being able to do division more quickly, and enables quicker understanding of factoring.

      •  Factoring - Bingo! (0+ / 0-)

        It's much tougher to see the relationships quickly when you don't know the times tables. I'm currently tutoring a young man in algebra who is weak in his general arithmetic. He can eventually get to the answers, but it is painfully slow.

        Free: The Authoritarians - all about those who follow strong leaders.

        by kbman on Tue Dec 10, 2013 at 12:47:18 PM PST

        [ Parent ]

      •  The non-rote way to learn the times table (1+ / 0-)
        Recommended by:

        is to learn the patterns.

        Anybody can multiply by 0 (You get 0) or by 1 (the number you are multiplying) without really having to think about it. That's two rows and two columns down.

        Multiplying by 5 is easy. Odd numbers times 5 end in 5, and even numbers times 5 end in 0. The first digit is half of the other number, rounded up. So 5x7 is 2.5 rounded up, or 3, followed by 5: 35.

        Counting by 2s is easy.  (0) 2, 4, 6, 8, who do we appreciate? Half done right there. And then the same numbers over again with a 1 in front.

        Counting by 4s is easy. Count by 2s, and leave out every other one.

        Multiplying by 9 has a simple rule. Take one less than the number to multiply as the first digit, and pick the second so they add up to 9. So 9x7 starts with 6, and you put a 3 with it to get 63. Check it out. Adding the decimal digits of a multiple of 9 always gives a smaller multiple of 9.

        What's left? 3, 6, 7, 8. We're getting there.

        Counting by 3s isn't as trivial as counting by 2s, but it isn't hard. It helps to remember that 3 times an odd number is odd, and 3 times an even number is even. Also, if you add the digits of a multiple of 3 you get 3, 6, or 9. So 3x7 is 21, which yields 3.

        For multiples of 8, the first digit mostly goes up by 1, and the second digit always goes down by 2.
        48 <--The exception, but 40+8 isn't a problem

        Two rows and columns to go, for 6 and 7, except actually you only need to learn how to multiply them by themselves and each other, because we have already done every other multiple of the last two. So

        36 42
        42 49

        Done. Of course, in the classroom, you should take some time to practice each rule and make sure you understand it before moving on the the next, and throw in a few other useful rules, such as doubling: 1 2 4 8 16 32 64 128 256, which is essential for computers, and squares: 0 1 4 9 16 25 36 49 64 81 100, or adding up odd numbers

        0 1
        1 3
        4 5
        9 7
        16…Wait a minute, what's going on here? Ah, for that you need a teeny bit of algebra. And then I would like to introduce you to my friend Galileo, who used that simple pattern to work out gravity. You could look it up.

        All of mathematics should be taught by bringing out the inherent patterns, because real math actually is the study of patterns. Geometric patterns, numeric patterns, logic patterns…And then it's a lot more fun than doing it without knowing why or what for.

        Ceterem censeo, gerrymandra delenda est

        by Mokurai on Tue Dec 10, 2013 at 01:06:48 PM PST

        [ Parent ]

    •  I agree mastering times tables at least to 12 (8+ / 0-)

      and fractions are a building block you will use forever. All elementary school students should know those cold.

      "let's talk about that"

      by VClib on Tue Dec 10, 2013 at 08:38:31 AM PST

      [ Parent ]

  •  yes and no (6+ / 0-)

    algebra isn't the only reason to learn multiplication more or less by wrote.   The practical uses probably outweigh the use of algebra for most people throughout a lifetime.

    One can think of it as a building block that helps many people grasp the other more complicated notions as one works to learn more sophisticated mathematical skills.  As one starts to explore fractions, it removes an impediment to some of the most basic manipulations of fractions.   If you can pull easily the factors of an 'answer' from memory, it is easier to concentrate on the higher level problem of how to manipulate those fractions.  

    It is somewhat like learning to walk.   One's brain performs thousands upon thousands of experiments in spatial positioning versus gravity, until the relationships have become unconscious, the knowledge always there (until injury and old age robs us of flexibility and strength), and not an impediment to what we wish to accomplish.  We take it for granted, we forget the little steps, the falls, the learning process.

