The Limitations of Improving Summative Assessment

A year ago my school started a project of trying to improve the way we do summative assessment. We had lots of different systems and not a lot of coherence, and decided to move in the general direction of standards-based grading.

A year in, it was a great learning experience for me. I had used elements of standards-based grading before, but working to assess students in consistent ways across classes and deciding what is worth being consistent with was a valuable exercise.

Here’s the thing. We put in a ton of effort over a year. Assessment was a huge focus of our meeting time. And I’m not sure we saw particularly strong results. I do think what we did helped, I’m just skeptical that fiddling with grading is the best way to improve a school. As Shawn Cornally says, it’s like putting lipstick on a pig. The pig is the collection of institutional obligations we have that mean we have to give grades. The lipstick is our fancy new assessment plan, which is really just tinkering around the edges of a broken system.

I’m not an expert on the literature around professional learning, but I’ve been diving into research on how teachers improve this summer. When research looks at the elements of teaching practice that help teachers improve, summative assessment is conspicuously absent. Improving the curriculum matters, teachers’ pedagogical content knowledge matters, purposeful formative assessment matters. I’m sure more deliberate summative assessment helps too, but of all the levers that help to improve schools, it doesn’t seem like it’s very high on the list, and we only have so much time to spend on new initiatives.

This is also consistent with conversations I’ve had with lots of teachers who jumped on the standards-based grading train five or ten years ago when it was the hot new idea in town. Most of them are still using some elements of standards-based grading, but they’re also not too starry-eyed about the transformation that standards-based grading has the power to bring.

None of this skepticism makes me regret the work we’ve put in. I’m a more thoughtful teacher now than a year ago when it comes to assessment. But it does make me want to put my effort elsewhere in the coming year.

I know there are folks out there who disagree with me. I’m curious for some pushback. What am I missing?

A Reminder to Be Bold at the Start of the Year

Ordinary, said Aunt Lydia, is what you are used to. This may not seem ordinary to you now, but after a time it will. It will become ordinary.

-Margaret Atwood, The Handmaid’s Tale

It’s a bit of a gloomy quote to start a blog post, but it’s also something I find to be a profound truth about humans: our capacity to adapt to new situations and a new normal. Often when I talk to teachers about a new idea or perspective on their teaching, they tell me, “well when I was a student I wouldn’t have liked that,” or, “I wouldn’t have learned if it was taught that way.”

Maybe that’s true, given your experiences and what you were used to. But you have a year to spend with your students. You have the opportunity to set new norms and new expectations, to create the classroom culture you want to teach in.

Assuming that students won’t learn a certain way because you wouldn’t have liked it is also a narcissistic approach to teaching. Human memories aren’t very good, and I’m skeptical that any teacher can look back on their school years and separate their likes, dislikes, and emotional attachments from what actually helped them learn.

This isn’t an argument for blind change. Instead, it’s an argument to be bold about how I think about what is possible in my classroom. These might be structural changes like grading less to spend more time on relationships and student thinking, shuffling groups more often, or asking students to move around the room. They might be about redefining what it means to collaborate on mathematics or asking students to approach unfamiliar problems in new ways. And there are more potential transformations down the road that I don’t know about yet. Many things seem impossible until they’re real.

In a digital, connected world, I have incredible opportunities to learn from other teachers about how they create powerful classrooms. This is a reminder to be bold enough to learn from and imagine possibilities beyond my own experiences.

Elements of Great Professional Learning

It is impossible to begin to learn that which one thinks one already knows.


I’ve been reflecting more and more the last few days on professional learning — how I have learned about my practice, how I want to continue to learn, and what that learning can look like when it is done well. I don’t claim to know very much about profession learning but here’s where my thinking is now, and how I plan to pursue new opportunities in the future.

A Rich Vision of Teaching 
The most powerful professional learning for me has always begun by pushing the boundaries of what I think great math teaching can look like, in ways small and large. It might simply present a new tool or approach I hadn’t thought of before. It might share a conception of what an impactful math class can look like that goes beyond my previous goals. It might share an engaging new approach to a challenging topic that I had thought was boring before. I can’t learn what I think I already know; learning needs to start by showing me what is possible and giving me new goals to work towards.

