Alfie Kohn has a revealing essay* posted on Education Week, currently available for free to the public.
Kohn is a well-known advocate of “progressive” education and his article exhibits nicely the basic error that “progressives” make, as well as the opposite error made by far too many advocates of “traditional” education.
On the one hand, Kohn criticizes the traditional teacher-as-lord-and-master approach as consisting of “mandates handed down from on high… where test scores drive the instruction and students are essentially bullied into doing whatever they’re told.”
I think that is a fair rap.
“To divide fractions, invert and multiply.” (Why?)
“Democracy is the best system of government.” (Then why not carry out open-heart surgery democratically?)
“Humans are descended from fish.” (How do we know this?)
To simply order children to believe the “right” answer causes them to accept that one can only learn the truth from authority, and that they, and humans in general, lack the ability to reliably determine the truth for themselves.
And, if kids ever start to wonder how the “authorities” learned the right answer, since the authorities themselves also are mere humans, the kids may fall into a naïve skepticism, thinking that no human can ever really know any truths at all.
But, sadly, Kohn offers, as a false alternative, the old “progressive” solution of giving kids the “opportunities to discover answers to their own questions,” i.e., the “constructivist” approach where kids have to create knowledge for themselves rather than systematically being taught what humans have discovered, at enormous effort, during the last three thousand years.
That really would be a swell approach – if kids had a spare three thousand years to work out everything, and if all kids were as bright as Euclid, Einstein, etc.
So, how to avoid the false choice of “progressive” vs. “traditional” education?
The answer should really be obvious from everyday life.
In real life, we explain to kids that you need to brush your teeth because you will otherwise get cavities, you need to wash your hands because there are germs on your hands that can make you sick, etc. We give explanations.
The idea of giving rational explanations, as opposed to the false dichotomy of either issuing irrational commands or forcing the students to discover everything for themselves, is really not that complicated!
E.g., why “invert and multiply” to divide fractions?
Well, division is the inverse operation to multiplication: if you multiply by some fraction and then wish to undo the multiplication, inverting and multiplying will indeed undo the original multiplication.
Liping Ma, in her brilliant Knowing and Teaching Elementary Mathematics, a “must-read” for all homeschooling parents, goes into much greater depth on this issue of dividing fractions: this is one of the toughest things to explain clearly in elementary mathematics.
But it can be explained. It is unrealistic to expect kids to discover for themselves how to divide fractions, or to fully understand on their own why it works, even if they do stumble upon it. However, it is also not necessary to teach the standard algorithm as an arbitrary rule imposed, for some mysterious reason, by adults.
As Ma explains, if one wishes to use division as the inverse of multiplication, if one wants division to be a means of carrying out repeated subtractions, if one wants the “cancellation law” to apply to division, one has no choice: there is only one right answer, the one given by the standard algorithm.
Ma advocates a “profound understanding of fundamental mathematics”: i.e., both a serious conceptual understanding of elementary math, as well as a practical mastery of the elementary math facts and the standard algorithms.
That indeed should be the goal in all academic (and non-academic) subjects: a conceptual understanding of American history combined with detailed factual knowledge of dates and historical events; an understanding of the experimental bases for scientific theories as well as detailed knowledge of the important scientific facts; etc.
As a practical matter, it is sometimes necessary to say to a student, “We will see the justification for this next month or next year.” Sometimes, one cannot fully understand the evidence for a theory until one has grasped exactly what the theory is. And, it would be foolish to slavishly imitate all the false starts and errors made in the historical development of scientific theories, in the historical creation of various concepts in economics, in the historical discovery of various methods in mathematics, etc.
A student’s learning need not and should not recapitulate the historical process by which knowledge was originally discovered. The whole point is to make it easier for the student than it was for the original discoverer.
Often, the historical experiments or reasoning that led to a discovery are relevant: this is true, for example, of Rutherford’s discovery of the nucleus. But the important thing is to present the best proof and justification we possess today for a particular piece of knowledge.
The other error to avoid, which tends to be shared by both “progressive” and traditional approaches to education, is the false belief that kids have to wait until they are mature to be told of discoveries that the human race only stumbled upon in the last century or so.
It may have taken humans a long time to discover the Big Bang, the fact that humans are descended from fish, etc. But a six-year-old can grasp those ideas – they are not that complex. Even the basic evidence for those facts – e.g., the fossil record, the fact that the galaxies are expanding outward – can be explained at a simple level to six-year-olds.
That the human race had to be “mature” to discover such things does not mean that young kids cannot understand those discoveries.
An educational approach based on giving rational explanations, as opposed to the false dichotomy of either issuing irrational commands or expecting the students to discover everything for themselves, is really not that hard to grasp. Both progressivism and the traditional approach to education are wrong.
We need to teach our kids that humans can and do have a rational understanding of reality. Neither the “progressive” nor the “traditional” approach to schooling really achieves that.
Our kids deserve a "content-rich" approach that teaches them, at an early age, the marvelous and amazing facts that human beings have discovered about reality.
* Thanks to Barry Garelick at Kitchen Table Math for bringing Kohn's essay to my attention.