    Personally, I always had a few holes in my memory about the numbers, and I still tend to combine real time multiplication with addition and subtraction to reach a multiplication product,  and I am aware it costs me time and increases the risk of error.    I think rote memory should give way to the principles at some point, on the other hand, I know a lot of people who cannot seem to assimilate much more than adding and subtracting, let alone embrace the idea that multiplication is repetitive addition and play with the parts.   For those, rote memorization is probably not a bad idea.

    One of the problems of schools today is that no one and nothing ever seems to advance beyond memorization.   And short term memorization and then discarding the knowledge  triumphs over the rote multiplication tables that tend to stay with people a lifetime.   I do know that the flash cards that were the bane of my existence for a while are no longer used in our local district.  And I hear the teachers complain that the children can't do multiplication, let alone algebra.  

  •  I took AlgebraII-Trig in (7+ / 0-)

    high school, but fell behind when we got to factoring. My dirty secret was that I didn't know my times tables. I had to transfer to a slower, straight Algebra II class. I got As and A+s and was considered the "genius" of the class. I think if calculators had been in general use at that time I would have finally learned my times tables. Spell check has really improved my spelling because I see the correct spelling and finally remember it.

    "The object of persecution is persecution. The object of torture is torture. The object of power is power. Now do you begin to understand me?" ~Orwell, "1984"

    by Lily O Lady on Tue Dec 10, 2013 at 07:05:36 AM PST

  •  Seriously, if you can't memorize 55 things (17+ / 0-)

    in your life, you're not going to do well, no matter what you decided to do.

    My math teacher in 2nd started by having us recite the alphabet, then a few facts that every kid knows (their homeroom teacher's name, what town they live in, what state they live in) and then when we got up to 55 facts, he said, "Okay, that's 55 things that you know, things that you've been able to memorize. And that was pretty easy, right? Well, multiplicaion is the the same thing. We're going to teach you another 55 things, and once you know them,  you'll be able to multiply anything."

    Then he showed us how the 10 x 10 grid on a times table was actually only 55 different problems, since many of the results are repeated (2 x 4 is the same answer as 4 x 2). He also said that 19 of them are ridiculously easy (the 1s and the 10s), that they shouldn't even count. So that brought it down to only 36.

    Once we had those 36 down, we could easily do any multiplication problem, and then division, and then more complex math.

    Eventually memorization improves speed, and improves confidence. It's an important foundation.

    If I wanted to read how much Obama sucks, I'd be on RedState, not DailyKos.

    by ThatsNotFunny on Tue Dec 10, 2013 at 07:06:18 AM PST

    •  That's brilliant (2+ / 0-)
      Recommended by:
      PsychoSavannah, kbman

      And really good teaching, IMO.

      No matter how cynical you become, it's never enough to keep up - Lily Tomlin

      by badger on Tue Dec 10, 2013 at 09:27:03 AM PST

      [ Parent ]

    •  I can memorize entire movie scripts (0+ / 0-)

      but have never been able to memorize the times tables.  I knew someone who memorized times tables up to twenty-five but couldn't memorize a fourteen-line sonnet.

      "Memorizing things" is not a single monolithic skill.

      •  Dad helped me learn the time tables (1+ / 0-)
        Recommended by:

        School only asked us to know them through the 10's, but Dad knew them through the 12's and he taught me.

        By the 4th grade I knew the 10's and from the 1's  through the 5's just by osmosis and what we'd done in school, and I could figure the others out by adding on to the ones I knew. So without Dad helping and encouraging me I probably never would have learned them any better. He found out I didn't really know them when he was helping me with long division.

        So starting in 4th grade, when we were in the car we'd take turns counting by 6 or 7 or 8 or 9  or 10 or 11 or 12.  And after I could always count them off without making mistakes, we started taking turns turns quizzing each other.  And on my own just for doodling fun sometimes I'd make a times table from scratch.  

        Before the end of 4th grade I knew the whole times table and could write one out whenever I wanted with no errors.  By 5th grade I had them down pat backwards and forwards in any format.  It was a big help to really know them when I got to Algebra and Trig -- especially as this was a few years before they started letting students use calculators in math class.

  •  You can learn without it..... (4+ / 0-)

    I've tutored two girls in Algebra who counted on their fingers, and they passed and went on with their degrees.  I would have liked them to be able to know what 4 x 9 was without thinking, but they didn't get that the first time.  BECAUSE they both learn differently from most kids that fit the narrow pipe of education we dole out.  It was a struggle and hard work to find a way they could grasp Algebra, but worth it.

