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.

Article on Interest in "Maths"

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

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.

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

How cool is that! I just had to share. Thanks, James!