Thursday, September 10, 2009

Old vs. new

Doing some reading I came upon this blog entry about our school system: School Year.

The author, Kateland, finds a lot of problems with our current school system and the way it is going. She singles out the Ministry of Education as being the major cause of the problem. Without agreeing or disagreeing with her assessment of the Ministry, I would like to look at one of her thoughts.

Here is one of her comments: "Apparently it is considered much improved to visualize a group of seven things filled with 8 items each and then count out the answer but I cannot imagine solving algebra equations when I do not know instantly that “X” times “Y” equals “N” without a moment’s thought."

As a Math teacher, I hear what she is saying, and certainly in the past many people have memorized their multiplication tables and learned to solve algebraic equations. But today anyone can do any multiplication on their calculator, or for most students, their cellphone, and I can teach people to solve algebraic equations using algebra tiles in a way that does not require knowledge of multiplication tables. So it does not seem necessary to me that we force all students to memorize their multiplication tables.

I want to be really clear here. I definitely recognize that for many students, memorizing multiplication tables will be useful. But education today has to be about trying to teach every student in the class in the best way possible. Teachers can no longer teach any skill just one way. We need to use all the tools at our disposal, multiplication tables, calculators, algebra tiles, computers, and more to find a way to teach students in ways that they will understand, value, and remember.

To me the key thing as a teacher is to recognize which students would really benefit from memorizing multiplication tables and which students will be fine doing everything on their calculators. Or who should learn to solve equations with algebra tiles and who will simply be faster with the old, more abstract way. That is what teaching has to be about in the new, flattening, globalized world.


  1. Kevin, a few weeks ago I went into a variety store to buy a $1 candy bar. There was just one problem, the cash register was broken and the young man (16-17 year oldish) could not figure out how to do the tax without the cash register.

    Eventually, with the help of a pen and paper I was able to convince him (although he remained a tad skeptical) and then, we hit another bump. I gave him a $2 coin and he could not figure out my change without the machine telling him what to do. Then I taught him to count make change the really old fashioned way - pre-calculator/cash registers. As I was leaving he was on the phone telling the boss they had to close shop over the broken cash register...

    While it is all well and good to suggest some students will be just fine relying on their calculators, nothing replaces real knowledge - learned knowledge or numerical literacy. No one walks around with a calculator surgically attached to their palm.

  2. Well, from my experiences teaching High School, I would say that a lot of teenagers DO effectively have a calculator grafted to their hand. It is their cellphone.

    Still, I agree with you that the education system has failed this young man. But I think that a lack of mental math skills is only part of the problem. To me, his biggest problem seemed to be a lack of willingness to look for a solution to a problem. That is not something that is going to be remedied by teaching him his times tables or how to do percentages, assuming that he would bother to try and remember those skills once the course was over.

    He really needed to be better at solving problems. And skills like problem solving are what the new curriculum is attempting to teach. It is possible that the new curriculum is not succeeding at teaching students to be better problem solvers but then I believe the answer is not to go back to what we used to do but rather to go forward and try to find a way that will make more students better at solving problems.

    Returning to the young man at the store, it is clear that the system did not give him what he needed to be an effective worker. This goes back to my point that good teachers need to figure out what a student needs and give that to the student, rather than using a single approach. It does not matter whether the single approach is "old, tested way" or the "new, fancy way", a single approach will not get the job done in today's schools.

  3. My mother ran into a technical glitch trying to post a comment so she sent her thoughts by email.

    My mother's thoughts on this:
    "Relying on multiplying each sum out on your calculator instead of learning multiplication tables is like relying on a dictionary to look up common words instead of learning what they mean. Very tedious at the very least, if not impossible if the calculator or dictionary is not at hand. There are some things in this life that must be memorized."