Can we finally get rid of the long division algorithm?
How our 1,000-year-old math curriculum cheats Americas kids
Another voice talking about the irrelevance of so much of our math curriculum. I would encourage Professor Frenkel to think about what we could do without so that we could add the kinds of mathematics he is talking about.
OPINION: You Never Did Math in High School is an interesting post by Jeremy Kun on math as patternmaking. https://www.edsurge.com/n/2014-02-12-opinion-you-never-did-math-in-high-school
This op-ed appeared in the Boston Globe called Background in Art Should be a Requirement for Superintendent.
Interesting view of patternmaking for teachers.
If you have looked at The Pattern of Knowledge you may wonder how I was able to fill in that wide-ranging table. In that time before the Internet, when I did most of it, such research was not easy. As I describe in Elegantly Simple, I found the big pattern, the periods without a lot of difficulty once I knew what to look for. The phases, well that was another matter.
I spend many nights reading and searching, several years in part-time research, and nearly two years looking for this pattern nearly full-time. At first, I did not know what I was looking for, thinking that each period had a different pattern. But as I searched and thought further, I found all of the periods had a common pattern. I searched first in compilations of breakthroughs in subjects in appendices, art books, and history of the subject books. But I soon found them wanting. I had to go to original sources and actually read what the great inventors themselves wrote. In this endeavor I was most fortunate.
I took my undergraduate degree in physics at the University of Chicago. My physics education was first class but traditional. The rest of my education was not. Undergraduate studies, the so-called liberal arts courses at the U of C are in the College. In a tradition dating back to the Hutchins’ era, these courses in the humanities, social sciences, and even in the sciences are seminars based on using the Socratic method on original works. We rarely if ever studied pre-digested content. We had to read and understand the great thinkers themselves. We had to ask what the author meant and why.
This very non-traditional education changed my life, for it built the confidence to tackle any and every original work I cared to. I have found this a generally rare kind of confidence. I read hundreds of works and parts of works from the pre-Socratics through Einstein, Plato through Wittgenstein, Sophocles through Joyce.
Confidence is perhaps the most important quality students can build. For without confidence, we do not concentrate well. If we don’t think we can understand something, we will find it hard to keep our focus on it and we will not learn it. Today, schools may talk of grit and sticktoitiveness, but preaching grit is not learning confidence. And while we do want students to practice working on problems until they solve them, they build that grit through building confidence.
Confidence may indeed be the most important 21st century skill. My friend George Blakeslee calls it the 5th C and the basis for the four 21st century skills, creativity, cooperation, critical thinking, and communication. It is measurable attitudinally. And true confidence, not bravado, is the mark of a student who can concentrate and who has the skills and perseverance to learn anything she or he wants to learn. Should confidence be the goal of education? Well it certainly was what enabled me to develop Elegantly Simple and all my other inventions.. It lets me think out-of-the-box, work cooperatively, communicate effectively, and think critically. And I gained this confidence as we gain every skill, through practice.
Robert Frost defined a poem as “a momentary stay against confusion.”
I love this definition. My friend Larry Weinstein mentioned it in passing at lunch the other day. It describes so wonderfully why we construct unique patterns.
The rhyme and/or rhythm in a poem helps us to remember it. It provides us with a unique, a special pattern that we associate with the poem, and it enables us to more easily and quickly remember the next words or phrases. This is what I mean by uniqueness. Of all the possible words or sequences we could have used to describe something, the poet has chosen one or at most a very small collection of patterns overlaid on each other to grab us, hold us, and constantly remind us of his story.
For some this may be a visualization, for others a wonderful rhythm, and for still others an association, or perhaps all of those. Mending Wall has that uniqueness to me. It begins with:
Something there is that doesn’t love a wall,
And ends with:
“Good fences make good neighbors.”
It tells the story of two neighboring farmers doing their spring chore, the story of two very different people with outlooks on life we recognize, we already know their pattern. One questions, the other does not. This poem is beautiful to us. It captivates us. It tells a story that could be told in so many different ways, but it is a collection of patterns, laid one on another, special patterns of rhythm and sound,of image and action, of phrase and structure that makes this story simply one of a kind. It is like the wall, with stone carefully balanced on stone, each chosen to fit its place like this collection of words and patterns and like the unique patterns we build and use everyday.
Elegantly Simple presentation #1 is a draft of the first of the MOOC presentations. It is focused on the connection between art and science.