Filling Glasses

I’ve missed you. It’s been almost a year since I last blogged here, but there’s a pretty good reason for that — I was putting together a manuscript that has been accepted for publication. The book is the collected wisdom of the Math Forum on facilitating activities to help students unlock their mathematical problem-solving potential. It’s called Building Understanding Through Problem-Solving and the Mathematical Practices and will be coming out from Heinemann in the fall. Putting together the book used up all my words (and time, and wore out the ‘e’ key on my computer) but now that it’s done I’ve got lots to say!

There are lots of ways to say what the book is about, but one of them is that the book is about things that teachers can do to support students developing both the disposition and skills to look at a math problem (any math problem, not just the awesome ones) and think, “I have things I can try!”

The topics range from building classroom cultures of listening and valuing ideas, to supporting students to communicate their thinking for different audiences, to activities that help students break down that wall of resistance to anything that looks like a math problem, to support with key problem-solving strategies like guess and check, change the representation, or make a mathematical model.

One huge reason for writing the book is to try to step into the gap (still wide, but narrowing) that is left when we focus all our attention on concepts or on skills. As math teachers we are getting more information on how students best learn skills (like math fact fluency, how to divide fractions, or how write valid equivalent expressions), and increasing attention on how to ground those skills in concepts (like understanding that division means “how many of these are in those?” or knowing that two expressions are equivalent “when the two expressions name the same number regardless of which value is substituted into them“). However, there’s more to doing math than knowing and calculating — there’s the doing part. Stuff like looking for patterns, generating and testing hypotheses, generalizing results, etc. The stuff that’s in the Standards for Mathematical Practice (1 page), not just the stuff that’s in the content standards (lots of pages).

The other stuff — practices, doing math, problem-solving strategies, methods, whatever you want to call it — is the fun part. It’s the “glue,” or the “verbs,” or the “story” while the skills and concepts are the words or objects that we do stuff with. How we get students to be doers, not just consumers, of math is a fun and interesting question. Fun idea: concepts and skills can be delivered through telling. Doing math just plain old can’t — it has to be learned by doing (and my hypothesis is that through doing math the concepts and skills  can also come along for the ride a lot of the time, and will usually be better retained and connected).

The book we’re publishing can be thought of as an activity guide (with student work and stories) for getting students doing math, and the beginning of a set of ideas for how we can think about what it might look like for students to get better at doing math — how we can track students’ progress and help them become better and better young mathematicians.

So, please accept my apology for not blogging, and I hope it turns out that the book is useful and interesting.

Sincerely,

Max

Charlie’s Gumballs

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The consumer education movement aims to teach people how to seek out, use and evaluate consumer information so that they can improve their ability to purchase or consume the products and services they deem most likely to enhance their well-being. It seeks to teach consumers how to interact in the marketplace in a way that allows them to make the best consumption choices for themselves, given their values and lifestyles. (p. 33)                                              Bloom  & Silver, Harvard Business Review, 1976

In 2006, the Financial Literacy and Education Commission (FLEC) published: “Taking Ownership of the Future: National Strategy for Financial Literacy,” which defined the purpose of financial literacy as to: “empower consumers to be better shoppers” (p. v), to help deal with a “market place that is constantly changing” and to “understand and select the products and services that best suit their needs” (p. vii).

Learning to Read the fine Print: We have to find ways to help students learn to care about the details – learn to ask questions, learn to think it’s worth investigating financial agreements

Show Students the Fine Print (see examples below):

• Let them read it
• Let them make what sense they can of it
• Let them ask questions about it and explore outcomes

Credit Card Examples:

APR or “annual percentage rate” is an annualized interest rate. Different APRs may apply to different balances on your account, such as your purchase balance or your cash advance balance. We use the APR that applies to each balance to calculate the interest that you owe us on the account.

The bill we send you will state your due date and the minimum amount that you must pay us by that date. This amount is your minimum payment. If you do not pay the minimum payment by the due date, we may charge you a late payment fee. You will also be in breach of the contract.

You may pay all or part of your account balance at any time. However, for each bill, you must pay at least the minimum payment by the due date stated on that bill.

Sample problem from the Math Forum’s Financial Education focus:

Choosing Charity

In the wake of the recent tsunami, a company decided to donate to a disaster relief fund. The company started by pledging a certain amount of money. To encourage their 60 employees to make individual contributions, the company pledged to also donate an additional fixed amount for each employee who made a personal donation to the fund.

