sacha chua living an awesome life

Learning can be so much more fun when you learn with someone. Learning something with your spouse can be even better.

W- and I enjoy learning things together. Last summer, we taught ourselves woodworking. We checked books out from the library, spent hours at Home Depot looking at tools and picking out lumber, figured out how to get 16′ planks home without renting a truck or becoming a traffic hazard, and built deck chairs that actually fit us. Having a second pair of hands to hold something in place, having a second pair of eyes to check before you work – that saves a lot of time. W- also helped motivate me past the necessary-but-slightly-annoying parts, such as remeasuring the chair slats so that they fit properly. I probably would never have tried it without him, and now the chairs sit on our deck and provide an ongoing trigger for happy memories.

We’ve been teaching ourselves Dutch in preparation for our trip to the Netherlands for my sister’s wedding. W- made flashcards and has been helping me learn. Even with our limited vocabulary, we’ve quickly developed in-jokes, like the delight with which we encounter the flashcard for “spek” (bacon) or “gebakken ei” (fried egg), and how I mock-shudder at “krentenbrood” (I’m not fond of currants or anything raisin-like).

We’ve also been working our way through a Latin textbook as part of an Internet-based study group. We’re learning Latin together because we’re curious about a proper classical education. If kids of bygone eras could be well-versed in Latin, Greek, and French, why couldn’t we get the hang of it too? I’m inspired by books like The Well-Trained Mind: A Guide to Classical Education at Home. While the rest of the world wrings their hands over the state of education, W- and I want to do something. This is not a bad place to start.

Cooking provides many opportunities for learning. We’ve been moving further down the supermarket food chain:

How do we make time for this? Avoiding financial pressure helps. A frugal lifestyle means that neither of us needs to work a second job, or gets stressed out about work. We spend most of our discretionary time at home because we enjoy doing so. A nearby library provides almost all the books we want, and Internet booksellers fulfill the rest of our learning needs. Internet videos, audio recordings, and websites also give us plenty of resources.

Learning pays off in many ways. If we model this kind of curiosity and life-long learning for J-, she might be inspired to explore her own interests. It’s like the way I learned a lot from watching my mom teach herself about business and education and watching my dad learn about planes and photography. Who knows what J- and other kids will be able to do if they learn that learning is fun?

2011-04-24 Sun 09:07

Flashcards are great for memorizing. They break topics down into learnable chunks, develop random-access knowledge, and turn learning into a game with visual progress. Flashcards also make it easier for people to learn together, testing each other on concepts.

We’ve been teaching the kids in the study group using flashcards for multiplication facts, fractions, and the Greek alphabet. We also teach them how to use cognitive theory to improve learning–well, perhaps not in those words. For example, when J- wants to help her friends learn the Greek alphabet (having handily mastered recognition herself), we encouraged her to cycle through letters in small sets (5 to 7 characters at a time) instead of running through all the letters in one go. It’s the same technique we used when they were learning the multiplication table.

J- also shared the mnemonics she used to remember many of the Greek letters. For example, she described λ as “Lambda, like Mary had a little lamb, going down a hill.” They’re quickly developing in-jokes, too, like the way V- calls α Pisces, they call Μ big mu, and ω makes the kids laugh.

W- and I have our own flashcards: Dutch, in preparation for our upcoming trip, and Latin, because we’re learning that too. Electronic flashcards offer convenience, of course, but paper flashcards are so much more fun.

In this week’s study group, we plan to teach the kids about the Leitner system for flashcard efficiency. I found out about the Leitner system by reading the comments in the Emacs flashcard.el mode years ago, when I was learning Japanese. The Leitner system optimizes learning by reducing the repetitions for cards you know well and increasing the repetitions for cards you answer incorrectly. It works like this:

Start with your flashcards in one group (group 1). Review the cards in a group. If you answer a card correctly, move it to one group higher. If you answer a card incorrectly, move it back to group 1. Repeat with each group of cards. When you answer a card in group 5 correctly, you can archive the card until you want to do a general review again. This weeds out the cards that you can correctly answer five times in a row and lets you focus on the cards that you can’t consistently answer.

I think the Leitner system is really cool. It’s an elegant algorithm with a physical implementation. Neat!

2011-04-24 Sun 14:16

From April 26, Tuesday: J-’s studying for Thursday’s “in-class performance assessment” on integers. (In-class performance assessment? What happened to the good old word “quiz?” Too much anxiety?) We’re spreading the review out over the next two evenings.

The test will cover adding and subtracting positive and negative numbers. J- and her study group are already off multiplying and dividing (which apparently don’t turn up until grade 8 – really?). W- made up a quick worksheet for J- to practise adding, subtracting, multiplying, and dividing integers.

