To improve EQAO math scores, ON teachers should include drills

Originally published on February 6th, 2014.

As a former teacher, and later, a learning specialist and teacher-educator, I can confirm that it is acceptable practice when Ontario teachers use problem solving and discovery math approaches.

Yet, something is not quite right, otherwise there would not be a decline in EQAO standardized test results at the Grade 3 and 6 levels.

Some say the “problem” is too much “problem solving” and “discovery math.” I don’t believe that is the case. Rather, I think it is just that something is missing — multiplication table memorization and old fashioned basic skills drills.

First, however, I would like to clarify why blanket reform of how math is taught in Ontario is not necessary. Discovery math has been around for a very long time. It simply means a child is provided with a math related problem and in the solving of that problem, not only build on math skills they already have, but learn new ones through trial and error.

For example:

Back in the late 1970s when I taught Grade 5 math, I taught measurement by discovery. The preamble the students were given was that the classroom had been destroyed (by fire or flood) the night before and everything had to be replaced. They were provided with a sheet of paper that had the prices for all the replacement products. They then had to measure the floor and chalk/bulletin boards to know how much tile/slate/wall board was going to be needed and how much it would cost. By the time they were finished, they had indeed “discovered” everything they needed to know about measurement.

However, that was not the only way we taught. Over and above regular lessons, I had daily oral time tables practice and daily computational written drills.

Now, think about it. Above, I was talking about a measurement discovery exercise that today’s parents (now 40ish) probably experienced because that math curriculum unit was in an Ontario province-wide Junior level ministry document. Yet, when we did that, we not only didn’t yet have personal computers, we didn’t have fax machines or cell phones either. And, that is just over thirty years ago!

So, change and discovery is non-stop as is technological invention. Reform that goes back in time is simply not the right direction we should be moving our children. However, that is not to say, Ontario’s curriculum planners and teachers should not include the kind of standard lessons and drills we did back then within today’s curriculum mix. They should.

That the Ontario Liberal government is going to put $4 million into teaching teachers math skills is rather strange, unless the teachers in the classroom today were never taught the basic skills in the first place. Since it is not that many years ago that I taught prospective teachers, I doubt that very much. Rather, I think it is simply government covering over a problem with a band aid.

The crux of the matter is, then, that for Ontario’s children to improve on EQAO standardized math tests, teachers need to be encouraged and allowed to integrate old fashioned math practices, which as I said above, needs to include the memorization of timetables and basic number facts, into their current problem solving and discovery approaches.

22 thoughts on “To improve EQAO math scores, ON teachers should include drills

  1. Thank you Sandy for pointing out what seems so common sense.
    As for using discovery methods, I dare say that you didn’t expect your students to ‘discover’ how a ruler worked though. At some point in the first primary grades someone had to explicitly teach, for instance, what and how big a cm is, that there are 100 cm in a meter, what is a meter stick, that It has 100 cm on it and how to hold it up and line it up in such a way to see how long something is…etc.

    Good post!


  2. I am a retired teacher who agrees completely. If a child must continue to discover over and over again some basic math such as multiplication facts, he cannot very well handle more complex problems. He may understand the steps to reach a solution but if he has to go back to rediscover that 5X6=30 and 9+18=27 he will not progress very far. Somewhere along the line discovering has to become knowing. Drills can help that knowing.


  3. Old lady — The “knowing” that you are referring to then becomes the pre-requisite knowledge upon which new “knowing” is added — and so on.


  4. If you haven’t had a look at the Nelson series of math textbooks, drills aren’t the only thing missing from math education in our schools. The supporting resources are horrible for teachers, parents and students.

    I had two children, three years apart in the system at the same time. One child had terrific old-school primary teachers who did do drills and required lots and lots of practice. I didn’t find out until much later that these teachers took a lot of heat from their principal and their newer colleagues because they stuck to Saxon math and methods of drills that they knew WORKED.

    The other child, three years later did not have the benefit of drills, practice or Saxon math where one would master the basics first before moving on to more complex work. Discovery math without the basics results in some stark discoveries later on in post-secondary….and yes, students who haven’t a clue about basics actually do make it to University and College.


