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Teachers’ Corner

Fawn Nguyen teaches middle school math in sunny Southern California. After taking several Math Forum online workshops and professional development courses and using Math Forum PoWs on paper for many years, Fawn recently “met” Suzanne and Max on Twitter and starting chatting about how she uses the PoWs. This year, she’s started to use the PoWs online, and you might see her students’ work in the Solution and Commentary for the AlgPoWs and PreAlgPoWs. We asked her for permission to reprint an edited version of a blog post she wrote about how she introduces PoWs and other rich problems in her math courses.

By Fawn Nguyen

I love teaching problem solving for a very selfish reason: I always learn something new from it. I learn from struggling with the problem, I learn deeper mathematics, I learn from my students’ different solutions and their non-solutions, I learn from other teachers, I learn that I have soooooo much more to learn.

I use three types of PSs (problem solving activities)— weekly, in-class, and group.

Weekly PS

The first time that I introduce this, the process roughly takes on this form:

  1. I pass out the PS. (To save paper and photocopying, student just gets a strip of paper that has the problem on it.)
  2. I call on one student to read the problem aloud. I then ask everyone to read the problem again quietly on their own. If it’s a particularly lengthy one, I ask them to read it again.
  3. Questions I tend to ask, “What are you being asked to find out?” “What information do you already know?” “What are your immediate thoughts about this problem?” “Have you seen a similar problem before?” “Do you have ideas on how to start the problem?” “Wanna give me a guess on what the answer might be?”
  4. I tell students that since this is the first time they do a PS in my class, I’ll walk them through the process of writing up a PS. I walk them through Polya’s four steps:
    • Understanding the Problem
    • Devising a Plan
    • Carrying out the Plan
    • Looking Back
  5. I blah-blah-blah about the importance of writing in mathematics, and that I don’t ever want to hear any whining, especially of this sort “but this is not an English class…,” because help-me-God if I do hear it.
  6. I emphasize that all write-ups must be on notebook or grid paper.
  7. Students have one week to turn in the PS. They get a new PS each Monday, it’s due the following Monday. This is the only assignment that I do not accept late.

That’s roughly my introduction. Then I help them begin the problem in class. This should take up to a full period. Before I dismiss them, I hope for this exchange:

Me: When is this PS due?
Ss: Next Monday!
Me: When next Monday?
Ss: At the beginning of class!
Me: What if you don’t turn it in next Monday?
Ss: That’s too bad!

Next Monday comes around…

True to my promise, I ask the kids to pass forward their PS write-ups. As I quickly leaf through the pile of papers in my hand, I can expect (and you should too) to witness the following:

  • Their papers: ripped holes, ripped corners, half-sheet, unlined, spilled cappuccino.
  • Their write-ups: red inked, work written sideways and upside down (a complete mess), Dad’s handwriting, four papers are identical (including the non-legible and nonsensical steps), only two papers include the “looking back” step, Mom’s writing at the top of paper asking for extra time.
  • Their solutions: all the numbers in the problem got added, all the numbers got multiplied, oh look, this student performed all four operations on the numbers, $850,000 for the bicycle, Victor is 48 years old (while Victor’s father is 36), the building is 756,411 feet tall.
  • Their reasons for not having it done: I don’t get it, I forgot it at home, my Dad accidentally threw it out, my sister who’s in calculus couldn’t even do it, my uncle who’s an engineer couldn’t figure it out, I don’t think there’s an answer for it, I was absent when you gave it out, remember? I’m-sorry-I-forgot-to-do-it-but-I-love-your-dress-Mrs-Nguyen!

I take a deep breath. Mentally embrace these precious children. Remind myself that I’ll be with them all year. Worse, they have to be with me all year.

So at this time I pass out a PS scoring rubric and carefully go over it. I’ve always used a 6-point rubric but I really want to change it to 4-point. [Ed note: For an example of a 4-point rubric, you might like to download a PDF of the rubric we use]

I give them a new PS for the coming week and only do the first three steps — reading the problem and checking for understanding — as I outlined above. I remind them that I offer PS help at lunch time.

In-Class PS
I don’t grade these. Because I encourage kids to do math with their family and anyone with a pulse, it’s nice to learn once in a while (about one per quarter) what they can do completely on their own. One class period.

Group PS
I don’t grade these either. Of course this is my favorite type of PS because I get to watch the kids do the math, ask them questions, and listen to their discussions. Before getting into their groups (I almost always assign kids in groups randomly), students have about 10 minutes of quiet individual time to work on the problem. I do make a conscious effort to follow the 5 Practices [Ed note: Fawn is referring to 5 Practices for Orchestrating Mathematical Discussions by Margaret S. Smith and Mary Kay Stein ] whenever kids work in groups.

I genuinely hope that you’ll incorporate problem solving in some fashion, if you haven’t already, into your curriculum. If you don’t think you have time because you feel you have to cover x-y-and-z content standards, then please make the time. Learning math is a social endeavor, a really fun one, please provide students with lots of opportunities to think critically and struggle productively. I think it’s a beautiful thing when we can develop a classroom culture of doing mathematics so contagious that it spreads beyond school boundaries.

You can follow Fawn at http://fawnnguyen.com/