The definition of the word “humanizing” is personal to everyone. When we think about the phrase “humanizing the math classroom,” memories might come to us about how we were given timed tests, assignments that made us wish we were robots, or when you walked into your math class about to take a test and just hoping you remembered everything in your brain for those 50 minutes. In this blog post, I will share activities that I have done with my students to show students that
- They are safe in my classroom
- Their thinking is honored
- Math belongs to everyone
- We learn from mistakes
to nudge towards a more humanizing experience in the math classroom.
They are safe in my classroom
In “The Art of Possibility,” a book by Benjamin Zander and Rosamund Stone Zander, the authors mentioned that we have two selves: our central self (otherwise known as our authentic self) and our calculating self. Now, “calculating” in this phrase means the mental calculations one has to either fight or flight. Our central self is who we are at our core whereas our calculating self is who we are in uncomfortable situations. For students, they might show their calculating self in the math classroom because they feel like they are in danger. Our goal is to let students show their central self and let go of their calculating self. For me, this is the first thing I think about when designing a class, because I can have all the good math content here but if they are still in the fight or flight stage, things just won’t work. How do we bring students’ central selves here in the math classroom?
A short aside: I taught an Algebra 1 support class several years ago. In this class, there was a student who sat in the back who didn’t do any work, like, at all. Telling him to do work wasn’t working so I decided to spend a couple weeks just talking about what he likes and his aspirations, and he mentioned that he likes fixing cars and wants to be a mechanic. I mentioned to him that I am pretty bad with cars and I had him teach me some things. I didn’t press much math during those few weeks but rather just got to know him as a person a little more. After those few weeks, he would slowly raise his hand and ask for help. This helped me learn early in my teaching career that we need to show students that we care about them as a person before pressing them to do work. I was helping him bring his central self into the classroom.
Here are a couple activities that show students that they are welcome and safe in my classroom:
- A couple weeks before the semester started, I shared this video with my students stating my three promises to them. As you watch, what are promises you would give your students?
- On the first day of class, I ask students to think of 20 words/phrases to describe their experiences in the K-12 math classroom. The purpose of this activity is to hear about their experiences and talk about their ideal math class, and what we can change from previous math experiences. Here’s one class’s response from this semester:
I tell them to tell me what they notice and ask if this is their ideal math class. What would we take away and what would we put as a replacement? I do this activity on the first day to show students that their voice matters. I hear them, and I want to work toward their ideal math class with them.
- Also on the first day of class, I ask students to think of someone they know personally that is good at math. After giving them a couple seconds to think about that person, I have them share out their qualities. Here are some responses from this semester:
I tell them to notice that no one mentioned speed or memorization. Let’s focus on these qualities instead. Notice also that all of these qualities can be practiced, so no one is born with their mathematical abilities. Let’s practice these throughout the semester. We all have the ability to be good at math.
Their Thinking is Honored
This might sound obvious but we need to honor student thinking. Here is Max Ray-Riek’s video of 2>4 that I strongly recommend you watch to see how people listen differently: https://www.youtube.com/watch?v=h00Ux1qx2zw. Are you listening for the right answer? Or are you listening to really hear their thinking?
One of my favorite personal examples where it made me grateful that I listened to student thinking happened 3 years ago. We were learning about arithmetic sequences so I put up around 5 or 6 arithmetic sequences and told students to find the 100th term of each sequence, one of them being the sequence below:
I gave the class several minutes to work, and in my head I was really hoping students would think to start with the first term, find the common difference, jump a certain amount, then you can find the 100th term. I was hoping students would think this way because it really lends itself to the derivation of the arithmetic sequence formula. Now, students did mention that thought process when we came back together, but one student raised his hand and said “I got the same answer but did it in a different way.” I told him to show his strategy on the whiteboard and his thought process blew my mind. Directly underneath 3, 7, 11, 15, 19, he started writing the multiples of 4 and said “Well, I saw that all of these were just one less than the multiples of 4, so if I need the 100th term, I can do 4×100 minus 1.”
I was amazed at how beautiful and simple his strategy was, and moreover, his strategy directly shows that arithmetic sequences are just a certain difference away from multiples. This one interaction made me realize that I should lean less on “hoping” students answer using a specific method and more just honestly honoring their thinking.
