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Week 4: Chapters 8 - 9, Question #3 Which of the nine strategies for encouraging students to become more aware of the math they are learning...

Which of the nine strategies for encouraging students to become more aware of the math they are learning and their place in the learning process would like to try? What appeals to you about that strategy?


Duane Dorion's picture

The one that intrigues me the most is probablly peer assessment.  I think because of two reasons, one is it O.K. with Ferpa to do this?  Also, if it is O.K., I can really see where students can learn a lot from each other.  I remember doing this in high school and college myself and I learned a lot by seeing another way another student solved the same problem.  Sometimes, I would find an easier way of doing something than the way, that I approached it.  I can see that students can learn a lot from each other.  While working in groups, I can see that students would move around the room showing each other group how they solved a problem.  The whole group of students could learn a lot from the process.  Plus, students get a lot more efficient in a task if they teach it to others.

Patricia Helmuth's picture


I like the idea of peer assessment as well. I haven't done it all that much; although, I did learn an activity at a math institute that I went to, that reminds me of Boaler's Two Stars and a Wish on page 157, that I have used in my class. On the TASC Math exam, there is one question that requires a constructed response. The activity, that helps to prepare students for this constructed response item, goes like this:

  • Work on a contextualized math problem
  • Justify the conclusions you reached after working through the problem in written form (explain your method or your thinking).

After students are given some time to write, they pass their paper to another student. Then, each student writes one statement and one question on the work of their peer. This process continues until each student's work has been peer reviewed by 3 or 4 other students. I really think this method is valuable in that it helps students to learn:

  • To make clear statements about the work of their peers
  • To ask good questions
  • To write constructed responses that are clear and understandable
  • To take responsibility for their own learning
  • To communicate effectively

That's what immediately comes to mind but I'm thinking that this simple exercise can go a long way, not only in helping students in math class but also in developing real-life skills that carry over into the workplace.

- Patricia

Patricia Helmuth's picture

At the COABE conference in April, I attended an Adult Numeracy Network event, ANN Under 10, and I was intrigued by a short talk presented by Cynthia Bell. Her presentation centered on formative assessment and she, like Boaler on page 149, describes the difference between formative and summative assessment. Cynthia asked the question, “Are you using summative assessment formatively?”, and gave her own experience in the classroom of what that might look like. It goes something like this:

  • Teach a lesson
  • Hand out a worksheet
  • Realize that students are making lots of mistakes on the worksheet
  • Rethink how to communicate the math to students

Conversely, what are some good ways to formatively assess students before the worksheet debacle? Cynthia talked about one method, which is the #4 strategy that Boaler writes about on page 159, that encourages students to become involved in their own learning, while at the same time providing teachers with a way to formatively assess and adjust instruction.

Traffic Lighting – In this method, each student is given a green, yellow, and red card and throughout the progress of a lesson, students can hold up the appropriate color card to indicate their level of understanding. The idea intrigued me when Cynthia talked about it at ANN Under 10 and reading about the idea again in Boaler’s book has made me definitely want to try it.

Actually implementing it in the classroom, though, has me a little nervous. Boaler mentions in her book that initially, some students are reluctant to use the cards and I anticipate that some of my students may have that reaction because they don’t want to put themselves out there. Putting up a red or yellow sign says to the whole class, “I don’t get this.”

 I am determined to try it, though, because it seems like a simple enough adjustment to make, it would make me a better teacher, and it would give the students more control over their own learning. You can watch Cynthia’s talk here, where she talks about soup and asks some really good questions to ponder before implementing a new formative assessment strategy.

Amy Vickers's picture

Patricia, please share any reflections that you have after trying the strategy here in this discussion.  I imagine that others have similar concerns to yours and could learn from your experiences. 

I just thought of something...I wonder if it would help if you modeled using the cards when listening to a student's explanation of their solution pathway.  You could place your yellow or red card and then ask for clarification about a specific step.  This would demonstrate that it is fine to show any of the cards, that it means that it may be time for a question.

Pam Meader's picture

I have used something similar to the cards in my PD trainings. I have participants show thumbs up (got it), sideway thumb (almost there) and thumbs down (don't get it). I find it is a little less conspicuous then selecting a card as the participants can face me with their thumbs hidden from view of others. I have also used this in the classroom. It's a quick, great way to quickly assess where a class or group is in understanding a concept.


Patricia Helmuth's picture


I like your idea about using the thumbs up, down, and sideways. I might try that. I did try using the cards and had mixed results. It took some coaxing to get most students to buy into using them, but interestingly, some of the students who were initially the most resistant to the idea, turned out to be the ones who actually made it work the way it's supposed to. One student, in particular, was outspoken about how he wasn't going to use those cards. But one day when he had a question, I heard him say "hold up, wait a minute", and then he held up a yellow card.

I've also used them for students to agree or disagree with something that's on the board (it might be teacher or student generated). For example, I always do Number of the Day, everyday, and have been using the traffic lighting for students to agree or disagree with what their peers put up there. I don't always, though, trust the cards. If someone puts up an equation for the Number of the Day that is a bit more complicated than what is normally up there, and everyone holds up a green card, I'll probe: "How do you know that is correct?" "Why do you agree with that?" In this way, I'm hoping to train the students to use the cards truthfully.

Or, I might try using the thumbs idea instead and see how that goes.