    •  True confession (4+ / 0-)

      I KNOW the times tables, but I have never been able to immediately call them to mind.  When I see 4 x 9, I mentally and quickly go 9, 18, 27, 36.  That didn't keep me from doing very well on the math portion of the SAT, because I really LEARNED algebra.

      It's been more than 40 years since I took a math course, and I rarely used anything more than arithmetic in my work as a lawyer, but I occasionally test myself on the "SAT question of the day," and I never cease to be amazed at how well I can do on many of them that involve actually THINKING about the problem compared to the other people who answered the question.

      Bin Laden is dead. GM and Chrysler are alive.

      by leevank on Tue Dec 10, 2013 at 07:20:51 AM PST

      [ Parent ]

      •  Where do you find the "SAT question of the day"? (0+ / 0-)

        Mother Teresa: "If we have no peace, it is because we have forgotten that we belong to each other."

        by Amber6541 on Tue Dec 10, 2013 at 07:49:19 AM PST

        [ Parent ]

        •  Here you go: (1+ / 0-)
          Recommended by:

          Based on my results when I do it, I think I'd probably do even better on the verbal parts of it than I did back in 1965, but then that's not surprising, given the fact that I've spent the intervening years doing lots of reading and writing.  

          My math scores would clearly be worse than they were back then, since my knowledge of certain aspects of math (such as quadratic equations and solid geometry) has completely evaporated.  But when it involves logically thinking through how to approach a question that involves pretty elementary algebra, I seem to do better than at least half of the people answering the questions.  And to me, unless you're in a technical field, those are the aspects of mathematics that are readily transferable to lots of different fields.

          This is a true story: Another lawyer in the office I worked in and I were working on defending a case involving a toxic exposure.  I observed that we should try to talk in terms of 3 parts per million of the toxic substance, rather than 3,000 parts per billion, since it just SOUNDED smaller, even though it was the same thing.  This other lawyer was actually going to call our expert witness to verify that they WERE the same thing.  I finally convinced the other lawyer that it was obviously the same thing, since 3,000/1,000 = 3 and 1,000,000,000/1,000 = 1,000,000.  This was a bright person who had graduated from a good college and law school, but for whom math was apparently a bunch of calculations from a textbook, rather than a means of solving real-world problems -- even very simple real-world problems.

          I will be forever grateful for having grown up in Urbana, Illinois, where beginning in 5th grade, we started what was really pre-algebra (although they didn't tell us that's what it was) using what were then "new math" approaches involving actually thinking through how to solve problems.

          Bin Laden is dead. GM and Chrysler are alive.

          by leevank on Tue Dec 10, 2013 at 12:55:57 PM PST

          [ Parent ]

  •  But I think it's a much bigger stumbling block (9+ / 0-)

    than you make it out to be.

    Memorizing the times tables means that's one less thing you have to think about when you're learning something new.

    We learned those, and memorized basic addition up to 10. We even had timed drills on it, and on times tables, and on basic subtraction and division.

    It helps. A lot.

    A big part of why kids have problems when they get further in math is because they never really grasped the basics. I like the analogy to scales in music - it really is pretty much the same thing. You have to have the basics so ingrained you don't need to think about them before you can really advance very far.

  •  When the times tables... (3+ / 0-)
    Recommended by:
    Amber6541, Patricia Lil, Dodgerdog1

    ...were taught in my school my grandfather passed away. I missed those two weeks of school - and I have struggled with math ever since. I have to use a calulator or write the problem down and do it long hand in order to solve it. I did make it through college level algebra; however, I do believe that had I not missed those two weeks of class, and had I memorized the times tables I would have been much better at math.

    "Republicans only care about the rich" - My late Father (-8.25, -7.85)

    by Mark E Andersen on Tue Dec 10, 2013 at 07:32:31 AM PST

  •  How would they factor (5+ / 0-)

    if they are unknowing of the base integers?

  •  Memorizing times tables... (6+ / 0-) not rote memorization just for its own sake. It is crucial to developing the skill to do mental math computation, which in turn is really necessary to going any further in understanding conceptual mathematics. It's also an immensely practical tool in the real world, even if you don't pursue a career remotely related to math. Having those tables available to one's mind without thinking about it frees up mental space for more important concepts.

