Herbartianism Made Fun and Easy: Eye of the beholder

Did you ever have an illustration for something just handed to you, so obvious that you didn't even have to think about it?

(one of the few videos I could find about The Dress that didn't include profanity)

"Perception of reality is not the same thing as reality." (SciShow, The Science of That Dress)

Chapter Nine of Herbartian Psychology, "Graphic Hypotheses," begins with something that was first mentioned in Chapter Three:

"It is true that in Reid's comfortable dogmatism we are assured that we perceive the outer world exactly as it is, and therefore we all perceive it alike. But Locke admits that the outer world may be modified in certain aspects,--colour, smell, sound, taste,--but in other more fundamental respects remain unchanged. According to this view, man is the measure of colours, smells, sounds and tastes..."

In other words, the size and shape of something may be fairly fixed and common to almost everyone; but on the other aspects, you're on your own. Referring back to his perception games in Chapter Six, Adams says, "Even a simple straight line may mean something slightly different to each new observer, and the greater the number of lines in a drawing, the greater the range within which its interpretation by different observers may vary." However, "when two persons are talking about the drawing that lies before them, there is at least something to go upon, there is a sort of least common denominator of thought, to which all the ideas of each party must be reduced before agreement can be expected." "The fact is that while our mental impressions of a given object are continually changing, they always correspond with each other, and to the given reality."

So there's room for personal interpretation, but there's also the possibility that someone doesn't understand, doesn't have the right information, is just inaccurate. Not everything is relative. The Dress may be seen as white and gold or as blue and black, but nobody has suggested that it's pink and purple, or that it's actually a ski jacket or a pair of boots.

What does this have to do with Herbartianism and education?

First and most practically, teachers can use graphic narrations to evaluate how well students understand something. Hence the value of Charlotte Mason science notebooks. Adams gives the example of student teachers reading Robinson Crusoe, who were asked to make drawings of Crusoe's tent based on the information given in the chapter. The story said that the roof was covered "with flags and large leaves of trees, like a thatch." Apparently some of them took "flags" to mean the Union Jack, and that's what they drew. They weren't stupid, just lacking information.

Second, Adams discusses the non-value of bad or misleading diagrams. If a diagram or an illustration is "an integral part of the idea it illustrates," then it can be worthwhile; otherwise, we might want to reconsider using it.  "Milton has been often praised for his reticence in not fully describing Satan. Can we say as much for the illustrators of The Pilgrim's Progress?" "There are certain things that are better left undrawn."

Third, we are given the detailed description of a "Map Robinson Crusoe's Island" contest.The Boy's Own Paper advertised the contest and offered a prize, and Adams says that over a hundred and fifty maps were submitted. The contest contained a couple of possible snags, although those weren't mentioned in the rules. The biggest one is, obviously, that not everything is given in the story, and some things must just be imagined; but the text also contains a few contradictions and impossibilities regarding the geography of the island, so even a careful mapmaker would have to deal with those. You can read more of the details in Herbartian Psychology at the archive.org site, but for now, the educational question becomes the double difficulty "of communicating an idea from one mind to another....The idea must be dissolved, as it were, in words, and then again crystallized out in the new mind....The concrete of one mind must be reduced to its abstract terms, and then rebuilt into the concrete of the new mind." It's like what happens when you beam somebody up on Star Trek.

And obviously, there's a risk of something misfiring. Words are tricky things. As was said in the last chapter, we have to make sure we're using the "same system" as the person we're talking to; a newer way to phrase it would be "on the same page." But we also have to recognize that our minds are all unique; we're not clones, and we don't see things exactly the same way. Our "apperception masses" are all different; to every lesson or situation, teachers and students all bring who they are, what they know, and their own ways of seeing. White or gold, or blue and black.

As a postscript: If the mind is a spider web, Adams says, a teacher may be seen as "a benevolent spider...whose business is not to make plain the already geometrically clear lines of the web, but to see that guiding apperception masses are so arranged that they shall lead ultimately to the centre, by the way, however crooked it may seem, that is best for each seeker." (I'm not sure whether these seekers are supposed to be younger spiders, or what.)

But oh dear, I don't like to be seen as a benevolent spider, do you? I certainly don't feel qualified to decide which way to the centre is "best for each seeker."

Education is a discipline: to a point.

"That the discipline of the habits of the good life, both intellectual and moral, forms a good third of education, we all believe. The excess occurs when we imagine that certain qualities of character and conduct run out, a prepared product like carded wool, from this or that [i.e. from any one particular] educational machine, mathematics or classics, science or athletics; that is, when the notion of the development of the so-called faculties takes the place of the more physiologically true notion of the formation of intellectual habits." ~~ Charlotte Mason, "A Master Thought," School Education

We can make the educational mistake of thinking of and treating students as machines or as objects, as computers to be programmed or clay to be shaped.