Focused Effort 
I often leave conferences with a dozen different ideas I want to implement, or come back from winter break with a list of bookmarked blog posts full of all the new lessons I want to teach. Neither of those translates very well to enduring learning. It’s really hard to pick one or two goals just outside my comfort zone and dive deep into making them happen in my classroom. At the same time, I think it can be empowering to put everything else on the shelf for a bit and focus on one or two small, concrete changes that will make a difference for students.

A Community of Support 
It’s hard to put focused effort into learning on a regular basis. It’s also hard to read blogs, attend presentations, and talk to teachers about the incredible things they’re doing in their classrooms without feeling a little bit inadequate. I learn more when I have people in my corner reminding me that getting better at teaching is hard, but it’s also worth it. Rather than comparing myself to other great teachers I should just be comparing myself to where I was months or years before. A community of support can come in lots of forms, but I need those reminders to stick with my goals.

One final truth for me is that it’s far easier to get better at talking about teaching than it is to actually get better at teaching. I’ve been writing on this blog for close to four years. I’ve become more thoughtful and articulate about teaching and learning. But too often I’m stuck at step one, talking about what I want my teaching to look like. The real work comes from focusing on a few specific ways to get better and building the community I need to sustain that work over time. That’s where the magic happens.

A Letter to a Teacher Who Refers to Students as “Ladies and Gentlemen”

Hi! I want to talk to you about something. I’ve heard you referring to groups of students as “ladies and gentlemen”, as in, “let’s quiet down ladies and gentlemen” or “alright ladies and gentlemen have a great day”. When you use those words, you make an implicit assumption that all of the individuals you are addressing identify as either ladies or gentlemen. Some may identify as transgender, gender nonconforming, genderqueer, or other identities that resonate with them more than male or female. Even if no students in the room use those identifiers, your assumption impacts how they see themselves and how those young people form their identities in the future.

Equity work is a process of becoming thoughtful and purposeful about things that were subconscious before. Language shapes how we think. It’s not easy to change, and it takes time. But it’s worth doing.

Have you ever taught a transgender student? It was hard to change the pronouns I instinctively wanted to use. I unintentionally misgendered them, often at first, but I got better over time. I noticed that an adult at my school who often referred to students as “ladies and gentlemen” was also the adult who had the most trouble referring to that student by their correct pronouns. It was tough for everyone, but he struggled far longer and often misgendered them publicly. I can’t say for sure that one was the cause of the other, but it struck me as a useful object lesson of what can often seem like an abstract idea.

While changing your language to words like “folks” and “y’all” is not likely to change the world, I see it as a microcosm of the change the world does need. For thousands of years, human social norms have changed on a time scale of generations. Change happened slowly. People grew up exposed to different perspectives and as older generations passed on new ideas took root.

Today we have a clearer view of the equitable and empowering world we want for everyone. We can also see how far away we are from that world. Generational change will not be enough; we need action that will change hearts and habits today. And while language is only one piece of the puzzle, a willingness to work consciously to change behavior and construct new social mores is the work that will make the world a better place, one step at a time.

I hope that this letter does not feel angry or resentful. That’s not how I feel. Change is hard, but it hope it can also feel empowering. When you become more thoughtful about your language, you are also influencing the way others think and speak, and embracing the potential of every student who enters your classroom. I hope you feel empowered about your role in creating a better world, one microcosm at a time.

Thanks to Grace Chen and Nik Doran who helped me find the words to write this.

Talking About Students

I’ve been thinking more about equity since Grace, Brette and Sammie’s great session at Twitter Math Camp. In particular, I’m working to pay attention to the elements of equity that I attend to in my reading and thinking about teaching this summer, and the elements that I want to get better at seeing, recognizing, and acting on.

One thing I’ve been paying attention to the last few days is how I talk about groups of students. Most teachers see a difference between “high” students and “low” students and find this distinction useful in their pedagogy. At the same time, teachers use all kinds of different euphemisms to communicate their perception of different students. My go-to descriptors in the past has been “struggling students” and “high-achieving students”. I’ve heard other teachers talk about low-ability and high-ability students, students who are behind, gifted-and-talented students, top and bottom students, and more.