    Really, I think that both are necessary: there is no conflict between memorization of basic building blocks and understanding how multiplication works. It makes sense to teach kids why 7x3 is 21 so that they can work it out by following an algorithm, but it's ridiculous to say that they should use that algorithm for such basic calculations without ever just memorizing answers and moving on. Yeah, I can come up with the answer to 9x8 by counting on fingers or with blocks, but it would be a waste of time to do so. Rapid mental math makes so many more complicated tasks so much faster and easier.

    I think a lot of things I learned in my Catholic elementary school were a waste of time (such as all the futile years spent trying to learn to write cursive handwriting neatly), but multiplication tables are not remotely in that category. They aren't even hard or particularly time consuming to learn; we had pretty much finished with them by third grade or so.

    •  Another way of saying that is that (4+ / 0-)

      how your learn something affects how you retrieve it. If you can spit out the product of two (single-digit) numbers without running some algorithm or resorting to a calculator, you're much more competent doing things where that's valuable. If you can retrieve it quickly that way, you can get through the mundane mechanics of solving a problem more quickly and proceed to the more interesting or useful results.

      It isn't just algebra - a lot of learning science uses numerical or symbolic problem solving to demonstrate the relationships between things.

      The example I always liked from ed psych was months of the year - anybody can rattle off the months of the year in chronological order. Try doing it in alphabetical order. That takes facts you know (the names of the 12 months) and an algorithm you know (alphabetizing), both things you know really well, and applying that simple knowledge without resorting to paper is almost painful. It's the same for some applications of multiplication in math and science.

      No matter how cynical you become, it's never enough to keep up - Lily Tomlin

      by badger on Tue Dec 10, 2013 at 09:37:29 AM PST

      [ Parent ]

  •  Times tables are uninteresting (3+ / 0-)
    Recommended by:
    johnva, antimony, Batya the Toon

    I can't remember who it was who said that they are merely an algorithm to arrive at an answer. Using a cheap calculator is another algorithm to arrive at the same answer. One is not inherently better than the other. The time spent learning tables is time not spent learning other, more important things.  It's a trade off.

    The important thing in either case is to understand the concept. If you don't understand you will not be able to do algebra and you will not be able to understand fractions.

    I have a friend who was a math teacher in the grades where percentages (fractions) were taught.  He said he could always tell who would do well in math in higher grades by how easily they grasped percentages.

    •  I agree that they are just a specific tool... (1+ / 0-)
      Recommended by:

      ..and not a particularly interesting one. But mental math is way faster than using a calculator when we're talking about basic multiplication tables. So I would argue that memorization IS inherently better than using a calculator. I agree that it can be taken too far (it would be a waste of time to memorize log tables, or multiplication up to 50x50), but the basic factors are really, really recurrent in all math. So it's important to give people the most efficient tool for that particular case.

      They don't need to spend 5 years on it, but spending 6 months will SAVE time for the more important stuff down the road.

  •  Sorry, that's a bunch of bullshit (7+ / 0-)

    Anyone who wants to do any math (higher or otherwise) needs to just KNOW the multiplication tables.

    Yes, the kids can learn WHY it's repetitive addition, but there is no substitute for just knowing them....being able to recall them quickly and effortlessly.   And I honestly believe the sooner our schools get away from arrays, and "draw this equation" bullshit and just make the kids memorize it, the sooner math scores go up.

    I have a grandson in 5th grade.  I recently proctored the state assessment tests.  Watching the majority of the class counting on their fingers to do 6 x 7  and 8 x 9 was maddening to me!  In 5th grade!  It was how they learned it though, and instead of making them just memorize it all with an underlying knowledge of how you get the answer, they only know how to keep adding.  Time waster of the highest degree and once they are done counting, trying to remember where they left off to find the value of "x" is long gone from their brains.

    Not every kid learns the same, that is true.  But most everyone can memorize.  I see the kids who swear they can't memorize a math fact, but can rattle off every Star Wars character ever created, including the damn Clone Wars.  So, it's complete and total bullshit that "there are so many kids who just can't.  Waaaaah!"  Quit coddling the little fuckers and make them KNOW it.

