Three Moments From a Recent Lesson and Why They Worked

Notes from a middle school math class.

I taught a middle school math class recently here in Oakland, CA, the sort of experience I’d ideally get a lot more of in my life. It’s important for me to stay up on new slang, first and foremost, and also there isn’t a form of user research that adequately substitutes for actually using our curriculum and technology. Not for me anyway.

I’d score my lesson somewhere around a C-. Passing, but nothing I’m going to pin on the refrigerator. Throughout the lesson I was very aware that particular students were very eager to participate in class and doing quite well while other students were eager to not participate and were not doing as well. I do not blame the latter students. Teachers have lots of useful tools for drawing reluctant students into the work of the classroom. Mine need sharpening.

I want to report that while my facilitation felt uneven at times, there were three moments where I felt like I had the entire class dialed in. Interested and participating. Working and thinking. Here are those three moments and a word about why each worked.

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“How is this different?”

Here is the warm-up for my lesson. Our objective was to learn why the product of two negative numbers is positive through the metaphor of removing groups of anchors from a submarine.

At the start of the lesson, I opened up the warm-up from a previous lesson and said, “Here is what you have done before. How does what we’re doing today look different?”

A broad group of students was very active here, calling out several differences, including the most important one—the floats and anchors are in groups now.

Why it worked

Early in the lesson, I want to keep the math concrete rather than abstract. Remember Bruner. “Any subject can be taught effectively in some intellectually honest form to any child at any stage of development.” A five year-old could identify differences between the two screens. Remember Gutierrez. “A more rehumanized mathematics would depart from a purely logical perspective and invite students to draw upon other parts of themselves (e.g., voice, vision, touch, intuition).” Remember Schwartz. Contrasting cases help prepare students for future learning.

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Can anyone get 25?

The first screen invites students to try different combinations of floats and anchors on the submarine. Just play around. Easy access to the problem. Once that early energy had subsided a bit, I told the students I was struggling to get 25. “Can anyone get 25? I’m having a hard time.” It felt like everyone was on board here, with some kids telling me loudly this would not be a problem for them, no sir, and other kids visibly bouncing between 24 and 27 and back again. When kids decided it was impossible, I asked them how they could know for sure.

Why it worked.

The challenge was easy to understand and seemed inside their zone of proximal development. The target was literally visible on the screen and in between two numbers they knew they could reach. Also, students had the opportunity to do something the teacher said he can’t do, which for many students is very appealing.

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“I’m going to pick four of the most useful sketches.”

On this screen, I asked students to synthesize their ideas and write the value of 2 • (-4). “I’m looking for sketches that really make your thinking clear,” I told the class, “and I’m going to pick out four of the most useful ones to share back to you.”

Then I shared these sketches one at a time.

Great, right? The class was completely quiet during this review, as wrapped up in the moment as I was.

Why it worked.

There is nothing more interesting to kids than … kids … than themselves and their classmates. I think this probably goes for most humans and a bunch of other mammals. People love to be seen as valuable, to be seen for their assets rather than their deficits, and I think that goes triple for people learning math in math class, where you are often identified by what you don’t know rather than by what you do.

Thanks for digesting this experience with me. I’m heading back to teach another class as soon as possible, hoping to lean into each of the ideas here and ideally pick up a few more.

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Odds & Ends

• 🚨 A new viral math problem just dropped! I love this one because I think one answer is way more defensible than any other and the rest of the answers basically map out the entire human psyche.

• NCTM released their position statement on artificial intelligence in math education. Lots to like here. Phil Vahey offers some useful credits and critique.

• Deborah Loewenberg Ball asks in Education Week, “Why Is the Nation Invested in Tearing Down Public Education?” A really essential perspective here: “Missing from this story is that U.S. students fared better than most of the rest of the world during the pandemic. That view doesn’t fit the hopeless crisis narrative, a narrative to which Americans seem wedded.”