But we can equally make the mistake of thinking of education itself as a sort of machine. If we put in the right ingredients, plug it in, crank it up, out comes the product, whatever flavour we want.

What, more explicitly, is this mistake that Charlotte Mason says we might be making? First, she says that a certain amount of discipline is obvious and necessary; fine, we agree. But when the belief creeps in that certain subjects are important because they create disciplined thinking, and when we think that the discipline of studying mathematics or science will strengthen not only those lagging parts of our brains but also the lagging parts of our character--there we have the big misconception.  Practicing the discipline of one subject area will not make you an overall good thinker, or a better person. It will not keep you from building a little cat door for the little cat and a big cat door for the big cat.

One night when Pa was greasing the traps he watched Black Susan come in, and he said:"There was once a man who had two cats, a big cat and a little cat." 

Laura and Mary ran to lean on his knees and hear the rest. 

"He had two cats," Pa repeated, "a big cat and a little cat. So he made a big cat-hole in his door for the big cat. And then he made a little cat-hole for the little cat." 

There Pa stopped.

"But why couldn't the little cat--”" Mary began. 

"Because the big cat wouldn't let it," Laura interrupted. 

"Laura, that is very rude. You must never interrupt," said Pa."But I see," he said, "that either one of you has more sense than the man who cut the two cat-holes in his door."

The Herbartian belief, in Charlotte Mason's day, was that certain studies would develop "the faculties." Mason argued that the human brain showed no evidence of such faculties, but that what neuroscientists were beginning to see was the physiological effect of mental habits. Neuroscience continues to advance today, and with fascinating results, for instance with stroke victims whose brains demonstrate an amazing ability to create new patterns and habits.

So as Mason says right after the passage that I quoted, there's sometimes a very fine distinction, but a very great difference in effect, between two types of thought and practice.  Like the right amount of yeast that raises a bowlful of dough, discipline is a necessary part of education.  But only in its proper proportion, used for its proper function.

(The pizza dough story is from The Daily Mail.)

Best education book I've read this month

In the too-short-to-be-a-book-review department: the best education book I've read this month is The End of Ignorance, by John Mighton. It's about math, but it's also about brains and learning and schools and human potential.   Definitely recommended.

Better math, better learning (John Mighton and JUMP Math)

Do you know what neuroplasticity is?

What do you think about recent discoveries about the way our epigenetic system helps us process information?

University of Toronto professor Dr. John Mighton slung some of this around last night to a roomful of teachers and interested others, in between demonstrating why we invert and multiply when dividing fractions, and giving some hints about teaching the nine times table. (Funny, I just reminded one of my own Squirrelings about that yesterday, the fact that the digits have to add up to nine. Teachers don't know this?) He also shared the (to me) appalling information that, according to his research of provincial math curricula across Canada, there is not one province that specifically, in its curriculum guidelines, says that children must be taught to solve questions like "what is 2/3 of 9."

What he had to say went well beyond pushing his math program or his books, although he was there specifically to promote his book The End of Ignorance. As I listened I kept mentally hearing quotes from Charlotte Mason overlapping with some of the scientific findings Dr. Mighton was describing along with his own experiences tutoring children. (You can read the appendix to his book here.)

The most recent discoveries about our brains show that they can develop new abilities, rewire themselves and learn material beyond what was previously expected. It's not so much that you're born a math genius or not. The evidence points to the fact that most kids can learn anything.

So why don't we all learn way more than we do?

Dr. Mighton mentioned a Scientific American article, "The Expert Mind," that points out that you can learn the rules of chess, and play chess as an amateur for the rest of your life, not ever getting any better than a beginner. (Yep, he's got my chess-playing style nailed.) On the other hand, players who are taught small groups of powerful moves and so on become very good, very fast. (Wouldn't the same thing also apply to those who are taught to bang out songs on the piano but never go beyond that?)

He also described being inspired by a volume of letters by Sylvia Plath, in which she explains how she learned to write: by imitating great writers. He pointed out that Plath developed one of the most original voices in 20th century American poetry, so it obviously was no handicap to begin with imitation.

