Thursday, May 10, 2012

Their Way

There's something empowering about giving young mathematicians the opportunity to wrestle with math in a way that invites them to invent the strategies that end up teaching the rest of the class how to think more efficiently.  I suppose it kind of seems backwards.  The strategies come from the students instead of the teacher?  Yep.  It's certainly a new way of thinking for me and requires a step of faith, but I've found it to be a powerful approach to math.  When pressed conceptually instead of handed strategies on a silver platter, they do rise to the occasion.

I posted about my approach to contextual problems and math journals here, so I won't go into a lot of detail.  Basically though, when given a contextual problem, the kids attack the problem without any preconceived ideas from me.  In fact, they're encouraged to try several different ways of solving the problem.  I always say, "When you're done, you've just begun."  While they're working, I choose a handful of kids to draw their strategies on the board.  Those kids eventually explain or teach their strategy to the rest of the class at the end of the lesson.

I'm always on the lookout for strategies that will challenge the majority of kids to think more efficiently.  If one of the strategies drawn on the board does just that, I take a picture of it, enlarge it, give it a name based on its owner, post it on the board, and refer to it often.  Look below to see what I mean.

Let's take a closer look.  This is basically the order in which the strategies arrived throughout the year.

Amricka's and Garrett's way became useful at the beginning of the year when the kids wanted to draw 60 of something.  Pictures are a great tool when you're barely a first grader, but when numbers get big it's not so efficient anymore.

Dakota's Way eventually showed the kids that there's something even better than tallies.  Drawing groups of ten is much easier than drawing tons of tallies.

Dylan's and Rebekah's Way came later in the year and gave them another tool for solving problems both large and small based on the idea of the open number line.

Gus' Way showed them that breaking numbers apart using place value helps them think efficiently about numbers.

Scotty's Way actually showed up early in the year.  It demonstrated that mathematicians explain their thinking with equations.

This is the first year I've left visual reminders of their strategies on the board.  It was a good move.  (Thanks Duane Peck!)  I believe having them visually available helped kids make more efficient leaps in their thinking.  Thanks Idaho Math Initiative for pushing me to make more efficient leaps in my thinking too!

1. What a neat idea to capture their thinking in a picture and post it for them to refer to! Peers can be great teachers for each other!
Lori
Conversations in Literacy

1. Lori, they definitely learned a lot from each other. I love to see it work that way.

2. Brilliant! I love that it gives them the teacher role...they are teaching each other and have ownership of their work.

Laurie

1. Laurie, it sure does help them learn when they're put in the teacher roll, doesn't it? Thanks for coming by.

3. Such a cute idea to personalize their 'ways'. I bet they love that!

Emily
Tangled with Teaching

1. Emily, they do love that we name a strategy after them. Thanks for dropping by.

4. This is great!! It definitely allows them to be the "creater" of the lesson. It's also strengthens their problem solving skills. Awesome!!

Tammy
1...2...3...Teach With Me

1. Tammy, yep they're not afraid to solve problems. I always hated story problems. I hope my kids have a different experience.

5. I Love this idea. Thank you so much. I'm going to try it out. This is what I LOVE about these teaching blogs :))

❀Barbara❀
Ruby Slippers Blog Designs

1. Barbara, I'm thrilled to hear that you're going to try this out. I'd love to hear how it goes.

6. I am totally nabbing your idea! I posted about math today too! Great minds think alike ;)
Julie
Light A Fire in Third

1. Julie, nab away and then show me how you made it even better! Great minds!

7. When we allow kids the opportunity to problem solve on their own first, they become good problem solvers. However, many of us are guilty, at times, of dispensing information and then having the kids do what we tell them to do. THEN, when we want them to think on their own, they don't know how to do it. I like your idea of reversing this process. I REALLY like the way you take pictures and post your students' thinking. :)
Connie:)

1. Connie, I've certainly been guilty in the past. I'm enjoying reversing the process like you said. The kids can do amazing things when we let them. As always, thanks for coming by!

8. Love the idea of taking a picture and posting the child's solution. I often have students come up the the SmartBoard draw and explain their solution to a problem, but have never taken a picture. This will make a great reference tool for some kids. Thanks for the great idea!
Sandra
Classroom Companion

1. Sandra, I'm glad that you find this tip useful. It's been a great resource in my room for sure. I hope that it proves to be the same for you and your kids! Thanks for commenting.

9. Wow! I love the idea of getting the first finishers up to the board and then taking pictures of their strategies. Thank you! I can really use this.

❀Barbara❀