This chapter is all about creating math tasks that are open ended and allow for deep mathematical thinking and problem solving. There are specific ways that you can design (or tweak your current) tasks/lessons/activities so that they encourage creative problem solving.
It is important to design math lessons that engage our students in critical, thoughtful problem solving. Asking students to solve the same type of problem over and over doesn't open up mathematical thinking or encourage students to really engage with math.
I've always been big into creative math projects...design a zoo using specific exhibit parameters given in fractions, design a neighborhood by spending up to $1,000,000 buying three houses and writing checks for each purchase that show different ways to represent each amount, etc. Looking at the list above, however, lets me think about meaningful math tasks that aren't long, meaty projects. I can design meaningful math tasks that can be accomplished in a day.
My Three Favorite Quotes (and how I will use them to change my classroom practice)
This is a different structure for learning than many students are used to. Many students are used to neat little worksheets where minimal thinking and attention are required. After much discussion and lead-in during a lesson this week, I set the students off to work. Several of them had no idea what to do.
I called them back over and we discussed how we wanted to learn math and grow our brains. If the students want meaningful, open-ended math tasks rather than sit-and-get or worksheets, then they really have to listen and focus during teacher-time. I promised to keep the blah-blah-blah to a minimum if they promised to really focus. If they couldn't commit to that, then they could choose to go the "worksheet" method, where the instructions were printed neatly at the top and everyone worked to get the same answer.
They all made the first choice. I knew they would. Teaching and learning through open-ended inquiry is a hard transition when students aren't used to it. We're getting there. The first step was to understand the expectations and then choose to meet them. I think it will be totally worth it to light up and unleash their creativity in problem solving, rather than encourage computing math robots.
This one is also going to be hard, hard, hard. Moving through the lessons in The Week of Inspirational Math, my students had to get used to this idea. They are often primed to tick off a quick answer and then move on. When they had to look at it several times and solve it several ways or look for more than one pattern, initially they stalled. After a few days, I started to see some opening up. Again, this will take time, but I think it will be so worth it.
One of my larger goals this year is to improve our communication skills. I want all students (even the shy ones) to feel confident that they have something important to say (because they do) and feel comfortable contributing it to our shared knowledge. I want students to speak with their eyes up and with strong voices because they matter (and because they've had practice). Allowing and expecting them to defend their work is a step towards this goal.
I think I was moving in the right direction in my math lessons, but being more intentional about the math tasks I assign will definitely improve my instruction. I'm really excited to keep reading towards the practical, classroom changing conclusion!