The problem in schools today is that kids are often expected to do without some simple training in basics that they need if they're to seriously develop their abilities--specifically in math, but in the other areas as well. The issue of whole language vs. phonics is one example; spending too much time on discovery-based math learning (including overuse of manipulatives) without teaching the needed basic skills is another. (Remember Mr. Person's blog post, Hands-On, Brains-Off?) Just because kids can work with models or manipulatives doesn't mean they can generalize enough to answer questions that are given in another context; and conversely, just because they haven't been able to learn something by playing with pizza pieces or whatever doesn't mean they can't learn those concepts if they're presented with a more "guided discovery" approach. (Some people apparently read The Myth of Ability and get the idea that John Mighton completely eschews manipulatives; this isn't so, he does use chocolate bars and other concrete examples when it helps to demonstrate a point.)

Add to this the fact that our working memories aren't always that great; you might "discover" something during a lesson, but forget it later. And this is not limited to children; Dr. Mighton mentioned (I think it was in The Myth of Ability as well) that he was once impressed by some mathematical discovery, and then realized that he himself was the one who had published the article some time before.

We need to pay more attention to the ways that kids learn and behave in groups; this might not apply so much to homeschooling (and might be a reason we're homeschooling), but it's still important to understand. Actually most of us know it instinctively already: when you were in school, didn't you have a pretty good idea who the "smart ones" and the "dumb ones" were? And if you thought you were one of the "dumb ones," the odds are that you started to limit your own ability to learn because you thought you couldn't.

And in our culture...as most of us also know...it's socially acceptable to laugh, wince and say "I just never could do math."

So we need to change that.

We need to find ways to increase students' confidence in themselves--no matter what their background, no matter how they've been labelled. [UPDATE: sorry if that sounded a bit too much like the I'm-so-special-boost-my-self-esteem thing. I'm talking only about helping students understand that they do genuinely have the ability to learn.] We need to avoid making the faulty assumption that certain parts of the population are born with less ability to learn than others. (Charlotte Mason's methods were used with children of all classes and backgrounds, blowing the Victorian idea of only-wealthy-children-can-learn to pieces.)

We need, according to Dr. Mighton, to have more confidence in teachers' reports of success with these methods. He talked specifically about the fact that his JUMP Math program has been accepted more in Western Canada than in Ontario, in spite of the fact that classroom teachers who have tried it have been more than satisfied with the results they've seen. Bureaucracy rules and change is slow.

We need to use "guided discovery" methods, especially in cases where manipulatives did not work well; where it would really make more sense to just teach what needs to be taught rather than expecting students to keep reinventing the wheel. We need to teach subjects such as mathematics in short, progressive steps, always "raising the bar" (a favourite Mighton phrase) just a little--or even just making the next step seem a little harder; never rushing ahead or adding in a lot of extra clutter. Dr. Mighton talked about one special-needs student who understood 1/4 + 1/4, and then 1/7 + 1/7, and then 1/36 + 1/36 and so on; but got agitated when asked to add 1/4 + 1/4 + 1/4. However, after being given more opportunities to add things like 1/400 + 1/400 and 1/855 + 1/855 (my examples), he suddenly asked to go back and try 1/4 + 1/4 + 1/4 again; and this time he was successful.

"Here we may, I think, trace the solitary source of weakness in a surpassingly excellent manual. It is quite true that the fundamental truths of the science of number all rest on the evidence of sense but, having used eyes and fingers upon ten balls or twenty balls, upon ten nuts, or leaves, or sheep, or what not, the child has formed the association of a given number with objects, and is able to conceive of the association of various other numbers with objects. In fact, he begins to think in numbers and not in objects, that is, he begins mathematics. Therefore I incline to think that an elaborate system of staves, cubes, etc., instead of tens, hundreds, thousands, errs by embarrassing the child's mind with too much teaching, and by making the illustration occupy a more prominent place than the thing illustrated."--Charlotte Mason, Home Education

Is this just a return to rote learning? No. Even Charlotte Mason had her students practice times tables, and insisted that learning in subjects such as mathematics and grammar must be continuous--that each bit must build on the next. As Charlotte Mason said--look at the evidence. I have personally seen our 10-year-old's success with Mighton's JUMP Math fractions unit this fall, at a time when she particularly needed to rebuild confidence in her math ability.

If kids stumble through school not being able to read, to spell, to do basic math--then is it their fault for being stupid, or our fault for not teaching them properly, or for making them think they are incapable? (I don't think Dr. Mighton blames classroom teachers but rather the system in general.) If we have astonishing success with children who were thought unable to learn--how did that happen? (Some educators could learn a lot from homeschoolers.) If we discover, or rediscover, some method that works well for a wide range of students--can we put down our prejudices and simply use what works? Don't we want all children to be good readers and writers, to go beyond the minimum, to enjoy all learning including mathematics? Shouldn't we be doing whatever it takes to reach those goals?

You can decide.