I’m coming at this with the assumption that words matter, and that the way that I talk about students influences the way I think about students and make decisions about teaching.

I’m also coming at this thinking about what it means to have an asset-orientation toward students and their learning. I want to avoid deficit thinking — talking about students in ways that assume they are static, that their challenges define them, or that their prior experiences predict their future success. Lani Horn uses phrases like “lazy”, “a C student”, and “at-risk” as examples of this perspective. Whether or not these descriptors are true, they aren’t particularly helpful in moving forward and teaching that student. An asset-orientation replaces this language with a focus on students’ strengths and their potential to grow in the future. Importantly, an asset-orientation doesn’t ignore students’ prior challenges, but it is focused on the future and next steps moving forward rather than students’ past performance and experience.

Teaching toward equity and empowerment means acknowledging the differences in students’ prior achievement. It means paying particular attention and putting focused energy into supporting students who have been less successful or felt less included in the past. I don’t want to hide from those distinctions. At the same time, doing this work with an asset-orientation means approaching each day by acknowledging students’ prior experiences but leaving behind assumptions about what they can do that day and in the future.

When I’m talking about students who teachers might call “low students” or “strugglers”, I want to try to start using more language like “students who have struggled in the past”, “students who have been tracked into lower classes”, and “students with low prior achievement”. Those are more specific phrases, and they make no assumptions about what students are capable of in the future. I want to work on always accompanying that language with an explicit focus on what I am going to do to support students and what my goals are for them moving forward. My goal is not to erase students’ prior challenges in math class; my goal is to acknowledge those challenges but leave them in the past, and focus on what all students are capable of in the future.

I hope that this type of thinking will allow me to see one aspect of teaching and learning through a new perspective. I have no illusions that changing my language in small ways will make a large difference in my teaching. But as I work to see my classroom and my pedagogy through an equity lens, all I can do is add to my toolbox, one idea at a time.

Community, Learning, and the Profession of Teaching

I just returned from Twitter Math Camp, and my mind is busy reflecting on a wonderful week of learning and building community with great math teachers. I’m fascinated by our little community. I’m also fascinated by my passion for it and my feeling that it has made such a difference in my career. And I feel particularly grateful; I was weaned on #MTBoS. The hashtag was first used while I was student teaching, and I was reading 30 blogs and following many of you before I stepped foot in my own classroom.

In sessions and conversations at TMC this year, I feel like I understand more and more how this community has helped me to become a better teacher. From my first day in the classroom, I had a rich and ambitious idea of what great teaching looks like. Of student engagement, of what it can mean to do math, of worthwhile tasks, of teaching that is responsive to students, and more. That ideal kept me pushing myself, trying to get better, trying new things, adding new tools to my toolbox. It was a mirror to hold up to my teaching, to keep me humble and wanting more.

Equally important was the support from the community. Even before I was blogging or engaging on Twitter, this community modeled what it means to work hard to improve, to look failures in the eye and try to do a little better tomorrow, to wrestle with the big challenges of teaching and know that we’ll never solve them, just get a little better every day.

Another idea that came up at TMC was “the profession”. I’ve felt myself become more invested in the profession the last few years. Which is tricky; the profession is a big, amorphous thing. And I don’t know what’s good for the profession. I know I want more great teachers to stick around. I want more high-quality curriculum allowing teachers to focus on their practice in the classroom. I want opportunities for more teachers to engage in meaningful, sustained collaboration working on their practice, with time and support from their administrators. I want teachers and teaching to be viewed as essential to learners and learning.

But I think most of all what I want for more teachers are what I found at Twitter Math Camp. I want them to have experiences that continually enrich their vision of what mathematics and mathematics teaching can be. And I want them to have the support they need to recognize that no one is perfect but it’s worth working to get better.