The company treasurer determined that if one-third of the employees chose to make a donation, the company’s part of the total donation would be $7000. If 50% of the employees donated, the company’s part of the total donation would be $7750.

Find an equation that expresses the company’s part of the total donation in terms of the number of employees who donate.

If every employee chose to donate, what would the company’s part of the total donation be?

If the company’s part was $8875, what percent of the employees chose to make personal donations?

Tools to Start Conversations & Develop the Practices of Financial Decision Making:

Living Wage Calculator

Council for Economic Education’s National Standards for Financial Literacy

CFPB’s Credit Card Contract Definitions

How long will it take to pay off my credit cards

True Cost to Own a Car

What is my employee total compensation package worth?

National Endowment for Financial Education — resources for educators, check out the High School materials

Charity Navigator

Subway Tokens

Samantha purchased subway tokens from a machine. The instructions said that, for any amount of money you insert, you would receive the maximum number of tokens your money can purchase, along with your change.

Samantha put a $20 bill into the machine. She received 12 tokens and $2.60 in change.

Which is the Dominant Team?

There are eight teams in the Northern New Jersey High School Soccer League. Here are the recent results:

• Eastside beat Clifton, Montclair, Nutley, and Kennedy High Schools.
• Montclair beat Nutley.
• Bloomfield beat Don Bosco, Clifton, Eastside, Nutley, Kennedy, and Montclair.
• Hackensack beat Bloomfield, Don Bosco, Eastside, Clifton, Montclair, and Kennedy.
• Nutley beat Hackensack.
• Don Bosco beat Eastside, Nutley, Clifton, Kennedy, and Montclair.
• Clifton beat Kennedy, Nutley, and Montclair.

I was learning.

In December, 2011, I watched the CMC-North Ignite! talks in Asilomar. I continued to watch, listen, and learn. In April, 2012 Annie, Max and Steve again performed at Ignite! in Philadelphia at NCSM.

I was still learning.

On October 29, 2012 I received an email from Karen Cowe and she wrote,

“You knew that one of these days I’d come knocking.” … “This will be the last Ignite! for me, so it would be great to finally get you up there!”

I decided this was my opportunity to use what I had been learning from watching. One way to cope with the pressure was not to tell anyone at the Math Forum what I was planning to do!

On Saturday, December 1, mission accomplished!

The next day I emailed:

“My Ignite! talk was successful according to several accounts. I was in good company. I was #5 out of 9 [Avery, Jennifer, Harold, Bill, me, Lew, Ruth, Scott, and Mike. There were about 400 in Merrill Hall where it’s held in Asilomar. Even the balcony seating was full. The good news is that I didn’t even think about that. I can’t really say it was fun but I told Karen Cowe I was honored that she asked me and satisfied that I managed to do it without getting too stressed. As Ruth Parker said to me, she can’t remember putting that much prep time into something that only lasts 5 minutes! I agreed!”

“Well, we’ll see what the video looks like first since I have absolutely no memory now of what I said! It really is an amazing experience. You’re sitting there watching the four that are presenting in front of you and each of their 5 minutes “feels” like a real 5 minutes (or maybe even longer). Then it’s your turn and the fourth speaker comes over, hands over the mikes, you get them clipped on, you walk over to the spot, and suddenly you go into time warp and it all speeds up so quickly — it’s really, really weird — it all seemed over in about 5 seconds.”

Now that I have proof that I actually did it: Suzanne Alejandre at CMC-North Ignite I know that I really belong to the Math Forum Ignite! Club.

And, as often happens, I am thinking of connections between my experience of watching and learning and how that might play out in a mathematics classroom. There are students who may take time before being ready to perform. Are they watching? Are they learning? When they’re ready, will they perform? I believe there are and they definitely will. And, as I talk about in my own performance, if we create classroom environments to help unsilence their voices, there is even more of a chance that they will perform!

Val’s Values

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Capture the Flag!

The Algebra and Geometry classes at Mathland Hgh School are planning to play a game of Capture the Flag in the woods behind the school. They’ve been discussing how to fairly divide the woods into two territories.

They’ve drawn a map of the woods and added a coordinate plane. The Algebra class will put their base at (-8, 15). The Geometry class will put their base at (4, -3).

Growing Up

I am 3 feet tall.

My dad is 6 feet tall.

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