    Listening to the NRA on school safety is like listening to the tobacco companies on cigarette safety. (h/t nightsweat)

    by PsychoSavannah on Tue Dec 10, 2013 at 08:15:41 AM PST

    •  Nope. (0+ / 0-)

      Memorizing math facts and memorizing literary facts are entirely different skills.  I have the latter but not the former.

      I never memorized the times tables, and I consistently aced my math classes once we got into higher math and they allowed us to use calculators.

    •  Actually, pure mathematicians do almost no (0+ / 0-)

      arithmetic, and applied mathematicians such as engineers, actuaries, and statisticians have so much of it to do that they use computers for all of it. Commercial arithmetic used to be important, but now cash registers compute and dispense change, so store clerks don't have to. Your computer CPU and GPU do a fantastic amount of arithmetic every second, just rendering fonts and calculating and displaying other graphic images, or decoding music and video files, but you don't have to know how any of it works.

      The people who are serious about arithmetic are Japanese schoolchildren who set out to become competitive in national abacus contests. Some of them practice so much that they can eventually do it without the abacus.

      Ceterem censeo, gerrymandra delenda est

      by Mokurai on Tue Dec 10, 2013 at 01:23:36 PM PST

      [ Parent ]

  •  Also, about fractions.... (4+ / 0-)
    Recommended by:
    Radiowalla, PsychoSavannah, jfromga, kbman

    Fractions are just multiplication and divison in a new notation and organization. I agree that they are where a lot of people start to have trouble with math, but I'd argue that the reason for that is precisely because they don't have a strong grasp of basic multiplication beforehand. IOW, someone struggling with fractions is just their fundamental lack of skill at the basics showing up. Because fractions is where it starts to get difficult if you don't know how to quickly multiple and divide. And you can't quickly multiply and divide if you haven't memorized the basic tables.

    All of math is basically an increasingly complex and elaborate series of abstractions built on lower level abstractions. The problem people have with it is that they are forced to move on to higher abstractions before they really intuitively "trust" the lower levels. And you can't gain that trust without a large amount of practice and repetition. Otherwise, factors are just magic numbers that come out of a calculator.

    •  Definitions, rules, and processes ... all made up (0+ / 0-)

      This is part of what I tell the students I tutor, that math is purely invented, that there is no math out there in the world in the same way that there is a chair or an orthopedic foot massager. This seems to help in the sense that they no longer think there is something fundamentally real about math that they just can't get or can't see.  No, we made it up. There are reasons for it, wanting to gain power in certain domains in life by being able to quantify and predict, but those needs are what drove the creation of the math. The math wasn't there ahead of time.

      (OK, in some cases in higher level mathematics, the imaginings of mathematicians have created functions which have later proven useful for finding solutions to physics problems, but none of my students are working at those levels, just struggling to get through their math requirements.)

      Free: The Authoritarians - all about those who follow strong leaders.

      by kbman on Tue Dec 10, 2013 at 01:19:03 PM PST

      [ Parent ]

    •  No, we can teach fractions visually (0+ / 0-)

      with pie slices before we get to multiplication. You are confusing conceptual understanding, which is always essential, with facility in calculation, which no longer is. I use computer languages that have fractions, aka rational numbers, built in, so that I can say, for example,

         1%2 NB. 1 divided by 2 yields one-half.

      where % is used for the division function, NB. is a comment symbol (from Latin Nota bene, Note well), and r is part of the notation of a fraction. Then I can say

         1r3 + 1r6
         2r3 % 3r4

      Ceterem censeo, gerrymandra delenda est

      by Mokurai on Tue Dec 10, 2013 at 01:33:55 PM PST

      [ Parent ]

      •  I'm not confusing them. (0+ / 0-)

        I'm arguing that the two go hand in hand, because I disagree with you that facility in calculation is no longer essential (at least on very basic stuff like multiplication of single digit numbers). Mental math is a better, faster tool than calculators are (and I'm saying that as someone who loves calculators and computers) for this basic stuff. And I believe that it reinforces the conceptual understanding, because seeing a lot of concrete examples of a rule makes the rule make more sense.

        I'm not arguing that people should go to extreme lengths to memorize stuff, but I do think they should for the basics. Those who do that AND learn the concepts invariably have deeper understanding of the concepts.

