Lockhart's Lament or You Should Read This Now!

I've read this before but apparently I didn't blog it. Can't imagine why--it's fabulous! Makes me want to go back and re-teach high school math to Wolfie. A living books approach probably would have kept him interested in math, which he isn't anymore. :(

Anyway, here is a bit of "A Mathematician's Lament"by Paul Lockhart, an elegant proof that we may be teaching our children about mathematics but we're certainly not teaching them mathematics.

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes. "

It's a great argument against schooling in general, since while he claims no other subject has been so sucked dry of life and reason for living, the same could be said about history, economics, and most science courses. I've even seen it done in English classes. Pretty much any class that uses a textbook is about as interesting as the pile of wood pulp used to make said textbook. Oh yeah, I went there!

I Am What I Am

Here is a great article about homeschooling a twice exceptional child:

I Am What I Am by Anne Ohman

"His note is taped to my mirror as a daily reminder of his unique contribution to our lives, to our universe. In handwriting and spelling that a teacher would surely frown upon, it reads, “I AM WAHT I AM.” Five words. Five short, simple words. But what a message. What a huge, wonderful, powerful concept for an eight-year-old boy to possess..."

Just What is Standards-Based Learning?

And can it be implemented in the public schools? The answer to the second question is yes, according to Alaska's Chugach School District. As you can see in the Edutopia article, rather than grades, Chugach students have "tote around report cards as thick as history texts. Each packet details the individual student's progress through the district's more than 1,000 learning standards as they move from kindergarten to high school graduation." Once students have mastered all the concepts in the standards, they graduate, whether they're 16 or 22.

Answering the first question second, standards-based education is when individual student's achievement is measured against a standard (duh), usually set by the state or local board of education. The most familiar instance for most people would be high school graduation requirements--4 years of English, three years of math, etc. etc. But even those "standards," measured in years, are rewards for seat time rather than learning.

This is an issue for all kids, not just the gifted. Anyone can do the bare minimum amount of homework, score averagely on tests and mostly sit in the back of the classroom doodling or passing notes and accumulate three years of seat time in math classes (BTDT). Allowing children to do that (or, in the case of gifted children, expecting them to do that) is a great disservice.

Some of the greatest thinkers of our time, like Tom Magliozzi from Car Talk, are starting to realize that the way we teach needs to change. Read his New Theory of Education rant. He actually goes a step further than external standards/benchmarks and suggests that learning should be tailored to every learner, as the best way to make people want to learn is for them to be interested in the subject they're learning in the first place. Though he's still speaking in terms of school, his ideas are edging perilously (some might say) close to the unschooling philosophy, where all learning is interest-based.

It would be difficult to turn all public schools into tailored-learning centers. However, there are current standards that teachers have to address in their lessons. I think if the school boards were more upfront about what the standards are, the kids would be able to decide how to meet them while pursuing their own interests, guided by the teacher, rather than being led by the nose or, worse, ignoring him/her altogether.

What's So Great About Long Division?

In my last post, I mentioned that Xavier hates long division. Here are a couple of sites questioning the need for long division in the first place, courtesy of Zany Mom: (And you thought I ignored your email, didn't you! LOL)

Senseless of School Math

"Math learned as a side effect of using it is easy. Kids learn to see the big picture and how things fit together and how numbers work.

When kids are made to do pencil and paper math, they get lost in the details. They have to figure out 11/17 of 87 before they have been casually exposed to hundreds of personally meaningful ways fractions are used around them.

I think one of the most helpful things parents can do is to solve everyday problems in their head out loud. It forces you to see things in simpler terms so that you can do it in your head. If one is faced with 103-56 and does it the way you were taught in school, you'll have to juggle and remember a lot of numbers that don't relate to the problem in your head. But if you can see the problem broken down into understandable pieces, then it's much easier and kids get to see how numbers work. (One of the big problems with pencil and paper math is that the numbers feel fixed. You can't alter the problem into something simpler.)

