I Am Good at Finding Patterns

The end of the school year is usually an emotional time for me for a multitude of reasons: some students who I never reached, some personal goals unaccomplished, curriculum not covered, rushed lessons, unfinished conversations, the workload doesn’t fit into 24 hours day and “my kids” are about to disappear into the summer. So this post is not about a lesson or a series of lessons, it’s about emotions and perceptions.

Introduction

As the school year is coming to an end, so is our Mount Holyoke College Course. During the most recent session with Kaneka Turner, she shared her call to action with us.

  1. Interview a set of student you serve using the following:
  • Are you good at math? How do you know you are? are not?
  • Do other people know you are good/not good at math? How do they know this?
  • Is there anything about math class that causes you to be good/ not good at math?
  • If you could change one thing about math class what would you change and why?
  1. Consider the results of this interview and the implications for your math classes.
  2. Plan to or actually make 1 change as a result of the results.

I decided to start with taking two questions and asking my fifty grade 3 students to write an answer. I told my students that I need critical feedback so me and other teachers can be better math teachers, and I trust my kids’ honesty.

Question #2 (we are moving backwards):

If you could change one thing about math class, what would you change and why?

There were some interesting ideas, but a found that a lot of the answers were very personal and focused on what students find hard or easy, and then they want things to be either harder or easier.

Students want: more problems, more time, more division because multiplication is too easy, more geometry, more multiplication bingo, more Desmos, word problems instead of “just numbers”, learning more strategies, harder, easier, more times tables because I know them, more tests.

Students don’t want: subtraction because it is too hard, multiplication because it is too hard, too hard math, too easy math, no standard algorithm, no tests.

This was all alarming, but it wasn’t the worst.

Question #1

Are you good at math? How do you know?

Most of my students felt they are good at math. And they should. But the reasoning stunned me.

Some responses I hoped to get more of.

  • I am good at math because I am good at finding patterns.
  • I am good at math because I can find patterns.
  • I am good at math because I know good strategies and know how to use them efficiently.
  • I re-think what I learned when I get home.
  • When I get to solve problems it’s actually kind of fun!

That’s it, five responses, the rest I hoped I wouldn’t get.

  • I am not good at math because I don’t understand how standard algorithm works.
  • I am good at math because I learned division and multiplication before grade 3.
  • I’m ok because I am good at adding but subtraction is confusing.
  • I am kind of good because I remember my times tables up to ten.
  • I am good at math because I can times big numbers.
  • I am good at math because I am fast at multiplying and also correct.
  • I am good at math because I can add, subtract, multiply, divide and my brain works fast and smart.
  • I am good at math because I get more answers correct.

And the nail in the coffin.

done and over

Emotional moment # 1

I went through…

Denial: They didn’t understand the question. They just tried to give the “right” answer.

Anger: Why didn’t they get it? All year was for nothing!

Bargaining and looking for excuses: If only program of studies didn’t put that much emphasis on numeracy in elementary. I only have one outcome for geometry and two pages for operations. If only I have asked these questions earlier.

Depression: I am a terrible teacher and now it’s too late to do anything. I failed at one thing that I believe really matters. I’ve been leading workshops about math teaching all year and I’m a fraud. I’ve ruined my students’ math education and they will hate math for the rest of their life.

Acceptance: Now, what can I do about it? Because I can’t just leave it.

Continuing the Conversation

We started by getting together with all fifty kids and my teaching partner and brainstorming what it means to be good at reading. I hoped to get a T-chart and compare reading and math. We did make a T-chart, but a result was surprising. What do you notice if you compare this chart to students’ personal responses?

tchart

I noticed that there were more answers that I expected to get in the first place. Were my students just telling me what they knew I wanted to hear now? Did they get more ideas from each other? Whatever it was, my original plan to compare and contrast it with reading was not turning out to be dramatic enough. We noticed similarities.

Then I asked my kids what we did in math this year. They told me about addition and subtraction. I put it on the board and circled it. And then we kept going. We kept going for a while, and when the bell rang I asked the students who still had more ideas to add them on the post-it notes. Here is what we came up with.

board

And more from the notes: Is 5 closer to 0 or to 10, patterns in a triangle, polydrons, odd and even numbers, egg experiment with weight, paper (cardboard) SOMA cubes, multiplication gummy bears, Euler’s formula and making geometric shapes.

After lunch, I asked students to look at everything we have on the board, on the ideas on the post-its, and put a thumb up if they felt successful at something, did good at it. My students are used to showing the number of strategies they came up with on their fingers, so I saw how more fingers were following the thumbs, kids reminiscing on the year of math and counting their successes. They were beaming. Two girls quietly moved to writing more questions.

Questions

Emotional moment # 2

I told my students that I am writing their report cards now and no one is getting any 1s, and if they worry about it they shouldn’t. I told that asking good questions is sometimes more important than getting right answers. I told them how I’ve been sharing their work with other teachers who always said what amazing mathematicians they are. I stopped because I realized my rambling might actually spoil the moment. I left all their notes on the board. I want my students to keep seeing it and thinking about their successes. I want them to remember that arithmetic is just one thread in the math tapestry.

Final thoughts and questions

I am glad I did not just end my year with the assumption that I know what is going on through my students’ heads as they enter and leave my math classes. I still wonder what I did wrong, what I need to change next year so that my students have this realization about the nature of math as a subject earlier than May. I wonder if something in my words, my lesson design was reinforcing the stereotypes. Do my words and my actions and choices always align? I realized that I want to change how my students feel about mathematics, I need to explicitly design my lessons with this goal in mind. I need to be more careful and more reflective.

I wonder what’s one thing I should change in my math class?

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