Over the past few weeks I’ve been collecting articles, posts, and quotes on the nature of teaching and learning with the idea that I would compile them into a longer essay. But as my list grew and my thoughts crystallized, I decided instead to keep my comments brief and let these vignettes take center stage. To put it succinctly, what all of these examples suggest is that teaching is not preaching, no matter what the subject, and that learning is far more than simply receiving knowledge – no matter how brilliant the source.
First, from Richard Feynman on his time teaching teaching physics in Brazil:
After a lot of investigation, I finally figured out that the students had memorized everything, but they didn’t know what anything meant. When they heard “light that is reflected from a medium with an index,” they didn’t know that it meant a material such as water. They didn’t know that the “direction of the light” is the direction in which you see something when you’re looking at it, and so on. Everything was entirely memorized, yet nothing had been translated into meaningful words. So if I asked, “What is Brewster’s Angle?” I’m going into the computer with the right keywords. But if I say, “Look at the water,” nothing happens – they don’t have anything under “Look at the water”!
Later on:
I taught a course at the engineering school on mathematical methods in physics, in which I tried to show how to solve problems by trial and error. It’s something that people don’t usually learn, so I began with some simple examples of arithmetic to illustrate the method. I was surprised that only about eight out of the eighty or so students turned in the first assignment. So I gave a strong lecture about having to actually try it, not just sit back and watch me do it.
After the lecture some students came up to me in a little delegation, and told me that I didn’t understand the backgrounds that they have, that they can study without doing the problems, that they have already learned arithmetic, and that this stuff was beneath them.
So I kept going with the class, and no matter how complicated or obviously advanced the work was becoming, they were never handing a damn thing in. Of course I realized what it was: They couldn’t do it!”
He draws an analogy between the way these students are being taught science and the act of learning a language merely by its sounds and rules:
Then I gave the analogy of a Greek scholar who loves the Greek language, who knows that in his own country there aren’t many children studying Greek. But he comes to another country, where he is delighted to find everybody studying Greek – even the smaller kids in the elementary schools. He goes to the examination of a student who is coming to get his degree in Greek, and asks him, “What were Socrates’ ideas on the relationship between Truth and Beauty?” – and the student can’t answer. Then he asks the student, What did Socrates say to Plato in the Third Symposium?” the student lights up and goes, “Brrrrrrrrr-up” – he tells you everything, word for word, that Socrates said, in beautiful Greek.
But what Socrates was talking about in the Third Symposium was the relationship between Truth and Beauty!
What this Greek scholar discovers is, the students in another country learn Greek by first learning to pronounce the letters, then the words, and then sentences and paragraphs. They can recite, word for word, what Socrates said, without realizing that those Greek words actually mean something. To the student they are all artificial sounds. Nobody has ever translated them into words the students can understand.
The entire essay is worth reading – actually, all of his essays in Surely You’re Joking, Mr. Feynman are – but these excerpts illustrate an attitude still present in a lot of educational environments.
Second, an essay from Mere Inkling on C.S. Lewis and the transfer of knowledge:
When I attended the University of Washington, we had to learn the old-fashioned way—by studying. Now they are anticipating downloading information directly into students’ brains.
Literal brain dumps are actually still in the future . . . but researchers have documented the first indisputable brain-to-brain interface between humans!
My first paragraph is not an exaggeration of what researchers think may one day happen.
The project could also eventually lead to “brain tutoring,” in which knowledge is transferred directly from the brain of a teacher to a student.
The student would view this shortcut as advantageous. (It could also save a great deal in tuition expenses, if each course only took, say, an hour or two of brain interfacing.)
The university sees another advantage—circumventing limited teaching skills.
“Imagine someone who’s a brilliant scientist but not a brilliant teacher. Complex knowledge is hard to explain – we’re limited by language,” said co-author Chantel Prat, a faculty member at the Institute for Learning & Brain Sciences and a UW assistant professor of psychology.
The editor of Mere Inkling, Robert Stroud, goes on to counter this idea with some questions and quotes form C. S. Lewis on education which are highly worth reading also, but my thoughts turn to the above-quoted Chantel Prat.
Even if we were able to transfer knowledge in this way, we would fail to truly teach or learn by that method. As shown in Feynman’s experience, learning is not just about the collection of information, but rather training ourselves to figure it out. Teachers, when they’re good, guide their students through that discovery, and geniuses who come up with new and better ways to do things enable us to discover more things more quickly, but invariably, we still have to struggle through the process ourselves. Memorizing “2+2=4″ gives you no knowledge unless you can walk through the process yourself and then reapply it to other equations.