“The enemy of your enemy is your friend,” I heard her say as she solved the exercises, writing down the correct signs for all the products and quotients. I grinned. I’d taught them that mnemonic two weeks ago. It’s a way to remember the results of multiplying or dividing numbers.

As I explained to the kids: you don’t have to stick to this in real life. Pou can certainly be friends with the friends of your enemy. But this might help you remember the signs for multiplication and division:

• The friend of your friend is your friend. Positive times positive is positive.
• The friend of your enemy is your enemy. Positive times negative is negative.
• The enemy of your friend is your enemy. Negative times positive is negative.
• The enemy of your enemy is your friend. Negative times negative is positive.

2011-04-26 Tue 20:05

Glad to see it stuck in her head! She answered all the exercises correctly (and quickly, too).

Frustrated with the inability to search the scanned images of the 1822 Latin textbook we’re using (Albert Harkness’ An Easy Method for Beginners in Latin – get the PDF, the full-text version is badly OCRed), W- has taken it upon himself to recreate the public-domain textbook as a fully searchable TiddlyWiki (sans illustrations). This meant that he needed to type in a great number of macrons in the words, and that meant finding a better way than copying and pasting from KDE’s character map.

Macrons turn up in many languages. In Japanese, you use them to indicate that vowels are doubled. 大阪（おおさか）can be romanized as Oosaka or Ōsaka. In Latin, beginner textbooks often use macrons (macra) to indicate pronunciation. (Why do we care about pronunciation for a dead language used mostly in church hymns? W- and I actually want to be able to use this conversationally, at least with each other. After all, if you don’t use it, you lose it.)

I suggested Emacs. In Emacs, it’s just a matter of using M-x set-input-method to choose latin-alt-postfix. With that input method, you can add macrons to letters by typing – after them. For example, typing “a -” will result in ā. Not only that, dynamic abbreviations (M-/) make it easier to retype words you’ve already written before.

W- wouldn’t hear of using Emacs, being almost as firmly wedded to vi as he is to me. ;)

Instead, we spent some time figuring out how to set up KDE and gvim to make it easier for him to type in macrons. HTML character sequences were out of the question, of course. W- used KDE’s settings to map his unused Windows key and menu key to compose keys. That made it easier to produce ē, ī, ō, and ū using the key sequence “Compose + hyphen + vowel”. However, “Compose + hyphen + a” produced ã, not ā. This was probably a bug based on some issue reports we found on the Net, but the suggested fix didn’t work (im-switch -c to change to default-xim). I found a page describing an .XCompose fix, customizing the key sequences. He copied the relevant key sequences from en-US’s locale settings for Compose in /usr/share/X11, restarted X, and it worked.

Now he’s off and typing!

2011-04-24 Sun 23:21

W- started the kids on a review of positive and negative numbers. They got the hang of those quickly, so they worked on fractions, exponents, scientific notation, and engineering notation. They multiplied numbers with exponents, divided numbers with exponents, dealt with negative exponents, figured out the two answers to x² = 1… Whee!

J- really wanted to review the Greek alphabet. We introduced it so that they can easily work with θ, α, β, and other characters when they encounter the letters in science and math. J- picked them up really quickly thanks to the flashcards we made. She used the same techniques to teach the other kids more of the letters, repeatedly cycling over small sets of letters, sharing original mnemonics (λ reminds her of “Mary had a little lambda” and a hill).

Watching the kids teach themselves Greek letters – and have fun doing so! – I wondered what on earth we were doing correctly, and if we could help other people do it too. Maybe it’s really just providing a space where the kids can get together and learn, and some guidance and exercises to help them grow.

J- says she learns more – and enjoys learning more – in our study groups than she does in school, because the study group is more fun, more focused, and easier to understand. It’s a happy middle between the intense focus and isolation of a one-on-one tutoring session, and the anonymity of a large class. I’m glad we’re doing it, and I’m amazed at how the kids are doing.

And they begged for more brainteasers! So now I get to dust off my collection of logic puzzles and go through them. Turnabout’s fair play, though, so they have free license to stump me with whatever they can throw at me. =)

2011-04-15 Fri 18:43

It was Friday, so J- and her friends were singing the Friday song as they hung up their coats and got ready for our math study group. It turned out that they had been so excited about coming home (to a math study group!) that they’d forgotten to arrange things with their parents, and V-’s dad had been waiting for her at school. Once everyone had called around and sorted things out with their parents, and everyone was well-fed, we got back to math.

One of the benefits of hosting multiple kids in a study group is that you get more information about what people are learning in school. V- said she needed help with positive and negative numbers, so that’s what we started off reviewing.

