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Kids are taught math as pets are taught tricks

I'm sure that publishing this quote from "The Four Pillars Upon Which the Failure of Math Education Rests (and what to do about them)", by Matthew Brenner, page 55, won't be appreciated by some readers. I'm not a math educator but Brenner's comparison of how kids learn math (not sure if he is referring only to the U.S. or not) struck me as so funny, so tragic, and so true all at the same time.

Kids are taught math as pets are taught tricks. A dog has no idea why its master wants it to perform. With careful training many dogs can be taught to perform complex sequences of actions in response to various commands and cues. When a dog is taught to perform a trick it has no need or use for any “understanding” beyond which sequence of movements its trainer desires. The dog is taught a sequence of simple physical movements in a specific order to create an overall effect. In the same way, we teach children to perform a sequence of simple computations in a specific order to achieve an overall effect. The dog uses its feet to move about a space and manipulate objects; the student uses a pencil to move about a page and manipulate numbers. In most cases, the student doesn't know any more than the dog about the effect he creates. Neither has any intrinsic motivation to perform nor any idea why the performance is demanded. Practice, practice, practice, and eventually the dog can perform reliably on command. This is exactly how kids are trained to perform math: do a hundred meaningless practice problems, and then try to do the same trick on the test.

Your thoughts?

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  1. As a retired teacher of high school mathematics I can concur with the heading and the description of how mathematics is taught in the US. In EduSpeak this methodology is called Procedural Learning. The vast majority of mathematics teachers in the US – there are pockets of innovative learning methods and change – teach using a textbook proceeding from one chapter subsection to the next in a ‘monkey see, monkey do’ fashion. Watch me work an example on the board, you try to work a similar example, now practice several more similar examples. Then they move on to a different example and the process repeats. The students are then tested on how well they can work these examples for a grade.
    There is a movement to shift to Conceptual Learning in which the students are supposed to understand as to how and why certain algorithms work in given situations.
    However, the really significant problem is the elementary grades where the vast majority of teachers are not only female but they are teachers who have a high level of math anxiety. (Why did they pick elementary? Because it’s just +, -, *, and /. What can possibly be so difficult about that?) These teachers do NOT have, what Li Ping Ma calls a DEEP and PROFOUND UNDERSTANDING of the mathematics involved.
    These teachers just drill the kids with inane worksheets because they, themselves do NOT know how and why the number system operates the way it does. That’s why they teach PROCEDURALLY = teach the kids math tricks. This problem continues into middle school because most MS math teachers are form elementary school teachers with bridge certification. In high schools this situation continues even though the teachers have specific certification in the HS mathematics subjects. Only in those high schools where there is a strong Department Head, who drives the change to Conceptual Understanding, does this happen. Also, there are those individual innovative teachers who take the risk and on their own move away from a textbook driven curriculum. I know that a textbook is NOT the curriculum BUT just take a look how mathematics is taught in HS; it’s by the book chapter by chapter from front to somewhere close to the back.
    Now, dear readers please do not misunderstand. I am not saying that Conceptual Understanding replaces Procedural. These two work hand in hand where the procedural is much easier to perform when one has a conceptual understanding of the mathematics involved.

  2. The pdf is 165 pages, so it will take a while to read. It looks good from the table of contents. Thanks for pointing this out. Where did you find it?

