Category Archives: teaching

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Meaning and acknowledgement

J- brought home her report card this week. She did well in so many subjects that it’s hard to pick which strength to build on first. Her mathematics study group sessions and science projects paid off, as did her personal interest in music.

To celebrate her work, W- and I made a colourful card. She likes making greeting cards for us, and it was fun making one for her.

It’s important to acknowledge good work. One time, W- was reviewing J-’s answers to the math exercises he gave her. “Very good,” he said. He crumpled the finished piece of paper.

I plucked it from his hands and smoothened it out. “Ahem,” I said meaningfully.

“Oops. I tossed the other one already,” confessed W-. I retrieved the previous paper from the recycling bin and uncrumpled it. W- made a point of scoring both papers and adding smileys. J- beamed.

Ah, behavioural psychology at home. You can influence people’s motivation by acknowledging or devaluing their work. In The Upside of Irrationality: The Unexpected Benefits of Defying Logic at Work and at Home (Dan Areily, 2010), I read about experiments that explored how motivated people were if they thought their results were meaningless. As it turns out, people are strongly affected by the immediate perception of the usefulness of their work.

In a task involving assembling Lego figures, participants who completed figures and put them into a box did more and enjoyed the task more than participants whose figures were disassembled right after they finished completing them. Another experiment described in the book involved finding pairs of letters on pages, a small payment scheme that stopped at the 10th sheet, and three scenarios where:

  • people wrote their names on the papers they completed, and they were positively acknowledged by the experimentr
  • people completed and submitted papers with no names and without acknowledgement
  • people submitted papers that were then shredded, unread, right in front of them

49% of the people who were acknowledged went on to complete ten sheets or more, while only 17% of the people whose work was immediately shredded completed 10 or more. Only 18% of the people whose work was ignored completed ten sheets or more.

Verbal acknowledgment of good work is good, but could it be at odds with the physical message of tossing the paper into the recycling bin? Best to be coherent. So the paper is celebrated, labeled, and put into a folder.

W- reminds me of this principle too, when I forget. On the way home from work one day, I brought up how he spent some time selecting and copying items from the workbook onto a piece of paper for J-’s exercises. “Should we get a workbook without explanations, so J- can test herself?” I asked W-.

“No, it’s okay. Besides, it shows her that I value this,” W- said. “If I give her a workbook so that I can do something else, it’s not the same.”

We invest learning with meaning and value, and that helps.

Portal 2 and teachable moments in argument

Portal 2 became an obsession in our household after W- shared with us the Youtube clips of the ending songs, Still Alive and Want You Gone. I downloaded the demo today, and J- flew through it eagerly. The final demo level came all too soon.

Aha. Teachable moment.

“Do you remember the three Greek words we have in the kitchen?”

“Ethos, pathos, and logos.”

“Right.” I wrote them down, with brief descriptions, under the title, “Why should we get Portal 2?” I read the title out: “Why should we get Portal 2?”

“Umm… Because it’s educational?”

“How?”

“Speedy thing goes in, speedy thing comes out, that’s all I have to say.”

I look at her and do the you-can-do-better-than-that smile.

“I’m not good at this stuff.”

“Try writing all of your ideas down. You can make your arguments stronger by editing them afterwards.”

We’re still a bit fuzzy about the categories, but it’s great to see where she’s going. Here’s the list she came up with:

Ethos:

  • helps improve sense of humour
  • I will actually do my homework properly and thoroughly
  • can create a topic of conversation
  • can create more interesting stories to tell others

Pathos:

  • spend time together solving puzzles and getting a good laugh or two (bonding factor)
  • fun! (lolz!)
  • more inside jokes

Logos:

  • hand-eye coordination
  • momentum
  • solve puzzles – helps make you better at solving puzzles
  • may help me with typing faster
  • can create inspiration for writing a book or drawing a picture

“Try thinking of reasons why we might say no, too,” I said. After some thought, she listed:

  • might take up too much time
  • too close to screen too often
  • may not play it as often, may be wasted

“Now think of ways you can address those concerns.”

“Maybe I can set a time limit, like 30 minutes…”

“That would take care of the first and second concern. How about the third?”

“It’s like you don’t want to play it too much, but you also don’t want to play it too little…” she said.

“Right. Because if you played only a couple of levels more, it would be a waste. But you played the demo and…”

“… it was amazing…”

“… so the rest of the game…”

“… will probably be ten times as amazing…”

“… and you know you’ll enjoy it. There, see what happens? When you think of why someone would say no and you address those concerns, your argument becomes stronger.”

“Oh, I get it now.”

“Great! Would you like to take this further by organizing your arguments into a proper speech, like this”, and here I sketched out what the speech would be like, with English mixed with fast-forwarded gibberish and hand-gestures so that she could get the sense of it.

She laughed. “Sure!” she said.

Persuasion is a useful skill. Good to find opportunities to help people develop it!

2011-06-22 Wed 21:21

Study group: Flashcards and the Leitner method

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

The enemy of your enemy is your friend: mnemonics and negative integers

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.
A B Result
Friend + Friend + Friend +
Friend + Enemy - Enemy -
Enemy - Friend + Enemy -
Enemy - Enemy - Friend +

2011-04-26 Tue 20:05

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

Study group update: negative numbers, exponents, and awesomeness

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

Math study group: Positive and negative numbers

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