Ken Robinson Answers

I've written about Ken Robinson a few times (One and Two). The idea of creativity in mathematics was a sub-theme for my summer calculus class. Students at the end felt that some of the open-ended assignments (projects of their choice), non-standard problems (like the mobiles) and emphasis on problem solving helped open them up to creativity in math. But they suggested more specific demonstrations of how to be creative. (Boy, is that insightful.)

TED occasionally has question and answer sessions with their speakers who really ignited something with their presentation, and Sir Ken recently did this. (Here's the article.) He addresses math specifically:

"If you want to promote creativity, you need, firstly, to stimulate kids minds with puzzles and questions which will intrigue them. Often that's best done by giving them problems, rather than just solutions. What often happens in classrooms is, kids sit there trying to learn in a drone-like way things of not much interest that have already been figured out.

The best math teachers I know, like the best English teachers, are always giving kids puzzles. They're given things to work on where math skills are required but may not be the focus of the activity. There giving them problems to solve. Or they're made to engage with age-old mathematical problems. For example, I'm thinking about the problem of latitude. How do you go about measuring the planet? I mean, somebody had to do that. How do you do it? Professional mathematicians have such a cornucopia of fascinating puzzles, questions, proposals and conundrums. A great math teacher really has endless opportunities to stimulate kids minds and get them engaged with things they'd probably never thought about before. Rather than just giving them techniques." -Ken Robinson

It's not hugely original, but it's nice to get confirmation of things we believe from outside sources. He touches on engagement several times in the Q&A, and I do believe that's the central issue in teaching, and I love to ponder what is the key for math. Going to more and more of these reading conferences, I am insanely jealous of the teachers who talk about the book that turned a student on to reading. Problems don't seem to have the same effect.

Math Teachers at Play 13

The new carnival is up at Blog, She Wrote. The Money Games are there, as well as the generally nice idea of runnign a store for money practice at the Pumpkin Patch. I like some of the puzzles at Critical Thinking Puzzles. The card trick that's linked really makes you think about how much information there is in arrangement.

Money Games

Here are my two favorite money games. Change for the Better is based on a James Ernest design. He's the genius behind Cheapass Games (don't be put off by the name), and the game this is based on, Fight, he used to have on his business card. It really has some non-trivial strategy and thinking to it. Later I made the connection - or one of my preservice teachers did - with Smart, the excellent poem by Shel Silverstein. The other game I think I invented, Make It Take It. The idea was from a group of teachers who wanted students to be forced to find non-standard combinations of coins, instead of always taking 27 pennies, for example. That suggested a dwindling resource game to me. It's poissible to combine both with some visual representations of money, which is a nice support for struggling students. The handout is here, if you like worksheets or some of the representation support.

Smart
by Shel Silverstein

My dad gave me one dollar bill
'Cause I'm his smartest son,
And I swapped it for two shiny quarters
'Cause two is more than one!

And then I took the quarters
And traded them to Lou
For three dimes -- I guess he don't know
That three is more than two!

Just then, along came old blind Bates
And just 'cause he can't see
He gave me four nickels for my three dimes,
And four is more than three!

And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!

And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head--
Too proud of me to speak!

Change for the Better

Materials: Each player needs 1 quarter, 2 dimes, 3 nickels, and 4 pennies.

Rules: Play in groups of 2 to 6. Each player takes a turn. On their turn they put in one coin. They can take out a combination of coins that is less than the value of what they put in. For example, if you put in a dime (10¢) you can take back up to 9¢ – if it is there. Play continues until only one person has money left.

Instruction: Beginning players should just concentrate on the moves of the game. After students have gained some experience with the game, they can try recording their games to translate to symbolic representation. The data collected can then be examined for patterns.

Make It, Take It
a money game for 2 players or teams

Materials: Play coins or coin pictures or cards, amount cards. Record sheet if desired.

Play: Put the coins in the center. Shuffle the amount cards and make a stack. Players each turn over an amount card, and the player with the smaller amount goes first. On subsequent turns, players turn over an amount card, and see if they can make that amount with the coins. If they can, they take the coins. If they can not, it’s the other player’s turn. Play until all coins are gone, or both players in a row can’t make their amounts. The winner is the player with the biggest total value of coins they collected.

