Thursday, November 25, 2010

Mindless Math Mimicry

When the process of learning in arithmetic is conceived to be the mere acquisition of isolated, independent facts, the process of teaching becomes that of administering drill.
Math educator William Brownell wrote this in...


And yet his words feel like they could have been written today to describe how drill and kill, algorithmic instruction continues to hold an indelible grip over math classrooms all over the world.

Traditional education and its legacy of sit and get, do as your told and get the right answer quickly distracts us with its infatuation with behavioral mathematics.

Good math teachers concern themselves with helping children make sense of math for themselves.

Good math teachers understand that we no longer believe that human beings acquire knowledge by internalization, reinforcement and conditioning.

Good math teachers understand the superiority of Jean Piaget's Constructivism. In her book Young Children Reinvent Arithmetic, Constance Kamii explains:
Piaget's theory provides the most convincing scientific explanation of how children acquire number concepts. It states, in essence, that logic-mathematical knowledge, including number and arithmetic, is constructed (created) by each child from within, in interaction with the environment. In other words, logic-mathematical knowledge is not acquired directly from the environment by internalization.
Behavioural mathematics is malpractice for at least two reasons:

Firstly, behavioural mathematics places an exorbitant emphasis on time, and secondly, it convinces kids that product is infinitely more important than process. Both are poisonous pills for any classroom set on intellectual exploration.

Mad Minutes! and its emphasis on time is counter-productive for creating a classroom climate built on real learning. Alfie Kohn explains:
Teachers who want to encourage intellectual growth give students time to be confused and create a climate where it's perfectly acceptable to fall on your face.
A classroom determined to help kids find "right answers" are one's that oddly enough place more emphasis on process than product. Ted Sizer writes:
Good schools promote displays of incompetence (strange as that may sound) in order to help students find their way to competence.
Traditional instruction does not sell learning as a process; rather it teaches kids that math is really about being fast and right. And the best way for kids to achieve this kind of mindless math mimicry is to memorize at the cost of real learning.


  1. HI Joe,

    I see we share a few common gurus, Ted Sizer and Alfie Kohn offer powerful and quotable ideas to the dialogue about real teaching and learning.

    As a math teacher I found that creating the setting where my students would 'struggle' to learn math was essential. How often do we, as teachers, subvert this process through drill & kill and the dreaded "Here! I'll just show you!"

    One of my favorites, Cathy Fosnot, has stated that too often we teach math as if it were a 'dead language'; a set of rules and laws to be memorized, followed and not questioned. This is our challenge- to bring young learners to experiences where they are forced to use numbers and dimensions to recognize patterns and relationships in the act of solving problems.

    Numerical Regards,


  2. Here is the textbook which taught me most of the knowledge of geometry I carry around with me today:

    The hours I spend folding and assembling crystals, stars, and all kinds of wacky modular sculptures, had a more or less permanent effect on me. I still see geometry just about everywhere I go, much to my delight.

  3. I so agree with you. My mum is a maths highschool teacher. It used to really irritate me as a kid that she would never just tell me the answer but would make sure I understood the problem. Of course she was absolutely right! Now I see much evidence of kids in my daughters class who have been drilled by parents/outside coaching in drill and kill maths learning - at the age of 8 primarily abt killer memory for times tables. The teaches (very progressive school) promote real learning in this case, but attitudes of some parents undermine the approach.

  4. Students who make sense of math for themselves do not forget it over the summer. Perhaps if we allow students to really understand math, rather than memorize it, we could put to rest the cry for year-round school. In his book, Share and Compare, Larry Buschman writes that 20 years ago he developed a new instruction model that helped children "make sense of mathematics, apply reason when crafting solutions to problems, learn to communicate their solutions to others clearly and completely, and become confident and capable problem solvers." I wish more students had the same opportunity to understand math.

  5. Two things I thing you'll find to the point:
    1. The best book on math you never heard of:
    Math Miseducation: The Case Against a Tired Tradition by Derek Stolp.
    2. A short YouTube film:
    Jerry Heverly, Oakland, CA

  6. Hi Joe,

    I've been reading your site today and just added you to my RSS reader. It's nice to find a kindred spirit in regards to homework and math education.

    If you haven't already read this, I think you'll enjoy it.