  3. I agree with Brenner’s critique to a large degree. I agree with Wally’s analysis of the cause. I have yet to find an elementary school teacher in grades 1-4 who either majored or minored in mathematics. I am one of those who believe you should not be able to earn an elementary credential or degree in education until you have read everything Liping Ma (and for that matter Jim Stigler) has ever written.
    If I could waive a magic wand and fix our pathetic math education system I would dump ours and adopt the Singapore math system lock stock and barrel.
    Singapore tells us a great deal about what a world-class math education looks like, and how poor our performance levels in the US really are. Singapore combines the power of focused in depth practice, with a curriculum designed to make what is learned applicable. Take a look at these edtoids:
    Forty Six percent (46%) of Singapore eighth grade math students scored in the top 10% of the world. That means half of their students would rank as top-performing students in our schools.
    No one has done this analysis yet but I wonder how many of our math students would rank in the top 10% in the world if you eliminated the children of math teachers, and immigrants or the children of first generation immigrants from China, India and Japan? No Singapore isn’t another planet.
    At least 75% of Singapore’s math students placed among the top 25% of all eighth graders worldwide.
    Just 1% of Singapore’s math students placed among the bottom 25% of all eighth graders around the world.
    I use Singapore as a comparison for a number of reasons. Including
    1 Singapore’s curricular materials (textbooks workbooks, teacher’s guides) are paperback, in English, inexpensive and available online at http://www.singaporemath.com. Singapore’s Ministry of education has produced a set of PC based math games that align with their curriculum.
    2. Three decades ago the Singapore education system was sub par at best. Singaore is now ranked #1 in the world by TIMSS (International Math and Science Survey) and #2 by PISA.
    3. Singaporeans speak three different languages at home (Chinese, tagalog and English).
    4. The average class size is 40 and the teachers, students and parents don’t whine about it because it has no impact on learning.
    5. 85% of Singapore students use http://www.heymath.com as their supplemental math program.
    6. The Singapore math curriculum used by all of their students, is two years ahead of the US. That is all Singapore 6th graders study math problems and concepts that NAEP defines as advanced for US 8th graders.
    People forget Khan academy is a tool for tutoring not a systematic curriculum for teaching math. However the world has proven you can replace a classroom teacher for the first three grades with an online or semi automated process as has been demonstrated by the use of the APREMAT Spanish language math on the radio program now used by over 2 million students in the jungles of Latin America. APREMAT has been in use since 1999.

  4. As someone who knows a thing or two about dog lore, I would like to note the quote describes pretty stupid dog training practices, too. When dogs learn complex routines, they have to understand them and to find them, for the lack of a better word, meaningful. Well, dogs do not realize they are herding sheep to turn profit for their owner, or protect a country’s borders. But they do understand they are herding sheep, or sniffing for particular substances.

    Of course, the book talks about “tricks” which have no such meanings in the first place. I am a human and I don’t understand the meaning of “dog tricks” either. Ha, maybe THAT is the metaphor here? Not that the meaning of “math tricks” is obscured from kids, but that they have no meaning at all.

  5. I certainly got that feeling as a math student. I’d often ask my teachers, “why do I need to know this?” and “Why do we do things this way?” the only answers I got were “To pass the test.” and “Because that’s the way we do them.” As an adult I’ve found reason and use for some of the things I learned, and I wish so much that I could go back and tell my younger self, “pay attention- this equation will help you calculate the best way to feed your disabled child. That formula helps you evaluate shipping methods on eBay. If you can make sense of these things, you won’t be mislead by the statistics of the Nazi genetic counselor who wants you to abort your child.”

  6. Hi,

    I am the author of “The Four Pillars Upon Which the Failure of Math Education Rests (and what to do about them).” I just want to mention that you can read an executive summary of the (long) essay. Both can be found at:


    Also, I’m happy to receive questions, comments and suggestions directly.

    Matt Brenner

  7. Wally, as an elementary math teacher, I can say that I agree with your comment 110%. Our school is focused on bringing some number sense to our kids. Many, MANY of our teachers do not understand how numbers work, as you stated, and therefore teach the same way they learned things. They are unwilling to change because they don’t understand. They mask this deep deficit by showing how much they “know” about a child based solely on a passing or failing grade on a worksheet. We fight a battle with parents on a very consistent basis because in one grade level where careful steps are being taken to ensure a child really understand WHY they are doing something – the next grade level up holds a very different opinion of what is “right” and therefore teaches to the test in the most traditional way possible. Then after the state test is completed, the teacher feels validated in knowing that her children performed well so she must be a great teacher and her methods obviously work. I was a 4th grade math teacher and saw the GIANT GAPING holes that kids would come in with – all because nobody ever stopped to ask them what they understood. It is very sad that we claim to be lifelong learners – and yet we dig our heels in and refuse to LEARN about what is best for kids in math in the year 2011 – not 1958! Thank you for your post. It is very nice to know that we are not an island – there are others who agree with us!

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