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Reflecting On Writing

The school year has ended and I’m on to summer vacation. I’m working on a few projects, some related to teaching and some not. I’m also thinking about next year — my priorities, my goals, and my commitments.

In that reflection, I realized that one commitment I haven’t even considered ending was this blog. Writing has become a central part of my identity as a teacher. I think things through in writing. I encounter a challenge in the classroom and start thinking about how I can write about it. I set goals for what I want to learn, and writing about that process holds me accountable and helps me cut through to the essential takeaways.

At the same time, I’ve built a written record of how my ideas have evolved over time. I’ve become someone who can sit down and write when I need to — I no longer put off writing tasks as long as possible. Writing has opened doors and created relationships in my professional life that I never thought would be possible.

This is all to say thanks for reading. And for anyone out there who has considered starting a blog — I don’t know if it’s for you, but it’s absolutely worth a try. Most of all, my advice is to write for you. Don’t write worrying about what others will think or how it looks to someone you don’t know. Write because it will help you learn, help you reflect, and help you grow. You can learn a lot by sitting down to write about your teaching, once a day, once a week, once a month, or once a year.

Using Feedback From Student Surveys

Since grad school, I’ve been using the same set of student survey questions to assess my teaching. The questions are linked here, though I have since moved them into a Google Form.

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These questions are drawn from the Measures of Effective Teaching project, funded by the Gates Foundation. They write in their preliminary report about the design of the student survey:

The goal is not to conduct a popularity contest for teachers. Rather, students are asked to give feedback on
specific aspects of a teacher’s practice, so that teachers can improve their use of class time, the quality of the
comments they give on homework, their pedagogical practices, or their relationships with their students.

I think this is a great premise. If I ask students whether they liked my class or how good my teaching is, their answers are likely to be heavily influenced by whether or not they like me and how they are feeling that day. If I ask more specific questions about my instruction, I’m more likely to get useful and objective information about my teaching.

The survey above selects a subset of questions from the original study and were adjusted to use Likert scales. I’ve stuck with them because they are the questions I used first and I’ve found it helpful to gather comparative data over time.

It’s often a bit of a blow to my ego to hear what students have to say. At the same time, comparing different groups of students has led to valuable insights. For instance, at my current school, I initially did poorly on the question, “Our class stays busy and doesn’t waste time.” I got a 3 from my first cohort, which is an average of “Sometimes”. I then bumped up to a 3.4, then a 3.7, then a 3.9, which is nearly an average of “Usually”. This slow but measurable improvement in one aspect of my classroom management has been gratifying. This is not to say that one survey questions should define my teaching. There’s no reason I should expect a perfect score on that question, and I could do well and still not do much to support student learning. But I haven’t changed the fundamentals of my pedagogy in that time, and my students’ perception is that I have used their time more purposefully. For another perspective on the relationship between using student time effectively and classroom management, check out Matt Vaudrey’s thoughts here.

A frustration from the survey has been the question, “How clearly does this teacher explain things?” I have barely been able to budge this one, and after my improvements on two classroom management questions it has hovered at the bottom for my last two cohorts, somewhere just below “Usually”. Not that this is a terrible result, or that explaining things clearly is the only thing that matters in my teaching, but I think it does matter, and I would love to find ways to practice that skill and improve students’ perception that I explain things clearly.

I think that this survey is useful, but it also has limitations. I think it could be complemented effectively by some open-response questions that ask students to talk about one area I’m doing particularly poorly in, and to solicit broader feedback than is possible using Likert scales. A survey is just one way of assessing my strengths and areas for improvement. But it only takes a few minutes to have students fill out a Google Form, and I’m most happy that I’ve stuck with the same questions over time so that I can compare cohorts and try to measure my own improvement.

