1. Make sense of problems and persevere in solving them.
How are second and third grade teachers helping their students make sense of problems? During a recent online course focused on problem solving in elementary classrooms, these thoughts were shared in our discussions. I’ve received permission to quote them and provide them here as starting points we all might use to have a conversation.
Barbara says,
I think that if we teach our students that there are multiple ways to solve a problem (our goal—flexible thinkers) then they will become more independent in their problem solving. If they have a bag full of tricks…lots of different ways to solve a problem they will be able to explain why one way works over another way for them (or for that problem). I also think that if they become comfortable with lots of different strategies they can dialouge with other students about the stratey each one chooses to use. While I think the Brainstorming Representations is a bit wordy for 2nd graders to use, I like the idea of having a paper to help students think about HOW they are going to solve the problem before they solve the problem. I also think that the idea of a group working together would encourage constructing viable arugments….after all to decide HOW to solve it the student would be talking about all of these strategies that they have learned….Maybe they will draw a picture, act it out, build a model, use blocks or a number line. We have introduced many of these strategies but we continue to focus SO much on getting the problem figured out and a lot less time on how we might solve the problem. I think that is where I struggle….giving students the time to think about HOW to solve problems.
Our third grade class referred to the different strategies we employed to problem solve as tools in our toolbox (brain). We spent time at the beginning of lessons discussing which tool worked best for us and for the task at hand. What would be helpful would be a written visual, poster, or notebook item that we could also refer to when accessing our tools.
Do your third graders come with some strategies in their pocket, so to speak? I wonder about having an area in your classroom (maybe in the outline shape of a brain?) could be designated to post the different strategies and build it through the year. What might it look like? How might the students help create it so that it’s more than just a list on the wall but something that really helps them feel it’s a reflection of their brain (toolbox)?
The biggest obstacle for my students when making sense of problems is language and vocabulary. The majority of them can solve abstract problems (numbers only), but they get confused on word problems. We encourage them to underline the math language and to circle the numbers. They read the problem more than once and discuss with a partner what they think the question is about. We teach, re-teach, reinforce, and review phrases such as, “how many altogether? what is the difference? product? sum? how many more than?” This helps the students to better understand the abstract representation of a concrete problem.
We encourage perseverance by respecting all ideas and answers, sharing strategies and solutions throughout the class, and not stopping with the first answer or first strategy.
The conversations students engage in to understand the problem are important, as you have pointed out. One idea to try is to remove the question at first — we call that the “I Notice/I Wonder” activity.
We’ve found that if students are presented with the “scenario” and not the full problem, they are more apt to get into the problem. This article is from a middle school point of view but I have a feeling you could apply it to your elementary setting:
Problem Solving–It Has to Begin with Noticing and Wondering
http://mathforum.org/articles/communicator.article.dec.2010.pdf
You might find this one interesting, too:
Focus on Student Practice
http://mathforum.org/articles/communicator.article.mar.2012.pdf