One Student at a Time

After attending the NCTM conferences a couple of weeks ago, and especially after the inspirational #ShadowCon talks by  Kaneka Turner and Robert Kaplinsky, I heard my call to action, and I set out to reflect on what I was doing to empower students and invite them to the math table. For much of my teaching career, I’ve believed that the idea that a student wasn’t a math person was an impossibility, that there are so many parts to math that surely any student could be strong in at least one of those parts when given a chance, and when they put in the requisite effort, and that could spread to success in other parts of math. Over time, the details of my beliefs changed and morphed as I got to know more and more students, but the overall sentiments were the same. Then I read Jo Boaler’s book “What’s Math Got to Do With It?” which led me to more of her writing and research, and gave me a framework to think about and explain my own ideas, which very much aligned with what she was saying.

But even though I felt like I was doing a lot of the right things, and was attempting the right approaches, it had been a while since I had received any concrete validation that I was making a difference in any students except the “strong” ones who came in as “math people” and already had confidence in their ability.

A student came into my classroom earlier this year, telling me that she was not a math person, no good at math, couldn’t do it. If you’re a math teacher, you’ve heard this same story countless times, I’m sure. Well, I made sure to point out some of the really great things that I had already seen from her, and pointed out some of the great discussions that we’d had in class based on some of the questions that she had and some of the “mistakes” that she’s made. I didn’t know if any of what I was saying was sinking in, as she still repeated her mantra of not being good at math as recently as earlier this week. Well, last night, I got an email that brought a bona fide tear to my eye:


I was thrilled that yes, she saw herself as good at math, and yes, she felt invited to the math table, and yes, I was doing the right thing. With great pride, I tweeted this out, and then started questioning things. How long would this last? Is she still going to feel like a math person tomorrow? Next week? Next year? What about the other students – I know that she’s not the only student that hasn’t felt empowered or invited, and I have a lot of work to do.

And then I remember the last conversation I had with my father before he passed away. One Friday morning in 2010, I was driving to work and talking to my father on the phone, as I often did. We were discussing a former student of mine that I had been tutoring, and I was concerned that even though I was making good progress with her, there were many other students from that school in East Oakland that could have also been successful, and I wasn’t able to help them. He told me, “You can’t save everyone, but you can save one person at a time.” Ignoring the potentially patronizing tone in retrospect, the main idea has become a cornerstone of how I’ve tried to approach my teaching career. It’s like the late Speaker of the House Tip O’Neill said – “All politics is local”. I may not be in a position right now to change the entire math education landscape, but I can work to change how my students view themselves in the world of math, and I can make sure to continue to work on it, one student at a time.








Post Conference Excitement vs. Follow Through

Here we are, a week and a half after the NCTM annual meeting/conference in San Francisco, and how has it changed my teaching? How does a conference change your teaching practice? I don’t know about other teachers, but I feel a great sense of urgency after a conference to implement all sorts of new ideas and changes to how I teach and what I teach and how I interact with students and … well, it’s exhausting, isn’t it? Exhausting, and once you have a moment to reflect, overwhelming.

It’s been over 10 years since I last attended an NCTM annual meeting, but I do attend the California Math Council annual conferences for Northern California every December at Asilomar, near Monterey. For almost every one of the 15 years that I’ve been teaching, I’ve gone to Asilomar, and seen numerous inspirational and thought provoking speakers, and have spoken there a couple of times in the past myself. After a couple of years, though, I realized that I had to make a plan for myself of what to do with everything that I learned. So here’s what I try to take away from every conference: next week, next month, next year. What’s one thing I can use next week? What’s one thing I can use next month? What’s one thing I can use next year?

And here’s what I came away with from this year’s NCTM conference.

Next Week: Empower Students

My takeaway for next week (which was last week) was based on Robert Kaplinsky’s amazing talk (which should be posted later this week at Specifically, I came back to my school and gave a short presentation at our weekly staff meeting in which I went over his themes of student empowerment, and our role as teachers to differentiate between types of leadership that we exhibit: power vs. influence. If we operate from a position of power, we fear students taking our power from us, we hoard that power, and we work within a context of “me vs. the students”. Instead, if we focus on how we can use influence through example and empowerment, we work with our students, we build them up, and we develop a context of “all of us together” as we move through the class to accomplish our goals.

Power vs Influence

I can’t do this talk justice, but I can share with you the image that was burned into my mind due to it’s juxtaposition of such contrasting figures.