Final tip for anyone who wants to use this: the below formula might be useful to anyone converting Likert scale ratings into numbers to more easily average and find trends. You can just drop this into a new tab, name your tab with the raw information “Data” and drag to convert every rating to a number.
=IF(OR(Data!B2 = “Much better”,Data!B2 = “Much harder”,Data!B2 = “Much more”,Data!B2 = “Always”,Data!B2 = “Extremely well respected”,Data!B2 = “Strongly agree”,Data!B2 = “Extremely clearly”),5,IF(OR(Data!B2 = “Somewhat better”,Data!B2 = “Somewhat harder”,Data!B2 = “Somewhat more”,Data!B2 = “Usually”,Data!B2 = “Very well respected”,Data!B2 = “Agree”,Data!B2 = “Very clearly”),4,IF(OR(Data!B2 = “Similar”,Data!B2 = “Similar”,Data!B2 = “Similar”,Data!B2 = “Sometimes”,Data!B2 = “Somewhat well respected”,Data!B2 = “Neutral”,Data!B2 = “Somewhat clearly”),3,IF(OR(Data!B2 = “Somewhat worse”,Data!B2 = “Somewhat easier”,Data!B2 = “Somewhat less”,Data!B2 = “Rarely”,Data!B2 = “Slightly well respected”,Data!B2 = “Disagree”,Data!B2 = “Slightly clearly”),2,IF(OR(Data!B2 = “Much worse”,Data!B2 = “Much easier”,Data!B2 = “Much less”,Data!B2 = “Never”,Data!B2 = “Not at all well respected”,Data!B2 = “Strongly disagree”,Data!B2 = “Not at all clearly”),1)))))

Theory Meets Practice

I’ve been thinking recently about the difference between the principles of an idea and how that idea functions in the classroom; the difference between theory and practice. Conversations about education, especially those in popular media, tend to make broad generalizations on principle without ground-truthing to figure out how an idea plays out with real live teachers and students.

The principles of personalized learning, that one-size-fits-all education does not meet the needs of every student, are undoubtedly true. But in practice, that idea often functions to put students in front of computers for long periods of time, creating lifeless classroom where learning is reduced to spreadsheets and joy is sucked from the room.

The principles of Understanding by Design are useful to organize purposeful curriculum. But in practice, that idea often functions to require teachers to write an objective or enduring understanding on the board, without actually engaging with backwards design or creating a more meaningfully sequenced curriculum.

The principles of constructivism, that students must create their own meaning of new ideas, communicate something true about human cognition. But in practice, that idea often functions to ask students to figure everything out themselves and withhold necessary supports in the name of inquiry, a pedagogy that exacerbates inequities by hurting previously low-performing students the most.

The principles of mindset research, that growth or fixed mindsets have a large influence on future learning, are sound. But in practice, that idea often functions to reduce mindset thinking to platitudes about praising effort rather than ability, platitudes that are often hollow and certainly insufficient to the challenging task of changing mindsets.

These are just a few examples; I could go on. My point is that I have worked to practice this type of thinking; when I hear an idea in education, I try to stay just as curious about the broader principles as about how it functions in classrooms with the imperfections of teachers and the fickle nature of learning.

Number Talks in High School

I first started doing number talks (also called math talks) to start class when I taught 8th grade. If you’re unfamiliar with number talks, this site by Fawn Nguyen has some great stuff to get started. My first year teaching high school (Algebra II, Precalculus, and Calculus) I stopped, opting for Visual Patterns, Open Middle, Which One Doesn’t Belong?, and a few other rotating warm-up routines. I thought that the skills involved in number talks, while useful for middle school students, were less relevant for upper high school.

I came back to number talks at the start of this school year, and I’ve been happy with the results. When I wrote a problem up on the board one day toward the end of the year, a student blurted out, “oh, I love these”. That’s just one student, but engagement was usually high. Efficient strategies for these problems often did not come easily to students, which suggests that there’s potential for learning from them. More importantly, as they became comfortable with the routine, many students who were rarely willing to share started to speak up and take more risks.