A quick review: 2 – (-3) = ? . Boggles all around.

Okay. A step down: -2 – 4 = ?. Still boggles and some guesses.

I drew a number line and labelled it with the numbers. “Imagine a cat standing on -2. Which direction does the cat go if you’re subtracting 4?”

“Left!” chorused the kids. “-6!”

I drew the cat ending up on -6. We did a couple of other exercises along those lines. Nods all around. Okay.

“What about -2 + 3?” I drew another numberline. “Right! +1.”

“What about 2 – (-3)?” I drew the cat on the numberline. “Okay, we’re starting on 2. And we’re subtracting, so we would normally move to the left, but we’re moving -3 steps… so the cat walks backward three steps.”

“5!” said the kids. One of them asked, “Do your cats really walk backwards?”

“They do more of this hopping backward thing, yes, but cats can walk backwards if they want to.”

So we did a few more of those exercises, including things like -4 – (-5) and -(-(-2)). We also reviewed multiplying and dividing positive and negative numbers. The kids seemed comfortable with that, and answered our exercises with little prompting.

As we wrapped up our review of positive and negative numbers, A- arrived. She’s in grade 6, a grade behind the other kids, so we modified our exercises. She said she was taking up decimals in class. I asked her how she felt about the multiplication table. “Bad,” she confessed, at which the other kids begged (begged!) to do multiplication practice.

“But first, we’re going to talk about algebra very quickly,” W- said. He briefly reviewed what an algebraic equation really means, and the different parts of the equation: the constants, the variables, the operators, the assertion, and so on. We hope this will help them remember to keep their equations balanced, always doing operations on both sides of the equals sign.

“All right, multiplication,” I said, and we headed outside to practise multiplication. The way we do it is good for building confidence and a sense of numbers: we go through sets of five multiples until the kids can rattle them off smoothly. For example: 6, 12, 18, 24, 30. 6, 12, 18, 24, 30. And so on, around the circle. It’s really more of an audio recall task than a calculation task, and it gets them used to what the numbers feel like. They catch themselves now, when they make a mistake. And they’re enthusiastic and run ahead of themselves, doing sets of ten instead of sets of five, or challenging themselves further by doing jumping jacks while saying the numbers.

After multiplication practice, one of the kids piped up and asked, “Can we solve the equation in the breadbox?” Ah. Yes. Those. I’d spent some time the night before writing up simple equations and hiding them around the first floor of the house – possible exercises for J- or the study group, depending on how things went. So we agreed that they could look for the five Post-It notes I’d hidden IF they solved the equations as well. I settled in to review decimal multiplication and division with A- to help her catch up, and W- reviewed the other kids’ work on the algebraic equations.

Our Friday afternoon math study groups are a great ritual. Glad we stumbled into organizing them! I hope other parents can host study groups as well – it would be good for all the kids to see active involvement – but it’s probably easiest for us, logistically speaking, because we can often work from home and we both enjoy teaching. If you can, try it!

2011-04-10 Sun 12:05

For last Sunday’s study group, we focused on algebraic expressions. The kids were a little out of sorts at the beginning. “Math is boring,” one said.

“The way it’s taught in school, maybe. But math is really useful in life, so it’s good to learn it,” I said. I shared a few examples of saving money with math, enjoying life with math.

The group warmed up using a matching exercise, matching the word problems on the left side with the algebraic expressions on the right. Then we worked through some of the problems I’d prepared. In one afternoon, we talked about:

• cats and how much food they eat (1/4 cup, twice a day, 365 days, n cats…)
• T-shirts, sleeping cat toys, and chopsticks that look like lightsabers
• how much it might cost to eat onigiri for every meal, every day, for a year
• how long you might be able to eat onigiri given a particular budget
• Scott Pilgrim, Wallace, and Knives Chau
• more cats, including Neko on my head

There are several types of exercises. Completely abstract ones (here’s an equation, solve for n) get lots of confusion and little engagement. Practical exercises (how much would this cost after tax?) get some interest. Outlandish exercises drawing on the kids’ interests get lots of laughs – and solutions. So we mix practical exercises and outlandish ones, one to show math in real life and the other to get the kids involved. It’s like improv comedy, but for education.

This is where parents and tutors really need to step in and mix things up. Textbooks are written for everyone. They can’t take individual interests into account, and they can’t be revised each month to take advantage of pop culture references. When you make up your own exercises, though, you can do whatever you want.

I know J- likes Scott Pilgrim, Fruits Basket, and cats, so they turn up in math exercises. It’s not hard to pick up some standard forms of exercises from textbooks and translate them into more interesting situations.

Helping someone learn? Make up exercises based on their interests and see what happens.