Simply transferring the knowledge from the brain of the scientist to the brain of the student wouldn’t give you any better handle on the material than if the scientist said that same information out loud – it would still need to be unpacked and rebuilt by the student, helped by a teacher who can walk them through the process.
Third, St. Augustine explains in De Magistro (Garry Wills translation) why teaching is so difficult, even when we have great knowledge:
The most, then, that can be said for the scope of words is that they afford us an occasion for examining something, but they do not demonstrate it to our understanding. -36
And later:
Do teachers advertise that they verbally transmit their own acts of understanding, or the truths of their discipline, for students to receive and retain? What father sense a child to school with the silly aim of finding out what the teacher’s understanding is? Rather, when all subjects, even those concerning virtue and wisdom, have been expounded by those who profess them, then students, if they are really to be called that, investigate within themselves whether what they are hearing is true, strenuously putting it to the test of their own interior truth. That is the point at which they learn. And when they read an inner conviction of truth, they praise their teachers, not realizing that, even if the teachers knew what they were saying, the praise rightly belongs tot he taught ones not the ones who taught. – 45
Even if you don’t believe we have an interior truth (either in terms of innate reason or in the image of God), the point is that knowledge is be gained by the experimentation or problem-solving act of the student, effectively prompted by the words of the teacher, but not executed by the teacher.
Fourth, we see a similar rendering of this idea from Thomas Aquinas in De Veritate, Question 11:
In effects which are produced by nature and by art, art operates in the same way and through the same means as nature. For, as nature heals one who is suffering from cold by warming him, so also does the doctor. Hence, art is said to imitate nature. A similar thing takes place in acquiring knowledge. For the teacher leads the pupil to knowledge of things he does not know in the same way that one directs himself through the process of discovering something he does not know.
Now, in discovery, the procedure of anyone who arrives at the knowledge of something unknown is to apply general self-evident principles to certain definite matters, from these to proceed to particular conclusions, and from these to others. Consequently, one person is said to teach another inasmuch as, by signs, he manifests to that other the reasoning process which he himself goes through by his own natural reason. And thus, through the instrumentality, as it were, of what is told him, the natural reason of the pupil arrives at a knowledge of the things which he did not know. Therefore, just as the doctor is said to heal a patient through the activity of nature, so a man is said to cause knowledge in another through the activity of the learner’s own natural reason, and this is teaching. So, one is said to teach another and be his teacher. This is what the Philosopher means when he says: “Demonstration is a syllogism which makes someone know.”
The teacher is here useful, but not necessary, for the act of learning.
Fifth, we see this idea taken even further in a blog post from Book Geeks Anonymous on the damaging effects of teaching people that they need teachers:
In an interview with CUNY TV, Irish poet Paul Muldoon advanced his theory for why so many people, particularly students, struggle to understand and enjoy poetry. According to Muldoon, it has to do with the way that poetry is taught in schools: in high school, he says, students are given the impression that they will never be able to understand poetry without a teacher or other sort of “expert” there to tell them what they’re reading.
Muldoon makes a good point: most schools’ ways of teaching–not just poetry, but all subjects– cause students to doubt or neglect their own abilities. Because they, from the time they were waist-high, were spoon-fed their lessons, they become convinced that they cannot accomplish anything academic without involving a teacher. I believe college professors call this “freshman syndrome.” But this, I think, is only part of the reason why students struggle with poetry.
When we make the teacher a source of knowledge, rather than a guide through the process of learning, we set very specific, arbitrary standards – teaching students not how to interpret poetry, but how to interpret the teacher, to find the “trick”, identify the “catch” in any question of evaluation. And we don’t just do this in the humanities.
Sixth, another Feynman essay illustrates how we start this process early on, even in our elementary science textbooks:
For example, there was a book that started out with four pictures: first, there was a wind-up toy; then there was an automobile’ then there was a boy riding a bicycle; then there was something else. And underneath each picture it said, “What makes it go?”
I thought, “I know what it is: they’re going to talk about mechanics, how the springs work inside the toy; about chemistry, how the engine of the automobile works; and biology, about how the muscles work.”
