One of my goals for the year was to build confidence in and appreciation of math. As a high school and college student of math, I was able to build confidence, but not appreciation for, math. I understood the procedures, but not really the why. I was able to use algorithms, but lacked an appreciation for the beauty of math.
It wasn't until my own children shared their love of math with me that I began to appreciate the allure and artistry of math. They loved patterns from an early age, taught themselves how to multiply and one even threw himself a math themed party. When my younger son reached high school, he complained that the humanities were required for all four years, whereas math was only required for three.
I wanted math to be an experience that kids enjoyed and helped them appreciate the beauty of math. Most of what we did in Pathfinder Math this year was to focus on process. Kids were praised for effort, for trying strategies and for using what they knew to help uncover what they didn't. In the beginning of the year, we rarely talked about the "right" answers, but focused more on the question "How did you get that?"
Conversations around math were emphasized. I wanted kids talking, explaining and listening to one another so that they could build understanding and confidence.
Students enjoyed all of this. There were many good discussions about process and then something weird happened. I had hoped that we could segue into "How do we know this answer makes sense?" and instead kids were focused on "Is this the right answer?"
What went wrong? I've reflected on this often in the last four months. The question "Does this answer make sense?" is heavily dependent on number sense. Only if you have an understanding of how numbers work (in essence the beauty of math) can you tell if an answer is reasonable. Number sense had been a goal as well. We'd done Number Talks to help develop number sense and mental math, but clearly not enough.
Knowing that my opinions would only get me so far, I asked the students. On the last day of class, I asked kids to reflect upon the year - projects they enjoyed as well as things they disliked. I wondered what suggestions they had for next year and what they perceived was the most important thing they had learned.
The results were interesting and I realized I have lots of work to do over the summer. Here are a smattering of their responses:
What did you like best about this class and why?
- Interesting facts and weird conversations.
- That I learned a lot.
- I am with a lot of my friends.
- We did a lot of cool projects.
- I like how we got to eat in class.
The diversity in responses was cool. But they seem to all point to a community in which we can all learn together. We didn't nail this every day, but it was nice that the theme emerged from student comments. How can we expand on this for next year? How can we create the kind of community that appreciates math? Again, the students shed some light.
What suggestions do you have to make next year's class better?
- Could we create more physical things? The polyhedron nets were super fun!
- You should let kids choose more of the projects.
- We should always be able to choose our own groups and sit where we want.
- Add more math games.
- More chocolate.
- Give kids the ability to vote on a project.
What was the most important thing you learned in this class this year?
- More advanced math
- Math can sometimes be fun.
- To always use the Core Values.
- I learned how to work with kids I don't like.
- Being brave at doing things and even though it is challenging to never give up,
- When I first came to this school, I thought I would be really bad at math like last year but that wasn't actually true. I actually got better.
There were some successes in Pathfinder Math this year. And certainly, there was some fun to be had. I think we generated some enthusiasm for math and I did notice a decrease in negative comments like "I'm bad at math" or "This is too hard."
As I plan for next year, I will use the student feedback to help create a classroom space and a curriculum that honors more of what the students report they need. Offering more choice in projects and the daily experiences, providing more opportunities for kids to play with math and allowing them to create more manifestations and visual models of math will be added to the list of goals. Hopefully, these will bring us closer to a place in which math can be appreciated, enjoyed and even celebrated. We owe this to our students - and not just the ones who already love math.
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