  •  Memorization is (6+ / 0-)

    an important part of learning.  A basic foundation is needed - everything from abc's to times tables to Shakespeare starts with memorization - in order to free your mind to more easily work on advanced material.  

    •  I don't understand why... (5+ / 0-)

      ...this "rote memorization" vs. "conceptual understanding" debate is always presented as an either-or thing. I think that both are necessary, and my schools taught me both. You can't understand concepts without coupling them to memorization, and you waste time on memorization if you don't couple it to conceptual learning. They reinforce each other, rather than competing with each other.

      And yet frequently these things are presented as if they are at odds with each other by proponents of one educational fad movement or another. I guess that makes sense if your goal is just to make a name for yourself or sell textbooks, but I think if your goal is education then the name of the game is balance between these two things (repetition vs. understanding).

      But I guess balance is hard because it requires actual skilled teaching rather than following a recipe from a book.

      •  The amount of memorization that is useful (0+ / 0-)

        depends on what you want to do with the information. Memorization of vast quantities of information is essential for doctors, lawyers, musicians, and actors, all of whom have to be able to perform in real time on demand. For most other professional purposes, understanding is much more important, and the amount that has to be memorized is much less.

        Before printed books took over in education, memorization was vastly more important, and the educated put in a huge amount of time on it. See The Memory Palace of Matteo Ricci, by Jonathan Spence, for a historical example of the process at the intersection of Chinese scholar-elite Confucian culture and Western Catholic missionary zeal, and the need felt for it on both sides of that divide.

        Ceterem censeo, gerrymandra delenda est

        by Mokurai on Tue Dec 10, 2013 at 01:44:56 PM PST

        [ Parent ]

        •  I mostly agree with this. (0+ / 0-)

          But there are also studies out there that pretty much prove beyond doubt that repetition is necessary for learning most complex tasks. You can understand something conceptually and still not be able to practically apply it if you haven't had enough practice in doing that.

          The concept of musical scales are pretty simple to understand. Teaching yourself to automatically remember them when playing the piano takes practice. I don't see this as much different.

          I agree that most things don't need to be memorized these days; as a software engineer there is no way I could ever memorize all of the APIs I use without needing to look at a reference each time. But arithmetic on a basic level is a basic life skill because it's completely pervasive. Not knowing basic computation is like being illiterate in our society, given the degree to which numbers rule our lives.

          A basic example is pricing: how do you compare the unit price of two different sizes of a product if it's not marked on the shelf? Yeah, people can pull out a calculator at the grocery store to compare them, but they might not even think to do that without a general understanding of arithmetic (and I guarantee that takes more time than just estimating in your head, once you have that skill). So instead they start relying on heuristics that are sometimes wrong (like "the bigger size is a better deal").

          I can't imagine what it would be like to not know arithmetic. It'd be like being blind, in how much you would miss.

  •  Tables are useful. (1+ / 0-)
    Recommended by:

    But shouldn't be held up as the be all and end all. When I was being miseducated in math in Catholic school by the nuns, the tables helped. We didn't have hand held calculators, and the memorizing the tables sped up the calculation process, and avoid the errors of doing multiple calculations from scratch. I never bothered to memorize them myself, because my mind tended to pick up the tables and remember the tables.

    But I had this wacko violent psychopath nun who was obsessed with the times table. I had her for math in the 5th and 6th grade. "I can teach you all sorts of fancy math, but I can't do anything unless you know your times tables," she would say. Wrong on a few counts. She couldn't teach her way out of a paper bag, for one thing. And of course you can teach fancy math to someone who didn't know their times tables, but it would take them forever to do the problem. They could get the concept, but it would take them too long to do to pass a test.

    She loved catching kids that didn't know the tables.  She'd scream at them, pull hair, bang their head against the blackboard. He religious order is called "The Sisters of Mercy." They ran the those laundries in Ireland, and also the medical corp for the Confederacy during the Civil War. Gang of organized sociopaths.

    Just another underemployed IT professional computer geek.

    by RhodeIslandAspie on Tue Dec 10, 2013 at 08:52:06 AM PST

  •  agreed! (1+ / 0-)
    Recommended by:
    Batya the Toon

    I knew how to use both regular and reverse-polish notation on calculators, and some of the beginnings of how to program a computer, plus a basic understanding of how base-10/base-2/base-16 worked in first grade -- I was a smart, computer-loving kid.  I also was dead-last most of the time on timed times-table tests, which our school ran competitively -- grades were based on your rank (as long as you had them all correct), and it was very visible because kids ran up to hand in their papers as the teacher sat with a stopwatch.  

