The same student that made the Problem Solving/Leadership connection sent me a cool link to a Guardian article. It's about adding interest to a dry subject (heyyy!) by adding content like art or emphasizing big ideas like infinity.
See the article by Marcus Du Sautoy
Tuesday, June 23, 2009
Friday, June 12, 2009
Carnival
Trig Rummy is up in this edition of Math Teachers at Play, a nice way to experience some of the variety of math ed blogs that are out there. It's hosted this time by Homeschool Bytes.
Here's a quick game for young kids up to 1st or 2nd grade. I think I invented it, but it's basic enough that many people have done something similar, I'm sure.
Give Away - It’s better to give than to receive!
Players: 2 to as many as you can stand.
Rules: All players start with five blocks (coins, beads, etc.) For one player they should all be the same, but different from the other players. The goal is to give all your pieces away.
Turn: Player says how many pieces they have. Then they roll a die. Players give away as many as they rolled – except on a 6 they give away nothing. Choose one other player you are going to give your blocks to. The first player to give all their pieces away wins!
Questions: Good questions to ask include “How many will you have left? How many will I have? If you have 4, how many have you given away? I can give back 4 blue, how many red do I need to put in?” Work on counting on and subitizing. Subitizing is recognizing an amount by looking – for example, asking: “Can you tell how many blue beads you have just by looking?” Try arranging the pieces in common patterns, such as on dice or dominoes. For counting on, if the player knows how many of one color (like 3) count on the others (4, 5, 6, …) instead of counting them all from 1. Ask about strategy and try to get players to think about giving to those with least.
Here's a quick game for young kids up to 1st or 2nd grade. I think I invented it, but it's basic enough that many people have done something similar, I'm sure.
Give Away - It’s better to give than to receive!
Players: 2 to as many as you can stand.
Rules: All players start with five blocks (coins, beads, etc.) For one player they should all be the same, but different from the other players. The goal is to give all your pieces away.
Turn: Player says how many pieces they have. Then they roll a die. Players give away as many as they rolled – except on a 6 they give away nothing. Choose one other player you are going to give your blocks to. The first player to give all their pieces away wins!
Questions: Good questions to ask include “How many will you have left? How many will I have? If you have 4, how many have you given away? I can give back 4 blue, how many red do I need to put in?” Work on counting on and subitizing. Subitizing is recognizing an amount by looking – for example, asking: “Can you tell how many blue beads you have just by looking?” Try arranging the pieces in common patterns, such as on dice or dominoes. For counting on, if the player knows how many of one color (like 3) count on the others (4, 5, 6, …) instead of counting them all from 1. Ask about strategy and try to get players to think about giving to those with least.
Thursday, June 11, 2009
Polya's Army
Problem Solving is a big deal in any math class I teach, and I, like most math teachers, use Georg Polya's problem solving phases as a framework. Though I used to teach it as a four step process, I now recognize it as four phases, which problem solvers can progress through in many different ways, back tracking and skipping. The ultimate reference on this is Polya's book How to Solve It. My handout (adapted from Dave Coffey's) is here; it focuses on Polya's questions. (Questioning being another important comprehension strategy.) The modern day successor to Polya as a researcher and teacher of problem solving is Alan Schoenfeld. The link leads to his site where he generously shares a lot of his research and work. I recommend at least skimming Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making In Mathematics (pdf link), a novella of a paper. Around pp 60-67 there's an amazing section on novice and expert problem solvers and teaching interventions.
One of my calc students was taking his final early, on his way to the month duty for army reservists, and commented on how he remembers Polya's steps by a connection with the troop leadership procedure. He sees:
- understanding the problem - receive the mission, issue the warning
- make a plan
- do the plan - start movement, recoineter, complete plan
- revise and check - issue plan and supervise
Wednesday, June 10, 2009
One Page Wonders
One option for my students to review, in this mini-6 week semester (odd but true that it seems equally as hard for students to remember the beginning of the course), is a One Page Wonder. I can not remember how I stumbled across them first, but this page at the bookpublisher Tor was the first one I'd seen. They use an old topologists trick to turn a single sheet of paper into an 8 page mini-book that can begin at any page, also be several different four page mini books, or fold to show any one single panel at a time.
When making a story for a one page wonder, it's important to have panels that can go in various orders to get the maximum effect. The first one of my own I made was this Batman one for my son's birthday, and my daughter has made a clever Warriors (the cats) one for herself and a neat gift wonder. Doesn't take long to try, and you'll surely enjoy it - so give it a go!
What's the value for my students? Connections and synthesis are two of the comprehension processes from Mosaic of Thought, the seminal text on teaching for comprehension. (That link goes to the publisher, where there's a sample chapter. Also, they're just now having a sale, $7.50 off. Go quick!). In a one-page wonder summary for the class, you'll have to narrow down to 8 important points, and get to see them connect to each other in different ways. If I get any neat ones turned in, I'll share them here.
Here's the Batman one: (click images for the full size picture)
I even used them in a bible class (also with a vid of how they work).
When making a story for a one page wonder, it's important to have panels that can go in various orders to get the maximum effect. The first one of my own I made was this Batman one for my son's birthday, and my daughter has made a clever Warriors (the cats) one for herself and a neat gift wonder. Doesn't take long to try, and you'll surely enjoy it - so give it a go!