Variations:
Recommended starting amounts – 4 quarters, 6 dimes, 8 nickels, 10 pennies. Other amounts can be used. Teachers can add amount cards for more complicated amounts.
Players can roll two dice to determine the amount. (Note the dice variation requires more pennies.) Advanced play allows people to make change with the coins they’ve collected. For example, trading a dime from the center with two nickels they have taken before.
Players can use dollar value charts to keep a running total.

Example:
Bill and Keenya have been playing for a few turns.
Bill turns over 12 cents and takes two nickels and two pennies.
Keenya turns over 25 cents, but there are no quarters left. She takes five nickels.
Bill turns over 50 cents and can not make it.
Keenya turns over 6 cents and takes a nickel and a penny.
Bill turns over …

Instruction:
As with most games, it is recommended to play a game with teacher vs. the whole class to launch the game. Emphasize the variation in ways to make an amount by soliciting other possibilities from the students. Ask questions like “what card would be good to turn over next?” or “what card would leave me with no possibilities?” If someone is stuck, encourage good sportsmanship in helping them figure out a way to make the total. If that doesn’t seem to be working, or you are worried about their ability to make the amounts, students can play in a team of two vs. another team of two.

Many students will try a place value approach first, taking dimes and pennies. This will rapidly run them out of one or the other, forcing them to find other amounts. The amount cards concentrate on values that can be made with one, two or three coins, though several can be made with many more coins.

In summary, the teacher may wish to have students share their strategy for figuring their total at the end of the game. It is important to summarize by having students describe how they knew if they could make an amount or not. Another interesting discussion to start is if there is a strategy for better ways to play the game – is there an advantage to using fewer or more coins to make your moves?

Math Mama Writes...: Math Teachers at Play #11

Math Mama Writes...: Math Teachers at Play #11

The new Carnival is up, with Michigan Smith. I was interested in the Spirograph link. I've been trying to figure out a way to use spirograph to explore gear ratios for a cool fraction lesson.

Michigan Smith

This is a fun game that I've used 2nd-4th grade and at a family math night with some older kids. Also with my preservice teachers, of course. It practices measurement technique and familiarity with cm, as well as sneaking in some geometry about efficient paths and distances. There's not a lot of strategy, but there is some. The downside to the game is needing a new sheet each time you play - unless you laminate, of course.

The name Michigan Smith is my takeoff on Indiana Jones. This would be an easy game to dress up, or have kids make their own variation. The Gauntlet of Power picture is from the Magic the Gathering card of the same name, and is tm Wizards of the Coast.

The pdf is here at my faculty website. As an image it's below. Comments and feedback are always welcome.

Joke

From my brother:
A mathematician was confronted by his wife upon returning home at 3am.
'You said you'd be home at 11:45,' stated the wife.
'I said I would return at a quarter of twelve,' said the husband.

The funniest thing is that I'm always having these kind of conversations. Not from staying out too late, but from being too literal.

For your listening and viewing pleasure

One of the many interesting ceiling panels.

Goals of Math Ed

Arthur Benjamin, self-proclaimed mathemagician and a very popular mathematician among teaching mathematicians, at TED on why calculus is not an appropriate pinnacle for math education. To be replaced by: discrete mathematics (statistics and probability).

Teacher Props
Taylor Mali, teacher/slam poet on What Teachers Make. One of my calc students shared this. As Mike warned me, I'll warn you: profanity.

Interesting glass floor and 6 or 7 story dome of the main rotunda.

Planning
An audio link from the new teacher resource center: an audio interview with Suzanne Lieurance, a teacher trainer and children's author, about planning in threes. There's a lot here that's compatible with workshop teaching, emphasis on assessment and evaluation and teaching for engagement. A form for note taking is in the post here.

The graphics are from the beautifully restored Michigan State Capitol that we visited this weekend, which include a couple of nice mathematical designs . Lots of nice 4-, 8- and 16-fold rotational symmetry. And much nice frieze-type translational symmetry, too. The architect was Elijah Meyers, and this was his crowning work.