MariaD’s blog

Today, Katya (10) and I looked at this SAT problem:

The square of the result of adding 7x and y is equal to the result of subtracting the square roof of 4x from y.

Which of the following is an equation for the statement above?

(A)
(B)
(C)
(D)
(E)

Katya knew all the ideas involved, but it took us some half an hour to work through their names and symbols, connecting our private math language to the standard language of SAT mathematics. We drew some squares, messed with powers, joked about Ancient Greeks saying everything in words, colored the text to help translate it and in general had a jolly good time. At the end, the very elated Katya said: “At first, this problem looked very scary and did not make any sense, but now I can quickly understand every part.” I replied with a reference to a “Babylon V” episode we watched a couple of days ago.

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People who run classes both for school kids and for homeschoolers often comment that homeschool classes are “lively.” What does this vague feeling mean? There are several slightly less vague points I noticed, for example:

• homeschoolers are more eager to answer questions
• transitions from activity to activity happen faster with homeschoolers
• homeschoolers will ask “wait, what?” if they don’t understand directions, rather than doing nothing
• homeschoolers volunteer helpful explanations, examples, and anecdotes

In practice, it means that homeschool classes run faster. Today, driving around in the late afternoon and looking at all the tired school kids leaving buses, I was thinking of the sheer length of their workdays. Over the years, kids learn tactics allowing them to survive these daily school marathons. They grab pauses whenever they can, don’t invest too much energy in any one activity, derail, delay and slow down teachers trying to drive lessons too fast, and in general conserve strength. The slow pace often frustrating me in school-oriented textbooks and other teacher materials is there for a purpose. Schoolchildren need to pace themselves for long hours.

Marathon runners, by Infomatique

There are studies showing that most adults are capable of focused productivity for about three to four hours a day. Most homeschoolers report having one to four hours of “school work” a day. No wonder homeschoolers are used to a fast, lively pace while working. They know they can sprint during the class and rest later.

Sprinter, by Felice de Sena Micheli

Yet another study reports that gamers are more fit and active than the average. A meaningless piece of statistics, in itself, but with an interesting explanation by Dmitri Williams, the researcher. To quote the article:

Williams pointed out that TV watchers get bombarded by messages about “buying, consuming and eating,” while video gamers get messages about “taking action” within the game. “I think a part of it is that the culture of video games is not necessarily a culture of consumption, whereas the culture of television clearly is,” Williams noted.

What messages bombard learners of math? Do our math activities promote “a culture of consumption”? The other week, I was looking at several wonderful math enrichment books for teens, talking about delicious topics like fractals, topology, or combinatorics. Lovely pictures, wonderful problems, engaging texts. The books made me quite sad. There wasn’t much the readers were invited to do, other than eat up the book content.

“They” say that to achieve happiness, you need to balance “giving” and “taking” in your life. Look at any math curriculum material you remember. Are activities about giving or taking? Here are some examples that come to my mind, and they are all about taking, about consuming knowledge, about eating up that math content:
- read some explanations (watch a movie, look at pictures)
- solve some exercises to better yourself
- do an investigation/exploration project to tie your knowledge together

People usually assume consuming the knowledge of how to solve quadratic equations is better for you than consuming an hour of soap opera. For sure, consuming math knowledge potentially allows you to give something back, to create, to contribute. But where and how do you learn to contribute, to create, to give, if you are only taking and consuming all along your learning process? You may learn quadratic equation, but will you have any idea how to create with them? How to apply them to something contributing to the community? How to make them a part of your life that gives to others?

As a parent, I used to pride myself on advanced knowledge of my daughter. But now I am at best lukewarm about all the feats of intellectual consumption, even if my own dear child performs them. How can we promote an active, community-oriented life position in our children without squishing their free exploration, or exploiting them for mundane labor? Specifically, how can we help kids to give, as well as take, in their mathematical endeavors?

Goats eating paper, by C&T

More questions than answers, surely. Even Google only brings about fifteen hundred results mentioning “intellectual consumption.” One of them a blog entry from about a month ago, asking similar questions, by Dave. ::waves::

The question comes up regularly, so here is an answer. I wrote it as a comment in the Learning is Messy blog.

Biggest bento ever by brenda, Flickr, under the Creative Commons license. Follow the link for detailed notes on each part of the picture.

This Saturday, my family was a part of a homeschool fair for a local homeschooling network. Families put together displays of what they did during the last year or so. Reading your post and thinking about this recent event that brought together a loose network of a couple of hundreds friends of, and families of friends, I was reminded of the question people ask regularly, on why we don’t use schools for our child’s education. My usual response is that schools don’t fit our (life)style, but it’s too broad. In particular, though, this Saturday I saw displays of how families help their kids pursue strong interests and develop new ones, with the general basic education being a background to what each person is about.

To give one example, my girl is very interested in a Japanese culinary tradition of Bento: highly stylized lunches in cutesy boxes. Bento became a strong node in her network of topics. The network includes cooking in general, with the science as it applies to cooking, and traditions of different nations as they are expressed in cooking. Also drawing and art in general, history of art, and Japanese styles such as manga and anime in particular. And then there are more peripheral, but related topics, people and social objects in that network, such as our Japanese friends, design and fashion, sewing, roleplaying, writing, ninjutsu, web design, Flash programming and so on. My husband, and I, and our friends and extended family support this networked learning of our daughter in various ways: helping with an anime club organized by a friend, spending time showing her the ropes of the web design for the site she is making, installing Flash on her computer, finding good art studio and driving her to two hours of classes there every week for four years, helping her find anime on youtube and manga from online booksellers, supplying stuff from Rosetta Stone Japanese disks to chopsticks and sushi-grade fish.

It is very easy to find people and resources for this particular network of interests, because most of them are now fads among young people in the USA. I daresay if I formulated this as a unit study for a class, and offered it at any school as an elective, it would be quite popular. The problem is that “a unit study for a class” is not a network - it is a unit of an organization. It would feel very different, because the way we do it, people, ideas, objects and activities come and go, and everything is distributed in time and space, and the connections are “weak ties.”

More and more of what our family does for education is of the network style, as opposed to pre-organized (corporative) style. To give an obvious example, the vast majority of reading my child does happens in collaborative participatory spaces: blogs, roleplay chats, wikis, or fanfic nets. I am happy about it, because these spaces invite my child to read actively and to become a writer. But I don’t quite see this style - the network style - as natural (or possible) in today’s schools. Because schools are inherently organizations, and classes are organizations, and curricula are organized, and these groups and curricula aren’t open, live networks of people and ideas. Maybe in a few years?