We started our first study group session on Friday with a quick review of multiplication. J- and V- warmed up by reciting the multiples of 6 to 9. Good retention from last year, and we’ll see how practice helps them improve. After the warm-up, we went over a shuffled deck of multiplication flashcards.

The teachers had given them a quiz in school, so we covered some of the topics they found confusing. W- and I explained the difference between convex and concave shapes using angles and lines. I drew different figures and quizzed them on the classifications. J- and V- drew their own figures, and they classified them together.

Squares and square roots were another point of confusion. We started off with a graphical review of what squaring means, and what a square root is. I used a tip from John Mighton’s “The Myth of Ability”: I tweaked my exercise to vary in scale without varying in difficulty. (What’s the square root of 31337 x 31337?) After J- and V- understood the relationship between squares and square roots, we covered approximation and factorization as ways of finding the square root. J- and V- practised finding the square root of numbers like 225 and 144.

We’ve encouraged them to take notes so that it’s easier to review lessons. The extra study group time will definitely help, too. Grade 8 will help students learn how to solve real-life problems, so we’ll be sure to show more of the calculations of everyday life. Here we go!

From Tuesday: J- has started Grade 8, the year before high school. Last schoolyear, we invested more time into helping her learn, and that worked well. I wonder what we’ll learn about learning this year.

J- was preparing for a quiz on pre-confederation Canada. To help, the teacher had labelled the settlements with A, B, C, and so on. J had made her own mnemonics. For example, D stood for ReD River Settlement. But the letters weren’t assigned in any obvious order, so J- was memorizing an arbitrary association.

Placing the information on the map was much more useful. We scanned in J-’s handout, then J- traced it using Autodesk Sketchbook Pro. With a blank map, J- could then add layers with her labels. After a few tries, she could correctly label all the areas in less than a minute and a half. (… and so could I! That will probably come in handy for any citizenship tests.)

We created a new map for Canada’s current provinces, and we quizzed ourselves on that too. For kicks, we took J’-s jigsaw puzzle of the provinces of the Philippines, mixed up the pieces, and assembled everything without looking at the picture. That was fun, although I was a bit slower putting together Mindanao’s provinces than I was at Luzon and Visayas. (More travel?)

Out of curiosity, I flipped through the other pages in her folder. One of the sheets had a timeline of events. “What if we could learn the order of these events?” I asked J-.

1. She looked at me, probably as intimidated as I was. I remember having such difficulty with trivia like that in my history classes. Time to see if I could pass on some tips from Moonwalking with Einstein and other mind-hacking resources.
2. I told J- about the idea of a memory palace – exaggerating the characteristics of items you need to memorize, then imagining them in specific locations in a place you know well. We walked through the process of imagining reminders:
3. golden blueberry bushes in the front yard for the prospectors of the gold rush
4. our cats meowing to be let out of the door – Ottawa
5. a colony of dust bunnies on the shelf – BC became a colony
6. Americans politely fighting over the litter boxes – the American Civil War
7. Charlotte Lucas and Mr. Collins on the sofa, discussing their impending union – Discussion at Charlottetown
8. … while Mr. Collins’ 72 relatives crowd in front of the bookcase (recalling Lost in Austen) – 72 Resolutions in Quebec
9. Mr. and Mrs. News and Mr. and Mrs. Canada getting together around the kitchen table – Nova Scotia, New Brunswick, Canada West, and Canada East
10. Tripping over a giant rubber eraser in an HBC bag blocking the corridor – Rupert’s Land, HBC 
11. Walking up the stairs and meeting a man with a big toe – Manitoba joins
12. Peeking into the guest room and seeing a busy party – BC joins
13. Going to the bathroom – PEI
14. Going to J’s room and seeing her toys in a circle – Consolidated Indian Act

We imagined it while we were in the living room. She physically traced the steps and talked about the things she imagined. Then she mentally retraced the steps. Even after watching a movie (Pom Poko, by Studio Ghibli), she still remembered the sequence. Let’s see if she ends up using it in school!

It’s fun adding tools to J’s learning kit. She picked up the strategy of inventing mnemonics. She made flashcards to practise the Gnommish alphabet from the Artemis Fowl series. Now she knows about mapping and the memory palace technique. For dates, we might try the Major system, if we can wrap our minds around it. I wish I’d learned about these things when I was in school, but hey, good to pass on the hacks! =)

Thoughts:

1. It’s better to find useful associations than arbitrary ones.
2. Autodesk Sketchbook Pro and other drawing programs can be good educational tools.
3. Learning something might not be important, but learning how to learn something – ah, that can be valuable.
4. The memory palace technique is great for remembering sequences. Exaggerated images stick in your brain.

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 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

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.

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).

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