  5. bonefishcove — It’s common sense. I don’t understand how educators can forget about pre-requisite knowledge and repetition until a skill is learned. There is also developmental theory. Discovery and problem solving are fine as reinforcement but as Old Lady said, the only way you can “know” something is to repeat it over and over. I mean even John Dewey proved that with his “learning by doing.”

    Returning to drills has to start at the top. It’s obvious that Ontario’s Liberal government is intimated by the unions. Drills are hard work for a teacher and unions fight that I guess.


  6. Doretta — Sorry about that. I found your comment in the spam filter. It is a good thing I checked each spam before deleting. Anyway, as I just said to Old Lady and Bone, drills and practice should just be common sense.


  7. Somewhat off topic Al but I understand you just had to jump for joy. Frankly, I don’t know how any environmental group can claim they are a charity — unless they rescue wild animals or something similar. Civil disobedience, on the other hand, hardly qualifies.

    The point of this post is math drills, not oil drills. But, O/T voices have never been a huge problem at CotM. 😉


  8. In order for teachers to be able to teach those drills though they have to know some basic math themselves and be able to teach it. I heard a young teacher quip that her instruction at teachers’ college on math instruction involved no arithmetic at all. WHAT!!!!

    So what we’re getting are new teachers teaching math who have been taught in the same way that they’re teaching their students. Recycled bad methodology will get us nowhere fast.

    When my daughter’s 4th grade elementary teacher didn’t feel comfortable teaching math, the principal taught the class.


  9. Bone at 10:41am. “Didn’t feel comfortable?” A depressing thought but likely true.

    A primary/junior elementary school teacher’s certificate qualifies a teacher to teach ALL subjects. An intermediate level or high school qualifies a teacher to teach two subject areas — although at the high school level, one is primary.

    Yet, in some smaller middle schools, teachers have to teach both language arts and math to their homeroom Grades 7 or 8. Given you are talking about Gr 4, that teacher should be fired, not compensated by her principle.

    Which brings back memories. I even had to teach some music and believe you me, that was a challenge. I can sing in a group but not on my own. Luckily I could play the piano. However, for all the years I taught at the primary/junior level, what my fellow teachers and I did was share subject areas in a mini-rotary arrangement. I was an art specialist so I taught all the primary/junior art and two of the other teachers shared doing the music and phys ed. But, we were all aware that if one of us was sick, we were on our own.

    Certainly no principal should ever teach anything for a teacher on a regular basis. The OCT certificate states: All subjects at the primary/junior level. End of story.


  10. I won’t introduce the topic of “oil” to do with drills here… Very good stuff, Sandy! That is true education. On to a different age group of students, we had the misfortune of seeing my son lose his interest in Math in Grade 11 because of a husband and wife pair of secondary school “teachers” who would be better suited as facilitators at the university level. Leaving kids to “sink or swim” by being self-taught online is not really “teaching” anything. Anyway, now the lad is almost through his English major and looking at his Masters, so life does go on, when a passion is identified. Still, there is some regret for kids who’ve been victimized by the system. Math should be made fun and interesting, as you’ve described and illustrated from your experiences, Sandy. Then, it does naturally follow that the follow-up “self-teaching” will come on its own accord. The so-called educational system needs to take a closer look at the developmental changes in students’ thought processes, and not just let the self-acclaimed teaching specialists run the show out of alignment. These are nothing more than counterfeit educators collecting an easy paycheque.


  11. ” Leaving kids to “sink or swim” by being self-taught online is not really “teaching” anything.”

    Tripper – this is happening way more often than we know. Especially when there is no teacher qualified to teach it, as happened in our high school a few years ago. They didn’t have a teacher who could teach calculus so they offered it on-line “taught” by a teacher from somewhere else. Calculus isn’t one of those subjects that should be taught on-line because so very few students have that kind of discipline….AND, it’s a requirement for so many post-secondary disciplines.


  12. Thanks bonefishcove. We had a great high school Math teacher in my day, and though I can’t remember much about it these days (if you don’t use it, you lose it), I used to love Calculus. When I got to College, it was just a review, so I could excel at it and boost the overall average of my core subjects. You’re right about the discipline. I find that comes later on in post-secondary levels, whereas it is a severe misjudgment and lack of responsible teaching to float those students prematurely. It’s an injustice to their right for a decent education, and a misuse of municipal taxes. Hopefully the new generations aren’t damaged irreparably because of it, as they shall be our next leaders.


