Tag Archives: problem solving

First Day

September will mark my tenth year teaching in my current school district and my fourteenth year teaching. It is overwhelming to look back at all of the different ways I have started the year. I don’t feel like any of my first days were spectacular. This year things will be different!

I have been doing a lot of reading about the growth mindset. I recently purchased Carol Dweck’s book Mindset:The New Psychology of Success and I think I have the gist. It is all starting to make sense now. I have been trying for years to convince students that making mistakes is the only way to learn and if you aren’t making mistakes you aren’t learning. If you haven’t been reading about the growth mindset and fixed mindset, the premise is that once you believe that your intelligence can’t grow, it can’t (fixed mindset). You need to believe that learning comes from challenges and learn from the mistakes you make along the way (growth mindset). Great! Now that I had some research for these ideas I want a way to start off the year teaching them.

Two years ago I attended the Building Learning Communities Education Conference, while I was there I attended a session where the presenters were doing The Marshmallow Challenge. In the Marshmallow Challenge teams of four are given tape, 20 pieces of spaghetti, string, and a marshmallow. The task is to build the tallest structure that will support the marshmallow in 18 minutes. There is a great TED talk  by Tom Wujec that is also on the website. Tom stresses the importance of just trying something as soon as you have the idea, making a mistake and learning from it.

I’m really excited to start my year this way. I know there’s not a lot of math, but I want to set a tone. I want my students to be ready to accept a challenge, to make mistakes, and to learn.

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Ordering Fractions

I know. How dull! If I find it boring students must find it even more boring. As I mentioned before I’m kind of a number theory nut. After learning about the Farey sequence during my summer in PROMYS I knew it would be a great addition to my fraction bag of tricks. I tried it and students did it, but they weren’t getting where I wanted them. I don’t think I was asking the right questions.

I recently found this activity and tried the Farey sequence again. Students loved it. They wanted to try to get the next sequence. I shared it with a colleague and she couldn’t believe one of her students asked if it would be all right to do F9.

Here is F4:

Fourth Farey Sequence

from nrich.maths.org

I love lessons like this one. There is so much mathematics packed into it. We have mixed ability classes so students that are struggling with multiplication are sitting next to students that can solve equations in there heads. This problem allows students to move through at their own pace. I want students to practice comparing fractions. The fact that they are discovering patterns and symmetry along the way is a bonus.

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