    I saw absolutely no need to get faster.  I've biffed basic computations while writing on the board in graduate-level mathematics classes, and just gotten "none of us can add/multiply in our heads" chuckles from my classmates/professors.  

    Understanding how it works is key.  Memorizing up to 9x9 is useful, but not that important; memorizing beyond that is silly, IMHO.  

    P.S. I still have a little jolt of adrenaline when I have to add 5+8 or 7+4 together -- for some reason, I always flipped those as a 6-year-old and thus they make me nervous.  

    •  7+4 is actually one that gives me no trouble (0+ / 0-)

      and it's because of Tom Lehrer's song "New Math."

      I had (still have) that song memorized, and it includes the line "seven from eleven is four!"  Which meant that any time I saw any two of those numbers, I could find the third.

    •  I always (0+ / 0-)

      move a one if I have a glitch on simple addition, as in 5+8 is 4+9 which I never have trouble with.   But it is sad not to be able to add.   I frequently tell people I understand a lot about math but can't do arithmetic.  Understanding how is a much underestimated skill.  I am always amazed how people can't anticipate the outcome, so take whatever their calculator spits at them.  I see it at work where a computation is basically going to produce a fraction as a proration of annual figures for reports, etc.,  and people can't tell they didn't get something in the neighborhood of  1/2 the annual figure and catch a mistake before it gets typed into the spreadsheet or other program, etc. If I happen to be working with someone and the number pops up I can say right away, that's not right, redo that and they just ask, how can you tell, did you do it in your head and I say, not the actual number, but it isn't anywhere near half or 30% or whatever,  they just can't see how the math problem works.

  •  I live in a numberless world. (1+ / 0-)
    Recommended by:

    This isn't to say that there are no numbers there, but I am number-blind.  Spouse is always counting things and solving mental math problems.  I am oblivious and happy to let someone so gifted do all the heavy number lifting.

    As a result, I have forgotten almost all the math I once knew.
    Have to stop and think about the times tables and can't solve simple equations at all.  I just forgot the moves…

    This I consider to be an alarming liability and I have often said to myself that I have to take the plunge back into math.

    But sloth always seems to win out when push comes to shove.

    This is my confession.

    It's the Supreme Court, stupid!

    by Radiowalla on Tue Dec 10, 2013 at 10:00:57 AM PST

    •  There are huge parts of math with (0+ / 0-)

      no numbers and no algebra. You might enjoy Tilings and Patterns, by Branko Grunbaum and G. C. Shephard. It does have numbers in it, but you can ignore them. Or you could try any of Raymond Smullyan's logic puzzle books, or Hofstadter's hilarious Gödel, Escher, Bach. Don't believe anything Hofstadter says about Zen, however, particularly his mixing up the paradoxes of the Greek Zeno with the koans of the Chinese Zen Patriarch Eno.

      Ceterem censeo, gerrymandra delenda est

      by Mokurai on Tue Dec 10, 2013 at 01:55:56 PM PST

      [ Parent ]

      •  Right you are and thanks for the ideas. (0+ / 0-)

        I do need to brush up the computation skills because real life does require one to be able to manipulate numbers with some amount of skill.  I hate feeling so inept.

        It's the Supreme Court, stupid!

        by Radiowalla on Tue Dec 10, 2013 at 04:51:05 PM PST

        [ Parent ]

  •  I remember crying (0+ / 0-)

    while my mother drilled me on the times tables. I never did get them memorized.

    Algebra can be interesting for those who like puzzles, irrespective of what use one's supposedly able to put it to. Of course, that was my problem with math(s); I could never figure out of what use algebra would be. It seems to me, if you want to teach something like algebra you should start with the problem algebra solved. If I never need to solve the problems algebra proved so useful in solving, what the hell would I ever need algebra for? I do okay in algebra classes, but I forget most of it shortly after the class is over because I have no idea how to use it in a practical fashion.

    •  Was she drilling or making it into a game? (0+ / 0-)

      My Dad made it fun.  We were actually drilling, but it never seemed like that was what we were doing.

