Every term, a lot teachers (myself included) are disappointed that students didn’t learn exactly what we intended them to. Furthermore, they didn’t learn as much as we wanted or thought they could. I’ve been there before many times, and that result is the main reason I changed the structure of my class to focus on student discourse and making sense of problems.

The last question on the final today was “Tell me something you learned about yourself this trimester. (It does not need to be math related).” Of course, it’s a math test so most of them tell me something math related anyway which doesn’t bother me one bit.

I originally was going to just share some highlights, but reading these answers brought me so much joy, I am just going to share the whole list.

I learned:

• I understand math better when I’m given problems to try rather than just talking notes.

• How to help myself learn on my own by asking more questions to deepen my understanding.

• I can learn math with a group of people I don’t know at all and we can have fun as well.

• I can develop my own solutions to problems and make sense of ideas myself.

• I could be independent and do my work with less and less help.

• It’s ok to ask questions but I learned how to believe that I can learn math myself and figure things out.

• I don’t give myself enough credit for what I am able to do.

• I learn things a lot better when working with others.

• I am capable of being independent but still learn what I need to in order to be successful.

• I am able to figure things out myself even if it’s not explained to me first.

• Making sense of WHY I am getting an answer is much more important than the answer itself.

• Understanding why something happens is much more useful than understanding just how to do it.

• If I work through problems and bounce ideas off my teammates I CAN figure things out instead of being shown first. I enjoyed this, which surprised me.

• Applying yourself to learn the material instead of memorizing it is much easier.

• I CAN in fact understand the abstract concepts of math.

• If I can’t explain WHY something works, then I don’t fully understand the concept.

• I am a very hard worker and determined to reach my goals. I’m unstoppable when starting a problem.

• I am able to graph functions without a calculator because I understand how they work.

• The graphs of equations are really satisfying once you understand why they work.

• I enjoy being able to figure things out myself first.

• I really like to work with people to figure things out and I didn’t think I would.

• I am able to make sense of my answers and not just get the answer, which is much more important.

• Once the connections between concepts were more clear, math becomes much easier to understand.

• While I’m not the best at understanding things while I’m being taught, when I teach other people, I retain the information.

• How to explain myself better by teaching math to others.

• When I need to explain something to someone else, I understand it better.

• If someone doesn’t understand something, I am able to explain it in a different way that they can understand.

• The more I am engaged with the math, the better I do.

• Ask when you get stuck. The teacher will help you.

• I’m glad I took another year of math even though I don’t like it.

• I am able to teach other students when they don’t understand.

• How to work through things better with a group of people.

• The struggle is part of the process and you have to go through that barrier to learn new things.

• I can handle more stress than I thought I could.

• I am a visual, hands-on learner rather than just being shown how to do it.

• I can be a mean person and that can turn people off from friendships.

• I can better understand if I apply my mind.

• Applying what I learn to everyday activities, I understand them better.

• I should cherish my time with my friends and family before it’s too late.

• I need to stop slacking on homework because it only gets harder from here.

• There’s only so much in my control and not everyone will care about some things like I do.

• If I actually take time to study and make sure I understand, I will do better.

• I should probably study more in college.

• It’s ok to not understand and ask questions.

• When left to my own devices, I don’t do anything productive. I need to plan.

• I do better in a classroom where there aren’t strict rules and things are more free flowing.

• Don’t judge a person because you don’t really know what they are going through.

• Not to overwhelm myself with school work and if I’m tired, I should go to bed.

• If I study for my college algebra tests, I usually do better on them.

• I love my job and my coworkers.

• I don’t need to stress so much about the future.

• If I want to get good grades in a college class, I need to study more.

  I am better at math when I have a therapy dog.

Today was the last teaching day for my college algebra class for the trimester. I’ve had to clear a lot of hurdles this year, both personally and professionally. Yet I’m prouder than ever at what these young people have accomplished in the last 12 weeks, and so today, I read them a letter of gratitude:

I’ve only cried in front of a class once, and that was first hour, the day after the 2016 election. So I’m going to try to not do it again today, but I make no promises.
This trimester, my college algebra classes have done some amazing, special, and unique things. When I started teaching this course, I was told to lecture from bell to bell, the kids need to memorize the formulas, odd answers are in the back so assign the evens. Every trimester, I’ve tried to make some improvements on that model and, although not anywhere near perfect, I’m really proud of where this class is now. That has less to do with what I do to modify the course and more to do with how you wonderful young people engage in it. The marble slides activity on Wednesday was a defining moment for me with this course. Lecturing from bell to bell wouldn’t have made students as successful with that activity as you were. Not even close. The creativity and curiosity you bring to school with you every day is such a treat to get to experience for me as an educator. It has been my absolute privilege to get to learn from you this trimester. Thank you from the bottom of my heart for not only letting me experience you grow as mathematicians, but for the energy you brought to collaborate and push each other to engage in making sense of the mathematics we have sworn to you is important for your future. You’re going to encounter math that will be more difficult than the math you encountered here and that’s ok. What you’ve done here is shown me that what is asked of you in math class should make sense, and by working together to provide one another with your ideas and your thinking,you’ve built a foundation for understanding the math you’ll encounter down the road. I believe in you as you go out there and make the world a better place.