  13. Interesting article Bone. I guess I should have referred to my notion of an “integrated” approach as a “blended” approach. The notion that her child did not understand fractions is scary. Yes, Canada and most countries use the metric system which is all decimals. But, we live in a global economy and there are still places, like the U.S., using Imperial. Imagine, then, going on a vacation south of the border and not knowing what “1/3rd” means.


  14. Edu-babble alert: I need to explain something but if the reader does not want to know, don’t read any further. 😉

    My Ph.D dissertation was about the role of teacher beliefs (world view, ideology) on teaching and learning. I used my thesis supervisor’s model (J. Miller’s book is called Curriculum Orientations) which expressed the three paradigms of education — transmission or traditional, transactive, and transformational. In this link Jack provides diagrams to explain what I am saying.

    Standardized testing and drills are traditional obviously and teacher directed. Discovery and problem solving would have been transactive (Dewey) and involve some teacher direction but with a lot of group work.

    But the “constructivism” the author talked about in bonefishcove’s comment is the newest paradigm called transformative and teachers are no more than “facilitators” and “guides.” This latter view is based on, you guessed it, philosphers like Paulo Frieri and Karl Marx.

    My research conclusions after spending a lot of time observing teachers, was that an eclectic approach was best, techniques that reflected all three philosophies. Now, the terminology is “blended” but it means the same thing.

    When you read words and phrases like “authentic,” “critical pedagogy (the life’s work of Peter McLaren, to mention only one researcher in that field, actually taught for awhile at Brock while I was there)” and “journal writing” — they are in that third and somewhat new age transformational paradigm.

    I know describing this seems off the wall, but we really do need to understand that the math and reading approaches being used nowadays do reflect a very different notion of learning.

    So, using math approaches that do not blend all three paradigms simply are not realistic — as we already know. Kids will no doubt come out of school in the future being very creative thinkers but have no idea what the basic skills are in anything.

    In my last few years of teaching at the university level, I knew this was going to happen. One of my duties was thesis/project supervision. Most had no idea about basic organization. Oh, sure, they could do flow charts till the cows came home but when they had to sit down and organize how they were going to explain everything in paragraph format, they were lost. I made them use a tape-recorder, from which they then transcribed what they said. There was more but you get the idea.

    Sorry to be so long winded. A few years back I tried to explain all this in a few posts but was accused of it being edu-babble — which is why I included the alert at the start.

    In reality, understanding what is happening at a philosophical level is the only way to realize teachers and parents are now going in the same direction but on different parallel train tracks — never intersecting anywhere. Meaning, this new philosophy is now so ingrained at the research level, the best we can hope for is blending.


  15. Tripper — There is also the issue of cognitive development. It is as though that has been forgotten. Problem solving is abstract thinking and that doesn’t come to most kids until Grad 6 or so. Before that it is concrete operations. I can’t help wonder how many kids in Grades 3 and 4 are being left behind because the lessons are above where they are at. I used to teach entire undergrad education courses about development. So, it is especially discouraging for me.


  16. There’s one more form of math education Sandy that’s infusing our schools. It’s social justice math, which this article from a few years back talks about within.

    There’s MUCH more at play to teaching math these days that has ANYTHING to do with the actual teaching of math.

    “Blending” is the new buzz word for “we better go back to the basics”, and if not taught properly by a teacher who knows how, the we end up confusing students who if they’d had the benefit of basic skill instruction would be far better off than un-teaching the “oops” that the system has ingrained. It’s the whole-language regress all over again.

    Here’s the column that talks about how even math is seeing liberal infusion.


  17. Bone at 4:30pm. Can’t say I am surprised but disappointed. We don’t need the whole language equivalent in math that wasn’t whole at all. I can see that I am going to have a lot to write about here and lots for us to talk about. Perhaps it is just as well that I have been out of the “system” for a few years. Of course, practising teachers will ridicule that fact. But, someone has to stand up and say enough is enough.

    Change is not reform if it does not take the best of the past into the future.


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