Next Month: Continue to Encourage Math Fights

One of my themes for this last year (and something I hope to speak about more at Asilomar this coming year) has been increasing student discussion in class, and so I attended many talks and presentations around this idea. Getting students to talk about math is an effective way to help them learn to develop and defend their ideas, as well as to accept and listen to other students’ ideas. Embracing these differences, and talking through them, is only possible when the classroom is a truly safe place. I attended a talk by Kathleen Strange who discussed the importance of creating that safe place in the context of a Growth Mindset as referenced by many great leaders in Math Education. (For a good introduction, check out Stanford Math Education professor Jo Boaler’s writings and her website for more information).

Fixed vs Growth Mindset

One of the most important things to do to create this safe space is to have a place where (as Cathy Seeley said in another talk) “…mistakes are expected, inspected, and respected”. The process of discussing “mistakes” is so much more important than correcting them. Accepting mistakes keeps the conversation going, which keeps the thinking happening. Correcting mistakes ends the conversation, and ends the thinking. So, I’m looking at ways to continue to improve the classroom environment more explicitly over the next couple of months, and have some more reading and research and discussion and experimentation to do along the way.

Next Year: Implement/Formalize Standards Based Grading:

One of the other presentations I attended was by Michael Manganello and Matthew Grinwis about standards based grading. Because of the variable credit system in place in my school, we already have the framework for standards based grading, and actually have a de facto version somewhat in place. However, we haven’t really formalized it. But to understand where I’m going with this, I should explain a little bit about our credit system.

As with many schools, we are on a semester system, and a typical class is worth 5.0 credits per semester. However, we separate the credit a student receives from their grade. For example, suppose you have two students. One student does very well (A level work) for the first half of the semester, and then does very little or poor work (F level work) the second half of the semester. A second student works hard but receives average (C level) grades for the entire semester.  In a traditional system, both students receive a C and 5.0 credits, but that tells a very false story, doesn’t it? In our system, the first student receives an A, but 2.5 credits, and the second student receives a C and 5 credits. It’s not perfect, but it tells a much different story. That first student will need to make up those 2.5 credits at some point.

What I will be working on this summer is going through each semester of class content and breaking it down into up to 10 distinct standards that can be assessed. Each of these standards should be worth generally between 0.5 credits and 1.0 credits, depending on what is involved in each standard. Because I teach in an independent school, we are not bound to the Common Core standards, although they are, in my opinion, a good reference point to use. However, this also will let me prioritize and focus my curriculum for my Algebra, Geometry, and Pre-Calculus classes.

So, there you have it – what I took away from this conference to use in the future. What else did I take away? Some new friends, some faces of friends from Twitter that traveled, some awesome Desmos swag available in the Desmos store, and a lot of reminders that, while I still have plenty to learn, I’m on the right track and doing a lot of the right things as a math teacher. Next step – will I get a proposal together in time to speak (or debate) at NCTM next year. If you want to fight with me over what the value of 0^0 should be, or if the order of operations is arbitrary and should be changed, or something else, let me know (via Twitter: @Ethan_MidPen or email:




To Textbook Or Not To Textbook?

I’ve always been reluctant to rely on textbooks when I teach. For many, the explanations aren’t quite right for my students. Frequently, there is just too much stuff going on visually, which can impact students with sensory issues, executive function deficits, or attention deficits. And can we say enough about how terrible the problems are?

For example, from the Chapter 8 Test in the 2001 Glencoe Geometry textbook, we have this very important real world problem:



Now, I admit that I am not a xylophone maker, or even acoustical engineer, but I’m pretty sure that there is not a single reason why a xylophone player or builder, in the course of their day, must name the shape on the top of the xylophone as a trapezoid. Now, this is just one example, and maybe a particularly bad example for this outdated textbook, although it’s always stood out to me. Many bloggers out there have written about “real world math”, and how the textbooks aren’t fooling kids into thinking this stuff is real. In fact, the one textbook that I have used that was very good with real world math applications was the COMAP Precalculus text that was discontinued for several years with only one edition. A second edition has just been released, which I’m hoping addresses some of the other problems with the text – not terribly thorough explanations of the math, and an assumption that the reader has remembered significant skills.

A lot of math teachers have migrated to PBL (Problem Based Learning), and there are some good resources out there. But my question, something that I wonder about, is this: Is there value in teaching students how to use a textbook? I know that part of my schooling involved learning what to look for in a text, how to analyze the material, take notes, and in essence learn the material whether I paid attention to the teacher or not. These were great skills for me to develop so that I can continue to learn independently, 20 years after finishing my undergraduate degree, and five years after finishing graduate school.

So I think that part of my reflection and planning goals this summer are going to be around incorporating the textbook better into my class. Step 1 is probably to get an updated textbook, though.