Every now and then I do something off-topic with Aleph Blog. This is one of those times.

I’ve talked about math pedagogy perhaps half a dozen times since starting this blog back in 2007, and if you are a long-term reader, you know that I think the powers that be DON’T HAVE A CLUE AS TO WHAT THEY ARE DOING!

What, am I flustered? No, no. I am being perfectly serious, and in my opinion moderate. One of my daughters, my wife and I are all good math tutors. We can take on the hard cases and make them learn. In my opinion, the height of good math education in the US occurred in the 1950s, before I was born. I remember as a kid reading the older textbooks and thinking how wonderful it would be if these were the textbooks at my school.

But that’s not my main reason for writing this evening. I want to explain that students need a firm grounding in their math facts if they want to succeed with math. Otherwise, they will feel dumb, hate math, and not want to study it.

All of my children, with varying degrees of intelligence, were able to work through the 100 math facts for addition, subtraction, multiplication and division… getting them to get all of them right in five minutes by third grade, and three minutes by fifth grade.

Is memorization the highest expression of math skill? No. But it enables other skills that won’t emerge unless basic calculations are easily done. It is a mercy to children to drill them until the facts are lodged in their heads for easy retrieval.

To give a different example, my daughter who was our best math student came to me and said that the work I had done with her on precalculus was far better than what public schooled students had received.

Oddly, the public schooled students had proceeded far beyond my daughter in terms of titles of courses taken. But they lacked the ability to actually DO the calculations when they got to college. My daughter became a TA. MAny of them did not.

Part of what I did in teaching her, and other children of mine was always go back to first principles. As an example, with Trigonometry — the unit circle. I would show how everything is derived from the unit circle. The ability to work things out from basic principles is fundamentally different from the seemingly bright children who focus on learning the algorithm to solve problems, but don’t really get the concept as a whole.

Now, don’t get me wrong, problem solving was the main driver of math in our home school, but not to pass tests — it was to promote understanding.

Okay, back to the basics. Do you want your younger children to have a firm foundation in math? I have a spreadsheet that many people have used for drill. You can download it here.

It’s pretty simple. It gives the basic 100 math facts randomized for addition, subtraction, multiplication and division, and a new one my skilled daughter asked for, one that mixes all four, so the student has to think extra hard as the student tries to solve it.

95% of children with repetition and encouragement can memorize their math facts and become more confident to absorb higher level math. Take the opportunity to genuinely improve your child’s math ability, and get them to learn their math facts. After that, they can move on to higher aspects of mathematical reasoning. (Ignore the math ideologues in the public schools, it is as if they want children to do doctoral work before the finish elementary schools. The ideologues are sophomores in the truest sense — wise fools who try to tell you the mankind is different than what it genuinely is, without any real proof for their veracity. They hide behind the shelter of the government, even though they should be fired for incompetence.

In summary, with math, go back to basics. Your child will do far better than his peers.

PS — This is true of the basics across subjects. (Insecure school districts fake progress by having students take so-called college level courses that truly are not such, as my daughter saw amidst her “peers.)