Math Forum Blogs

Free Scenario: Visiting Friends #anyqs

Max — Mon, 20 May 2013 16:00:59 +0000

Visiting Friends

Parallel, Perpendicular, Intersecting? #wcydwt

Suzanne Alejandre — Sun, 19 May 2013 01:32:28 +0000

Last week a fourth grade teacher in Philly invited me to work with her students. She emailed me to explain, ”We are moving into intersecting, parallel, and perpendicular lines. Would it be possible to focus your lessons Tuesday and Wednesday around this skill?”

On Monday I was still thinking about possibilities. I was walking in South Philly and suddenly thought of taking some photos with my iPhone. Here are the photos I took that day:

I combined them from photos that I took in New York City some time ago and posted here:

http://mathforum.org/blogs/suzanne/2012/07/

I made a PDF with one photo per page, sent it to the teacher Monday late afternoon so that she could project it on Tuesday during class. Here’s how the lesson went:

After greeting the students who I’ve not seen for awhile (standardized testing prep consumed their school/teacher for quite some time), I wrote these phrases on the board:

parallel lines
perpendicular lines
intersecting lines

I asked them to talk to me — I asked them, ”What do these phrases mean to you?” It quickly became quite clear that they knew a lot! After some time listening to them I told them that I took some photos on Monday. I further explained that I had been thinking about today’s visit and had “parallel” “perpendicular” and “intersecting” on my mind. We looked at the photos together (projected on the SMARTboard by their teacher). The photo that we really started talking about was this one:

What do you see?

In case you’d like a copy of the PDF I created and sent to the teacher, I put it here so that it’s accessible:

http://mathforum.org/alejandre/linesbig.pdf

Free Scenario: Bubblegum #wcydwt

Max — Tue, 14 May 2013 20:40:40 +0000

Free Scenario: Flying High #wcydwt

Annie — Mon, 13 May 2013 16:00:30 +0000

Flying High

A plane traveling 400 mph is rising at an angle of 30 degrees. A second plane, traveling 300 mph, is rising at an angle of 40 degrees.

Free Scenario: Spring Garden Planning #wcydwt

Annie — Mon, 06 May 2013 16:00:47 +0000

Spring Garden Planning

Today I started to plan my garden. The rectangular garden where I am going to plant is three feet longer than it is wide.

One third of the garden area will be sunflowers.

Another quarter will be planted with brow-eyed susans.

Only a fifth of my garden will contain columbine.

A sixth of my garden will be filled with trillium.

The rest will be foxgloves.

A Tessellation or Not?

Suzanne Alejandre — Sun, 05 May 2013 13:42:12 +0000

… that is the question.

In the mid-90′s when I was working on my Tessellation Tutorial pages (which, by the way, helped me land my Math Forum job!) I had an online conversation with Michael South. I still have never met Michael in person but I remember feeling honored that he would take the time to contact me and engage in a conversation about whether some of what I was presenting as being a tessellation really was or was not. I captured part of our conversation on this webpage:

http://mathforum.org/sum95/suzanne/m.south.html

The ideas Michael and I discussed have stayed in the back of my mind and surface whenever I see something that is a repeating pattern. I often wonder what the unit is. Is the frog wallpaper in the ladies’ restroom in the Osteria Marco restaurant in Denver, CO a tessellation? Is it really made up of squares and the frogs are the decoration within each square? Or does it, at least, give that illusion? Whether it’s a tessellation (in the stricter mathematical sense) or not, it definitely caught my eye — the color, the fun frogs and the pattern. Annie had to go look for herself and she took the photo above after I showed her my photos and requested one of the “unit”!

Free Scenario: Filling Glasses #wcydwt

Annie — Mon, 29 Apr 2013 16:00:31 +0000

Filling Glasses

And… we’re back!

Max — Mon, 22 Apr 2013 20:54:18 +0000

Hi Mathtwitterblogosphere,

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

Free Scenario: Charlie’s Gumballs #wcydwt

Max — Mon, 22 Apr 2013 16:00:38 +0000

Charlie’s Gumballs

NCTM 2013, Denver: When reasoning matters: using mathematical thinking to make financial decisions

Valerie — Sat, 20 Apr 2013 03:06:06 +0000

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