The real story behind the war over memorized multiplication tables

It has nothing at all to do with mathematics, but a great deal to do with leftist ideology

These columns have tended to focus over the last two weeks on the apparent determination of the Alberta Department of Education to apply  what is called the “Discovery” method  to the teaching of elementary mathematics. Put simply, it means that the student “discovers” on his own the multiplication table rather than learning it by rote memory. What is rarely if ever explained, however, is why so-called “progressive” educators are so persistent in the student “discovering” the tables rather than simply memorizing them.

The discovery method was introduced in  Alberta  under the former Progressive Conservative government and set off an explosion of protests from university and high school maths teachers. The method, they said, just doesn’t work. It simply confuses many students and turns them against the whole study of mathematics. Nevertheless. “advanced” thinkers from the education faculties still push for it. Why? Therein lies a wondrous story, for the fact is that the insistence on the discovery method has nothing whatever to do with the teaching of mathematics. It has another origin, and it is one hundred percent ideological.

It goes back, that is, to the educational revolution launched early in the 20th Century by the philosopher John Dewey. How it took over the school system of much of the western world, dumping the serious study of history in the process, is detailed in two little books I wrote, one eight years ago, the other late last  year. (See note at the bottom of this column.) Dewey’s philosophy is known as subjectivism, because it holds there can be no such thing as an objective truth or morality. It holds that our concepts of truth, goodness and beauty are all mere feelings, illusions, fashions, which can be changed as life’s circumstances change. Similarly, our concept of the  beautiful is purely illusionary.

Therefore, said the innovators, the old dependence  on rules must go — rules ,as to what is rational and what isn’t, rules as to what is morally right and wrong, all standards that offer to distinguish good art from bad, or good music from awful — all these absolutes must go. History must go because, they said, every historical statement is nothing more than someone’s opinion. Moreover, history tends to set up some figures as role models or heroes, implying an objective standard of good. Similarly, the rules of grammar must go because they inhibit the free expression of emotion, and Euclid must be struck from the maths courses because he focuses the student’s attention on the rules of logical thought.  At bottom, only feelings matter. Reason doesn’t.

It is plain upon reflection that such thinking led directly to the two major cultural revolutions of the last century — the feminist revolution and the sexual. But the source and vindication of  both lay in the educational revolution, which nobody covered. The media totally missed the story. Yet it was the biggest revolution of them all because it has changed us as a people. And in Alberta, where the socialist government is pledged to conduct “a revolution in thinking,” it means, of course, that this is the way it wants us to view everything. It wants us to get rid of the old rules. This is what its sweeping changes in the school curriculum are about.

It’s a matter of record and pertinent that the performance of American schools since they adopted Dewey, measured against that of other countries, has been one of steady decline. Canada’s is not much better. The progressives, that is, have led us into an educational calamity of staggering dimension, and Alberta’s curriculum revolution will follow precisely the same path.

There are other problems. One is the mathematics curriculum. It lives on, thrives on, survives on, and totally depends on absolutes. Five times five will not equal 26, no matter how fervidly the believer “feels” that it does. And if the bridge falls down or the building collapses because the architect was adhering to his feelings when he assessed the calibre of steel required, rather than use his brains, this will not be accepted as exculpating him.  

Now the progressives could see that they were not going to win this argument. But neither could they at one moment tell the student that all the old rules were gone, and then hand him a whole regime of old rules in the multiplication table, and tell him he had to memorize them. But then somebody somewhere got a brilliant idea. Why not adopt just the teeniest bit of deception? Why not persuade the youngster that he’s “discovering” his own personal multiplication table?

Thus was born the “discovery” method of learning maths. Its effect, however, was to leave many students totally baffled. Well, that’s just too bad. We must progress, you know. We can’t let a generation or two of mere children obstruct the advance to the socialist utopia. But we’ll let the education minister explain all this when he unveils his sweeping curriculum.

Ted Byfield was founder and publisher of Alberta Report news magazine, general editor of Alberta in the Twentieth Century. a 12-volume history of the province, and general editor of The Christians: Their First Two Thousand Years, a 12-volume history of Christianity. His column on education appears in The, a web journal. He has recently authored two little books on modern pedagogy: Why History Matters and The Revolution Nobody Covered. You can order both copies here.


8 thoughts on “The real story behind the war over memorized multiplication tables

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  1. Something needs to be done. Ran into a grade 10 student who was unable to multiply by 10, a few weeks later, another grade 10 student (not from the same class) multiplied 12 by 10 — and got an answer of 1200, both of these students had averages of more than 75%. asked another high school student how many months in a year, answer 13, I replied “let’s use our fingers, starting with January, February, …. ” she used her fingers saying the months out loud ….. “yeah, 13”, …. rather sad.


    1. This is what happens when the schools quit educating in favor of indoctrinating, something we have been watching occur for some years in North America, and we in Alberta are about to be inflicted with a powerful injection of the same poison in the new curriculum. However we are, one hopes, about to watch also the creation of a new political party,and we should work to make sure that its educational goals are such that the pitiful young people you describe will cease to be so betrayed in our province. TB


  2. Just for a little nuance, ‘discovery’ was meant to provide children a way to construct their own understanding through exploration of many different methods for accomplishing different math outcomes like multiplication (or long division). The problem was not so much that children were taught ‘why’ math works (through different models), which is laudable, but the fact that the models were taught and the foundations abandoned. It is all good and fine to explain what 2×2 means (2 groups of 2) but the child, once he understands this, should memorize 2×2=4, and all the other times tables to 12×12, so that speed and accuracy in mathematics is the goal.

    Instead, many schools threw out the multiplication tables, and all the mathematics algorithms (like long division) and taught multiple methods, testing to ensure children had perfected every ‘technique’ or ‘model’, and graded on method-showing the work-instead of accurate outcomes or sums. The result is confusion for most children and NO actual mathematics foundations (like essential basic facts).

    Even if some children do gain understanding of the ‘why’ of mathematics through ‘discovery’-and are not left confused- the secondary issue is speed: If children do not know their multiplication tables (and other basics) the entire process of mathematics is slowed to a halt. Caught up in the search for the basics (times tables, addition facts, fractions and percentages) higher level mathematics that require multiple levels of math becomes exhausting and near to impossible for the student.

    Here is a lot of detail on this issue from


  3. Glad you are telling the populace, Mr. Byfield. I wonder how the governing officials would “feel” if we applied the same discovery method to determine what we citizens “feel” is the amount for which we can handle to do the arithmetic as the payment of school fees they expect to be paid to the last non-existant penny and to the property taxes, a portion of which funds the schools or even our Provincial Income taxes. If there are no absolutes, and no right or wrong how can the expect us to pay a specific amount that they mandate, if we didn’t pay what is expected we could not possibly be in the wrong, could we?


    1. It’s good to point this out. Having tried hard to assure us that right and wrong are merely changeable “feelings,” they then implore us to protect the environment, legislate social justice, tax the rich, abolish university fees, and on and on, every one of these assertions standing on some moral principle whose authenticity they have destroyed. In other words, they have cut off the branch they were sitting on. TB


  4. It is important to note that MANY elementary school teachers I have spoken with, despise the discovery method of learning. It is being imposed on them. If these directives were decentralized down to the regional level, many school boards would reject them. (Similar to our inefficient centralized health care system)


    1. In the coming week or so I’m going to describe recurring examples of the minister’s apparent indifference to public concerns over what he’s doing. Remember that he refers to local authority as “my school boards,” and describes himself as “giving my 61 school boards instructions.”


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