It was the kind of thing my father would have talked about: “What makes it go?” Everything does because the sun is shining,” And then we would have fun discussing it:
“No, the toy goes because the spring is wound up,” I would say.
“How did the spring get wound up?” he would aks.
“I wound it up.”
“And how did you get moving?”
“From eating.”
“And food grows only because the sun is shining. So it’s because the sun is shining that all these things are moving.” That would get the concept across that motion is simply the transformation of the sun’s power.
I turned the page. The answer was, for the wind-up toy, “Energy makes it go.” And for the bicycle, “Energy makes it go.” For everything, “Energy makes it go.”
Now that doesn’t mean anything. Suppose it’s “wakalixes.” That’s the general principle: “Wakalixes makes it go.” There’s no knowledge coming in. The child doesn’t learn anything: it’s just a word!”
Even if it were the right word (and here Feynman argues vehemently that “energy” signifies far too broad of a concept to possibly be the right word), the word itself is merely a symbol representing a concept – learning the word by itself gives you nothing, and teaches students that the answer to a scientific question isn’t about figuring out how things work and why, but is instead about learning – or guessing – the right vocabulary word.
Seventh, in offering a new way to teach shapes, Christopher from Talking Math with Kids, makes a similar claim about how vocabulary-centric learning often denies us conceptual learning:
Most shapes books—whether board books for babies and toddlers, or more sophisticated books for school-aged children—are full of misinformation and missed opportunities. As an example, there is nearly always one page for squares and a separate one for rectangles. There is almost never a square on the rectangles page. That’s a missed opportunity. Often, the text says that a rectangle has two short sides and two long sides. That’s misinformation. A square is a special rectangle, just as a child is a special person.
He goes on to describe a book of shapes that allows for children to think a bit more freely, and get a lot of new information – all without the arbitrary limitation of insisting on a set answer to a particular question. Each page displays four shapes, and asks the question: “Which one doesn’t belong?” And there are a variety of possible answers:
If you are thinking, “It depends on how you look at it,” then you’ve got the idea… There is no answer key. This is intentional–to encourage further discussion, and to encourage you to return to the book to try again.
The book will be available in PDF form for free download until the author makes it available for sale in hard copy.
Eighth, we can trace this same pattern to the teaching of ethics and values by looking at a recently popular opinion article by Justin P. McBrayer in the New York Times questioning “Why our children don’t think there are moral facts”:
This is repeated ad nauseum: any claim with good, right, wrong, etc. is not a fact.
In summary, our public schools teach students that all claims are either facts or opinions and that all value and moral claims fall into the latter camp. The punchline: there are no moral facts. And if there are no moral facts, then there are no moral truths.
However while I think this is a great essay, McBrayer himself falls into the exact trap he is criticizing. I agree with Self Aware Patterns’ dissatisfaction with McBrayer’s assumption that there are moral facts:
I can certainly understand the strong desire for moral precepts to be facts similar to mathematical truths or scientific conclusions. I wish they were myself. It would make ethical debates so much easier. It would merely be a matter of testing a proposition or perhaps putting together a logical proof. But moral values can only be proven in relation to other moral values. Eventually, as you dig down through the moral axioms, you unavoidably hit a wall of subjectivity.
He later adds that:
Moral values are more than just whimsical opinion, but they don’t rise to the level of being absolute facts.
What comes through is that the dualistic understanding of all knowledge as either “fact” or “opinion” is damagingly inadequate. In this case, the “fact/value” distinction is important, as is the “fact/opinion” distinction, but it is just as important to explore a “value/opinion” distinction, a “fact/axiom” distinction, a “fact/theory” distinction, a “theory/hypothesis” distinction, and more. Perhaps university is the right place to introduce these sorts of complexities, but I can’t help but think that it’s disingenuous – and damaging – to teach students that ideas are either correct facts you cannot question, or else utterly dismissible opinions that you cannot treat with rigor or respect.
Generally speaking, when we treat teaching like the mere transfer of unquestionable data, school becomes a place to leave the real world (and the real way we do things) behind, leaving us no tools with which to apply whatever we do learn in class. Of course, facts and definitions and details are absolutely necessary for both clear communication and for guiding students quickly through discoveries that others have already struggled to make, but the goal should always be to enable students to go out of the classroom and use what they learn in both expected and unexpected ways – to stand on the shoulders of giants, not cower in their shadows.
And of course, that is far easier said than done.