So for 103-56 you might ask how far 56 was from 100. Well, 4 gets you to 60 and 40 more gets you to 100 and 3 more gets you to 103. So 47." (emphasis mine)

Spoken like a true visual-spatial learner. ;-)
Not that there is anything wrong with that! I would do the same problem in my head the same way. But not all kids work this way. I never had trouble applying algorithms to math problems and I can multiply and divide fractions like a house on fire. LOL

Unschoolers and Mathematics

"People do NOT need to learn math the way it is taught in schools. In fact, they don't need to "learn math" at all. Math is INSEPERABLE from most everything else in life, and if you live a full life, you'll learn all the math you need because you need it. It's there. It's part of everything. You couldn't escape it if you tried really hard."

We're not unschoolers but I mostly agree with both of these sites. The problem comes in when the kids skip the lower difficulty stuff (with Wolfie it's dealing with polynomials) and then run into trouble with the higher level stuff they are interested in. We're having to go back and practice the polynomials and he hates it hates it hates it. The practice, not the math.

Unschooling live chat transcript from Teacher Magazine

Last week, edweek.org hosted a live Web chat with Ken Danford, executive director of North Star: Self-Directed Learning for Teens, in Hadley, Mass. From their promo material: "Founded in 1996, North Star is an education center for homeschoolers, catering mostly to students who've grown disaffected with high school. North Star offers an eclectic mix of courses as well as career resources, but what the students do with their time is largely up to them.

"There's no attendance taken," writes author Dan Robb in his recent TEACHER MAGAZINE article on North Star. "Nor are there bells, grade levels, or evaluations. Students are absolutely in charge of their own education." Adds Danford, "Unstructured time here is invaluable--is more important than the classes, in a way--because ultimately it's more important that kids have time and space to figure out who they want to be."

Some of North Star's students attest that this laissez-faire approach has reawakened their engagement with learning. And despite leaving the center without grades or a diploma, a number of North Star's alumni have gone on to elite colleges."

There are two of the predicable "What if they just want to play video games all day?" questions. Danford doesn't mention deschooling, perhaps because most of his audience is teachers, but he handles most of the questions well. I suspect the center is even less structured than it appears to be from his answers--again playing to the audience. With a staff of two, they couldn't possibly be as hands-on as he suggests. Not that that is a bad thing, but it's something that teachers just would not understand.

Unschooling through the Sudbury Valley School

From Education: Class Dismissed in Psychology Today:

"Summary: It's every modern parent's worst nightmare—a school where kids can play all day. But no one takes the easy way out, and graduates seem to have a head start on the information age. Welcome to Sudbury Valley.

"I've learned a lot about how my mind works by paying attention to how I unicycle," Ben declared in preparation for high school graduation. And from the time he was 12, Ben paid attention to nothing so much as unicycling. When students elsewhere were puzzling over, say, the periodic table, Ben, along with a handful of schoolmates, was mostly struggling up and racing down New England mountainsides, dodging rocks, mud and other obstacles. His "frantic fights to maintain balance" demanded both deep focus and moment-to-moment planning. But they gave him something missing from most classrooms today—a passion for pursuing challenges and inhaling the skills and information (to say nothing of the confidence) to master life's complexities.

At Sudbury Valley School, there's no other way to learn. The 38-year-old day facility in Framingham, Massachusetts is founded on what comes down to a belief about human nature—that children have an innate curiosity to learn and a drive to become effective, independent human beings, no matter how many times they try and fail. And it's the job of adults to expose them to models and information, answer questions—then get out of the way without trampling motivation. There are no classrooms per se, although students can request instruction on any subject or talk to any staffer any time about an interest. There aren't even grades. From overnight hiking trips to economics classes to weekly school meetings at which all matters—including my visit—are discussed and voted on by students and staff, all activities are age-mixed." ...
(Click the link above for the rest of the article.)