This has me reflecting on the ways I talk about this little community. It’s not about Twitter, or Notice/Wonder, or Desmos activities. It’s not about visual patterns or card sorts or exploratory talk. Those are means to the end. Instead, it’s about constantly expanding my view of what great teaching and learning can be, and constantly adding new tools to my toolbox for getting my own practice there. And it’s about the support I need to sustain that work over time. I love this community because it gives me purpose in my professional life, it points me in the direction I want to go, it gives me tools to get moving, and it gives me support when I want to give up. That’s what I want for teachers. And it doesn’t have to happen in my medium or in my community; that same thing is happening in many schools and local communities around the country and the world, and in online communities beyond the boundaries of the #MTBoS. But I think it’s essential that more teachers have experiences like these, and that the profession is supported and enriched, every day, every year, for every teacher.

Equity Eyes

I’m really enjoying my Twitter Math Camp morning session. The title is, “What is the relationship between the Standards for Mathematical Practice and equity?”, presented by Grace Chen, Brette Garner, and Sammie Marshall.

One scenario we looked at was a classroom situation drawn from this journal article. Students are analyzing data for where certain Netflix moves are popular, and are looking at a specific movie with Black characters and a Black director that was only popular in a few neighborhoods in Los Angeles. William and Jessica have hypothesized that it is “more popular in predominantly Black neighborhoods because of ‘support’.”

The class grows increasingly rowdy. Jessica and William [two of five Black students in a class of 30 largely Latino students] defend the movie and point out that it was also very popular in Atlanta (Marker D). Other students make coded comments about “low budget marketing,” Tyler Perry movies, and “whack-ass movies over there.” Ramon calls William racist; other students chime in and say “that’s racist” or “it’s not being racist.” Mr. Romero asks students to calm down, to little effect. Eventually, William sits back in his chair, faces the board, and says “Okay, next slide.” Mr. Romero takes this opportunity to move on to another example of big data. William and Jessica are silent for the rest of the class period.

The last line is what got me. I’ve taught classes where similar accusations of racism have been tossed around. I’ve mostly handled those moments poorly. But I don’t think I would have noticed that two students were silent for the rest of the class. I don’t think my attention would have zoomed in on that piece of information or allowed me to address it in a way that could at least reduce the damage done to my class culture and those students’ sense of safety in my room.

On the first day of TMC, Grace, Brette and Sammie asked us to consider creating a checklist of “equity eyes”. These are ideas that we want to be thinking about, relative to equity, that are not yet automatic for us. Then, they asked us to take those equity eyes to our experiences at TMC, and be ready to share how this impacted us.

My goal for equity eyes was to look at ideas through the lens of whether previously low-performing students were learning as much as or more than previously high-performing students. I then promptly forgot about that goal and went about my learning for the rest of the day. I was reminded of equity eyes again at the start of our second session on day two.

Reflecting on that experience, it was an important reminder of how hard it is to change. It was also an important reminder of how necessary it is to do the work and get a little better every day. Jay Smooth has a great TED talk, which I found via Ben Blum-Smith. Jay shares the “dental hygiene model” of talking about race. Working against racism isn’t something you turn on and off. Instead, it’s like brushing your teeth. It’s something you need to do regularly. No one is perfect, everyone should be working on it, and no matter how great your dental hygiene is if you don’t brush your teeth for too long they’re going to turn yellow and fall out. In the same way, if we hide from hard questions we will lose that perspective and the ability to grapple successfully with hard challenges as they come.

As Grace said in our session:

The more we think about it, the more automatic it gets and the less we have to think about it.

One thing I find incredibly important is balancing an explicit focus on equity in particular spaces to build capacity with embedding equity in everything I do. It’s hard to look at everday decisions, teacher moves, and conversations through a lens of equity. That lens isn’t built overnight; it’s built painstakingly and slowly and deliberately. It’s built by taking time to dive deep into equity work, and then stepping back and figuring out how it can apply to everyday classroom teaching.

Sadie shared with me a beautiful Hawaiian word, `ukana. It means the stuff that we carry with us. I see an equity lens as something I want to add to the stuff I carry with me. It’s not easy, but it’s something that becomes more and more natural as I do it more regularly.

Today I improved my equity eyes a little bit. I engaged with some hard questions with some thoughtful people. I watched myself fail. I’m still reflecting on it and organizing my thoughts here. I have a long way to go. Looking forward to continuing the journey.