What's the value for my students? Connections and synthesis are two of the comprehension processes from Mosaic of Thought, the seminal text on teaching for comprehension. (That link goes to the publisher, where there's a sample chapter. Also, they're just now having a sale, $7.50 off. Go quick!). In a one-page wonder summary for the class, you'll have to narrow down to 8 important points, and get to see them connect to each other in different ways. If I get any neat ones turned in, I'll share them here.
Here's the Batman one: (click images for the full size picture)
I even used them in a bible class (also with a vid of how they work).
Monday, June 1, 2009
Mobile Math
The emphasis is on the average as a balance. In calculus today, we covered center of mass, and built the connections among the moment, the weighted average and the idea of balance. Students used the ideas to create cardboard cutouts of curves and find the balancing point. They did a great job. Mine is the unimpressive cubic.
Thursday, May 28, 2009
Trig Rummy
My calc students have really been struggling with trig substitution, mostly, i think, due to lack of fluency with trigonometric functions. I'm a big believer in games for skill practice, as they are an engaging context that encourages more practice and ideally offer a chance for forging new connections.
So today we played Trig Rummy. Many of my card games are based on concentration, rummy, or go fish. And occasionally Euchre. (I still think the partially ordered quadrilateral Euchre has a future.) Links for printables are after the rules. I think it would adapt to high school trig pretty easily. I'd replace the calculus relations with graphs and triangle identifications.
Players: 2-4
Goal: get the most cards in play.
Set up: randomize cards and deal 7 cards to each player. (You may want to introduce the game with only 4 cards as 7 is overwhelming.)
Play: On your turn you may do one of:
• take any card from the discard pile (not just the top card).
• draw a new card.
After that you may do either or both of:
• pick up any sets you have.
• play any new sets you have.
At the end of your turn, if you did not play a set, discard a card.
Special:
• if at any point the discard pile contains a complete set, the first player to otice can cal “Rummy!” and take the set out to play for themselves.
• you can not play matching operator cards, like a pair of d/dx cards.
• There is a wild card, which you can choose to be -1× (times -1), or d/dx, or ∫ ⋅ dx.
End: After the last card is drawn from the deck, each player gets one more turn from the discard pile. Then the cards are counted up and the player with the most cards played wins. No penalty for unplayed cards.
Variation: Play until one player is out.
Example plays:
• Play sin2(x) matching 1 − cos2(x).
• Play d/dx with sin(x) matching cos(x).
• Play ∫ ⋅ dx with sec(x)tan(x) matching d/dx with ln|sec(x) +tan(x)| (since both are equal to sec(x).)
If a player lays a mistaken combination and no one catches it before the next player’s turn, they stay in play but turned face down. If someone does catch it, that player has to pick up the pair.
Feel free to use a trig cheat sheet.
Rules PDF - includes a trig cheat sheet
Trig Cards PDF - for 54 2-sided cards of trig identities and calc relations. Could use for flash cards or other games also.
So today we played Trig Rummy. Many of my card games are based on concentration, rummy, or go fish. And occasionally Euchre. (I still think the partially ordered quadrilateral Euchre has a future.) Links for printables are after the rules. I think it would adapt to high school trig pretty easily. I'd replace the calculus relations with graphs and triangle identifications.
Trig Rummy
Objective: the player will practice and gain facility with trigonometric identities and calculus relations.Players: 2-4
Goal: get the most cards in play.
Set up: randomize cards and deal 7 cards to each player. (You may want to introduce the game with only 4 cards as 7 is overwhelming.)
Play: On your turn you may do one of:
• take any card from the discard pile (not just the top card).
• draw a new card.
After that you may do either or both of:
• pick up any sets you have.
• play any new sets you have.
At the end of your turn, if you did not play a set, discard a card.
Special:
• if at any point the discard pile contains a complete set, the first player to otice can cal “Rummy!” and take the set out to play for themselves.
• you can not play matching operator cards, like a pair of d/dx cards.
• There is a wild card, which you can choose to be -1× (times -1), or d/dx, or ∫ ⋅ dx.
End: After the last card is drawn from the deck, each player gets one more turn from the discard pile. Then the cards are counted up and the player with the most cards played wins. No penalty for unplayed cards.
Variation: Play until one player is out.
Example plays:
• Play sin2(x) matching 1 − cos2(x).
• Play d/dx with sin(x) matching cos(x).
• Play ∫ ⋅ dx with sec(x)tan(x) matching d/dx with ln|sec(x) +tan(x)| (since both are equal to sec(x).)
If a player lays a mistaken combination and no one catches it before the next player’s turn, they stay in play but turned face down. If someone does catch it, that player has to pick up the pair.
Feel free to use a trig cheat sheet.
Rules PDF - includes a trig cheat sheet
Trig Cards PDF - for 54 2-sided cards of trig identities and calc relations. Could use for flash cards or other games also.
Tuesday, May 26, 2009
Another Math Blog
Which, come to think of it, would have been a good title for this blog.
I've been cosistently loving a lot of the links given by Y of X. It records the musings of Hendree Milward, a Connecticut math teacher (at Tunxis Community College?). Recently he's posted interesting links to the cool Institute of Figuring and an offbeat math poetry blog. If you read his blog, I won't have to bother putting up those links here.
I've been cosistently loving a lot of the links given by Y of X. It records the musings of Hendree Milward, a Connecticut math teacher (at Tunxis Community College?). Recently he's posted interesting links to the cool Institute of Figuring and an offbeat math poetry blog. If you read his blog, I won't have to bother putting up those links here.
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