Teacher candidates learning about children’s experiences with fractions: An example of an in-the-moment RotL

At the end of every semester, I always get excited to read the reports from my teacher candidates about their whole group math lessons. For weeks, my teacher candidates work to select a content standard, pull resources to get inspiration for a groupworthy task, plan connections to children’s experiences, and rehearse those plans.  And our methods courses are designed to support teacher candidates as they learn to teach… all while having fun and experiencing the joys of our profession.

With my colleagues at UTSA, our math methods classes draw immense inspiration from the foundational work of TEACH Math (Teachers Empowered to Advance Change in Math), DiME (Diversity in Mathematics Education), funds of knowledge, and so many other equity-oriented research groups in mathematics teacher education that are too long to list. Our teacher candidates engage in activities that help them to learn more about how students do math with their families and friends outside of school. For example, our teacher candidates engage in physical or virtual explorations around their field placement school. The teacher candidates visit places their students talk about in a getting to know you interview: where do you go, what do you do, and what do you see?

Over the course of the semester, the teacher candidates learn to train their ears, eyes, and senses to capture the strength in what children know… which is a DIFFICULT skill to adopt because we have been trained to look for errors and missteps.

Once the teacher candidates finish their lesson, they write a culminating report about what they learned about children’s thinking: What did you hear from your students? What can you say about your students’ thinking?  How might you adapt this task in the future?

We aim to help our teacher candidates move from looking only for correct answers to recognizing the strength of their students. Especially in the surprising and unexpected moments.  #LevelUpTeachers

What I really love when reading these reports is when the teacher candidates have “in-the-moment” learning opportunities about children’s multiple mathematical knowledge bases. When our students share what they know about mathematics, you learn so much more about their thinking! #ROTL anyone? #CreditToOlgaAlways

In this blog post, one of my teacher candidates, whom we’ll call Ms. Angelina (a pseudonym) graciously agreed to let me share what she learned after teaching a first-grade lesson about creating halves and fourths. In Ms. Angelina’s whole group lesson, her students used tools to cut play dough into equal-sized pieces. Ms. Angelina asked them to shape their dough into a triangle and to divide the shape into equal-sized pieces. Ms. Angelina expected them to cut the triangle into halves by making a cut from one vertex of the triangle to the opposite side. But a child surprised her. Ms. Angelina wrote in her report:

One of the children told me that he didn’t remember how to shape [or cut] it, but he thinks it would be equal fours if he cut it “into the Triforce”. Looking this up, I realized that it was a symbol from a video game that would in fact cut the triangle we used into equal fourths.

Not sure what the Triforce is? I didn’t either. [insert shrug emoji] As I was reading this, I Googled it and found out what a Triforce was:

 

 

OH SNAP. THIS KID MADE A LEGEND OF ZELDA CONNECTION?!?!?! WHAAAAATTTT. WHICH IS ALSO KIND OF A BUILDING BLOCK TO A SIERPINSKI TRIANGLE (fractal)?!?!? HOLY COWS Y’ALL. Are you surprised by this?!?!

But this wasn’t the only moment that Ms. Angelina learned about children’s connections to fractions in their lives. She continued to open up opportunities by asking her students how and where they see halves and fourths. Her students continued by saying:

Some students got a little more creative and talked about superheroes cutting asteroids in half in movies while others said you could cut a stop sign into halves or fourths if you really wanted to. Yet again I was excited to have another student who does not always participate, give a great and creative example…. He said he’d drawn an elevator. When I asked the boy, “why an elevator,” he told me that “elevators open in half, it is an example of a rectangle in half.” It blew my mind to hear such a unique and real world related example that I had never heard anywhere else.

I agree, Ms. Angelina. That blew my mind too!

[Side note: As I wrote this post, I thought, “I should find a cool GIF of an elevator door closing” but then got lost down a weird rabbit hole of GIFS.  Side note: Can I tell you how CHALLENGING it is to find a funny, yet appropriate elevator GIF to use on an academic blog that refers to children’s amazing connections to seeing halves? Well, instead of an elevator door GIF closing to show the notion of halves, I found lots of Star Trek GIFs of elevator door-type scenes. But because I don’t watch Star Trek, I found this instead….so you’re welcome.]

At the end of the day, we should create more opportunities for children to share how they see mathematics in their lives. Especially those in-the-moment spaces for children to share their experiences about a video game, traffic signs, and multi-story building references like an elevator.  I would have never thought about Legend of Zelda or an elevator as examples for halves and fourths, but that’s why we are teachers. Stay surprised by what your students say because remember… your students have the right to surprise you as a learner.

And I didn’t want to let you without some kind of elevator GIF [that didn’t include a cat]… here you go.