      •  how did your dad make it fun? (0+ / 0-)

        I can't imagine it.

        •  I think it was his attitude about it (0+ / 0-)

          he thought it was fun, so I thought it was fun.  We did it the same way you play the alphabet game when you travel, or the way we tried to name the street signs before they were close enough to read when we were driving in our neighborhood.  

          We didn't do it for a long time.  We'd do each set a couple of times and then we'd do something else, but we did it often.  If Dad was running an errand, I was tagging along with him at that age so we were probably doing it at least 5 times a week.

          There was no pressure, if I couldn't figure out the next number in the series in less than 4 seconds or so, Dad would say it, and move on down the list.  

    •  If we know how signups at, (0+ / 0-)

      the state exchanges, and Medicaid have been going (at least roughly, as we do), and we know how many we want signed up by what date (as we also do), we can use algebra to estimate how we are doing. Check brainwrap's diaries on the subject, and my comments.

      Does the prospect of using such information to take back the House next year rouse your interest in any way? We can apply algebra and statistics to politics in a multitude of other ways as well.

      You obviously do not have to know how to set up or solve algebraic equations to live your daily life, but you might possibly be interested in how much algebra others have to do, or set up for computers to do, to support your daily life.

      Ceterem censeo, gerrymandra delenda est

      by Mokurai on Tue Dec 10, 2013 at 02:12:11 PM PST

      [ Parent ]

      •  my point was (0+ / 0-)

        if I'd been taught algebra in ways that "support [my] daily life" it would have seemed useful and maybe would have stuck. I was not taught algebra in any such way.

        Rather than tell me how exciting algebra is - and that I'm "obviously" such a dummy for not getting it - SELL me on algebra by demonstrating how FUN and USEFUL it is and that I could DO IT MYSELF. You are under no obligation to do that, but then none of my teachers in all my years of schooling seemed to know how to make algebra an obvious support for my daily life either - that is, if they had any such notion anyway.

        Difficult as I found it, I did see useful aspects of statistics. Not much has stuck with that either, but you conflate the two: "We can apply algebra and statistics to politics in a multitude of other ways as well." Are you saying they are the same thing?

        •  I'm not tellng you that you are a dummy (0+ / 0-)

          Where did that come from? I have to ask because I have one of those neurologies that makes it hard for me to predict or understand other people's reactions to what I say.

          I'm inquiring whether you have an interest in something that I sometimes work on, something that is useful that you could also do yourself. Whether it would be fun for you is something you have to tell me.

          If you want other forms of fun and usefulness and doing it yourself with algebra, and you suspect that it can be so, I can certainly make some suggestions, after asking a few more questions. PM me and we'll talk.

          I edited a computer algebra book two years ago, one based on Free Software available to anyone at no charge. The title is Algebra: an Algorithmic Approach. I'm currently editing a book on the Free GeoGebra software, which combines algebra, geometry, and an approach to programming that has been tested and works with elementary school children.

          Ceterem censeo, gerrymandra delenda est

          by Mokurai on Tue Dec 10, 2013 at 03:22:35 PM PST

          [ Parent ]

          •  I heard criticism you didn't intend, it seems (0+ / 0-)

            My experience with math education has more frequently been torture than pleasure. As it is, I'm relieved I don't have to deal with math much.

            If I can imagine a reason to take the stuff up again, it's encouraging to learn that there may be ways to get back into it that are an improvement over my grade school experiences of the 70s and 80s.


            •  If you can stand to tell us about the torture (1+ / 0-)
              Recommended by:

              I can explain how it should be done. My mentor was taught the total nonsense that

              A variable is a number that can change its value.
              Any child knows that 2 cannot become 3, and programmers shudder at the thought of what would happen if it could. Most let this silliness slide by. She didn't, and was bollixed for 40 years. I explained that there are no variables, thought of as objects. There are only variable names, which act as pronouns. Any of them can refer to any object desired, just like "it". But unlike English and other natural languages, we can have as many pronouns as we like in math and programming.

              Ceterem censeo, gerrymandra delenda est

              by Mokurai on Thu Dec 12, 2013 at 09:46:30 AM PST

              [ Parent ]

Subscribe or Donate to support Daily Kos.

Click here for the mobile view of the site