Pedagogy: On Teaching Elementary Math
In the spring of 1929 the late Frank D. Boynton, superintendent of schools at Ithaca, New York, and president of the Department of Superintendence, sent to a number of his friends and brother superintendents an article on a modern public-school program. His thesis was that we are constantly being asked to add new subjects to the curriculum [safety instruction, health instruction, thrift instruction, and the like], but that no one ever suggests that we eliminate anything. His paper closed with a challenge which seemed to say, “I defy you to show me how we can cut out any of this material.” One thinks, of course, of McAndrew’s famous simile that the American elementary school curriculum is like the attic of the Jones’ house. The Joneses moved into this house fifty years ago and have never thrown anything away.
I waited a month and then I wrote Boynton an eight-page letter, telling him what, in my opinion, could be eliminated from our present curriculum. I quote two paragraphs:
“In the first place, it seems to me that we waste much time in the elementary schools, wrestling with stuff that ought to be omitted or postponed until the children are in need of studying it. If I had my way, I would omit arithmetic from the first six grades. I would allow the children to practice making change with imitation money, if you wish, but outside of making change, where does an eleven-year-old child ever have to use arithmetic?”
“I feel that it is all nonsense to take eight years to get children thru the ordinary arithmetic assignment of the elementary schools. What possible needs has a ten-year-old child for a knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years’ study by any normal child.”
In the article that follows the author, by L. P. Benezet, then superintendent of schools in Manchester, NH, details his carrying out of the experiment that he proposes.Although there is no formal instruction in arithmetic, students in the younger elementary grades are given much practice in estimating areas, distances, etc. and in making change and various mental arithmetic problems. The focus is on teaching reasoning and the ability to talk about mathematical concepts in clear English rather than performing mathematical operations. The results are quite impressive. It’s fascinating reading and has given me much to think about.
Bookishness: On Reading and New Media
I decided to read Little Dorrit four ways: paperback, audiobook, Kindle, and iPhone.
It was often maddening to keep finding and losing my place as I switched from format to format. But as an experiment, it taught me a great deal about my reading habits, and about how a text reveals itself differently as the reading context changes. Along the way, I also began to make some predictions about winners and losers in the evolution of books.
Little Dorrit was an accidental choice, but I could hardly have done better. Its length, multiple story lines, 19th-century allusions, and teeming cast of characters helped me to test the functionality of different formats. Beyond the artifice of my reading experiment, though, please don’t think that technology compromised my ability to appreciate this beloved novel, written in 1857 at the height of Dickens’s power and popularity. Just the opposite.
I haven’t had any experience reading books on Kindle or iPhone; but have enjoyed audio books and have read novels on my laptop. I’ve never tried to use more than one format at a time, though some books I’ have experienced both listening to them as audio books and on paper. I’m rather fascinated by the idea of switching from one format to another while reading one book and very interested in the question of how the physical medium affects the reader’s experience of the story.
I’d note that while I’ve never really tried it, Dom, is a huge Kindle fan after trying it for a month and really would like to buy one. He disagrees with the author, Ann Kirschner, about choosing the iPhone over the Kindle. He thinks the iPhone screen is much too small.
Faith: On the Liturgy: “It’s Bigger Than You Are!”
“Not for Lightweights”: What happens when a Baptist preacher takes a sabbatical and visits an Orthodox church for the Divine Liturgy? This one has been making the rounds, I’ve seen it linked at several blogs. It’s received quite a few comments. I was especially moved by his reaction:
After it was over another woman came to speak with us. She said, �I noticed the girls were really struggling with having to stand.�
�Yeah,� I said. �This worship is not for lightweights.�
She laughed and said, “yes,” not the least bit ashamed or apologetic.
So what did I think about my experience at Saint Anthony the Great Orthodox Church?
I LOVED IT. Loved it loved it loved it loved it loved it.
In a day when user-friendly is the byword of everything from churches to software, here was worship that asked something of me. No, DEMANDED something of me.
�You don�t know what Theotokos means? Get a book and read about it. You have a hard time standing for 2 hours? Do some sit ups and get yourself into worship shape. It is the Lord our God we worship here, mortal. What made you think you could worship the Eternal One without pain?”
See, I get that. That makes sense to me. I had a hard time following the words of the chants and liturgy, but even my lack of understanding had something to teach me.
�There is so much for you to learn. There is more here than a person could master in a lifetime. THIS IS BIGGER THAN YOU ARE. Your understanding is not central here. These are ancient rites of the church. Stand with us, brother, and you will learn in time. Or go and find your way to an easier place if you must. God bless you on that journey. We understand, but this is the way we do church.�
A little voice, slightly envious, whispered to me at the end there: would he have the same reaction coming to Mass at my parish on Sunday? Oh it is bigger than I am, definitely. But not so overwhelmingly so as I would like. I spend too much time silencing that critical voice that says: the liturgy should be better than this, we could offer more. Better music, more reverence, have a greater sense of its depth and greatness. It saddens me greatly that we seem to have spent the last half century trying to make the Mass more comfortable, more our size. I know that there are times and places to think about that and discuss it. During Mass is not the time and the place and I need to learn to silence that voice humbly and worship the best that I am able, offer it all to God, both the glories and the disappointments; but most of all be aware that despite my disappointments in the externals, I am still in the Real Presence of He who made the universe.