Overall, are we opening our minds so we will accept multiple strategies? Are we honoring their thinking? Are we showing students that we all have good strategies to share, not to just copy the teacher’s thinking?
Math Belongs to Everyone
I’m not sure about anyone else, but when I went through my undergrad studying math, I often wondered what the rest of the world was doing and where they were in their math journey. I could easily name 20 white male mathematicians but what about everyone else? If we want to show that math is for everyone, we should bring in math from different cultures. These are small steps, but one thing we can do is talk about number systems:
What do these number systems have in common? What makes each of these unique? I really like that their symbols are dependent on their environment. For example, Chinese used bamboo rods, Egyptians painted on walls so they had more elaborate symbols, whereas Babylonians carved on stones, and Mayans used peas and pea pods to count.
We can also talk about mathematicians to show that mathematicians aren’t just white men. This section alone can take an entire talk, but I’ll take some time to briefly share some mathematicians:
- Sonia Kovalevsky was the first woman to receive a PhD in mathematics and did so in 1874. She had to get a fictitious marriage because women needed permission from either their dad or their husband to go to college.
- Hypatia was the first recorded female mathematician who made contributions to astronomy and mathematics.
- Mary Jackson, Dorothy Vaughan, and Katherine Johnson helped send astronauts to space by calculating orbital trajectories.
- Benjamin Banneker made the first wooden clock in America, surveyed the nation’s capital, and made predictions on solar and lunar eclipses.
- Yang Hui wrote what we call “Pascal’s triangle” roughly 400 years before Pascal did! A student from China told me that they call it “Yang Hui’s triangle” in China and rightfully so. It makes me wonder what other mathematical terms are named after people who didn’t discover them first.
I also ask my students to draw a mathematician. What do they look like? What does their environment like? I give them 3 minutes to draw their mathematician and then share their drawings with their groups. Here are a couple of their drawings. Keep in mind they only had 3 minutes so I’m really impressed with their art!
I then share a study from Picker and Berry (2000) where they asked 12-13 year old students from 5 countries to draw a mathematician. As you may notice in the table below, as a whole, the majority of students were drawing male mathematicians.
Here are some of the drawings from the study. As you look at these images, ask yourself, “What do I notice? What do I wonder?”
There’s a lot to talk about here, but within this study, not only were drawn mathematicians mostly male, but they don’t seem like someone inspiring. How do we show students that mathematics belongs to everyone? How do we create a personification of mathematics that people look to and say “I look up to them” rather than someone they don’t want to become?
Overall, if we want to show that math belongs to all of us, we need to show the history of math with a more worldly view. Talk about how people from different regions of the world created a need for math, how they counted, and their contributions. And most importantly, how are we showing students that they themselves are mathematicians? It’s kind of cheesy but I made a “I am a math person” frame for students to take a picture with on the first day of class, and on the last day of class, I ask them to reflect on how they have grown as a mathematician throughout the semester, just as a nice bookend to the semester.
We Learn From Mistakes
If we want to humanize the math classroom, we need to acknowledge that we change our minds all the time and we often make mistakes. I have my students read the article, “Why Understanding These Four Types of Mistakes Can Help Us Learn” (https://www.kqed.org/mindshift/42874/why-understanding-these-four-types-of-mistakes-can-help-us-learn) and reflect on it. What’s a personal example of each of these mistakes? What did you learn from them? On the test we just had, did you make a stretch mistake? Feel free to ask me or a friend for help. Did you make a sloppy mistake on the test? Make sure you double-check your work.
Additionally, we need to normalize the idea of changing our minds. Oftentimes we stick with an idea just because it’s so ingrained in us that we think it’s permanent and we see it as truth. For example, I kept telling myself for the past decade that I’m a bad cook, and even though I would make good meals, it just never phased my identity of not being a good cook. We need to realize that things aren’t as permanent as they seem, so I will have students reflect with this prompt: At first I thought________, but now I think ______. This could be for test revisions or as a weekly reflection. It’s okay to change your mind. That’s what happens when we get new information.
Humanizing the math classroom cannot be seen as just a couple set activities we do in our classes. It is a frame of mind that drives all of our decisions for our students. These activities nudge towards a more humanizing math experience but it is up to the teacher and their commitment to honoring the people in front of us to fully make for a more humanizing math class.
Thank you for reading.