Here’s a selection of my favorite problems, many courtesy of Fawn’s site.

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Picking two numbers and an operation is often insufficient for a great number talk; I’ve found that careful selection of the numbers involved to ensure a variety of strategies is worth the effort every time.

I have one lingering question for next year. Engagement during number talks seems high, and seems to engage both high-performing and low-performing students. There is clearly a need for the skills that number talks are targeting. At the same time, I don’t have any real evidence that students are learning these mental math skills. I think they are, but that’s based on my intuition and a few anecdotes. One challenge is that I tend to cycle through a variety of types of number talk problems that require different strategies. One goal for next year is to reorder the number talks I use so that I expose students to one type of problem 2 or 3 times, lead a discussion that attempts to consolidate understanding of relevant strategies and when they may be useful in the future, and then revisit that problem a few weeks later. Hopefully this sequencing will provide more robust evidence as to whether or not students are actually learning.

Attention and Working Memory

I really enjoyed a series of blog posts I recently discovered summarizing how cognitive science can be applied to education. The section on attention in particular caught my eye. It’s worth noting that attention doesn’t just mean students are sitting up straight and looking at the front of the room. Instead, attention is about thinking. It’s about asking ourselves what students are thinking about, and how we can influence that thinking.

The last few years have seen a movement towards the discussion of “non-cognitive skills.”  But what these really get at are ways into attention:
  • Motivation is really about the voluntary direction of attention.  When we are motivated to do something, we pursue it more often; we give it more attention.  
  • Similarly, Carol Dweck’s research on mindsets–whether we believe our intelligence is fixed, or whether we think intelligence is malleable–her research really explores whether we sustain our attention in the face of adversity.  If we have a growth mindset, we believe that our work improves with effort, and so we direct our attention to it repeatedly.
  • Roy Baumeister’s research on willpower explores the factors that influence whether we sustain attention.  Our attention and resolve are limited, but we can exercise and adjust the factors that marshall our limited attention.
  • And out of Stanford, Clifford Nass’ research on multitasking (and our inability to do it) further informs how we channel, and lose, attention.
In all these–motivation, mindsets, willpower, and multi-tasking–we find we are really talking about attention, and that exploring these “non-cognitive skills” is really another way to understand how and why people direct their attention–or not.

I really like this interpretation of a number of “pop psychology” publications that are popular with educators. I want to add my own spin.

I think of attention in terms of working memory. We can only hold a few ideas in the mind at one time. The research cited above provides a useful window into whether students direct and sustain attention on what we want them to pay attention to in class. While creating environments where students direct and sustain their attention in school is important, perhaps more important is what they are paying attention to.

I see two more important questions, building off of the ideas above:

  • Is attention focused on the right stuff?
  • Is attention overwhelmed to the point that it’s hard to learn?

As I have grown as a teacher, I am better able to ask myself the question, “What are my students thinking about right now?” Motivation, mindset, willpower, and multitasking are one useful lens here. But a student who is effectively paying attention may still only be paying attention to surface features of the problem rather than its deeper structure, or to a calculation without considering why that tool is the appropriate choice in that situation. It’s not just whether a student pays attention; memory is the residue of thought, and what students think about is what they will learn. The more I am able to take students’ perspectives, the better I can design learning experiences that get their attention focused on the right stuff, the essential mathematics that I want them to learn, rather than surface features that fall short of my goals. Building this knowledge means pulling the right ideas into working memory, connecting them to larger ideas students already know, and making sure attention is laser focused on that thinking.

At the same time, even when student attention is focused on the right stuff, if the reasoning they are doing overwhelms their working memory, it’s unlikely that anything will be retained. Here, attention can be all in the right place, but there’s too much to pay attention to, and students lose the forest for the trees. The challenge of figuring out what they are trying to figure out prevents opportunities to step back, take a larger perspective, and consider how what they are doing is connected with other things they have learned and consider how they might use it in the future.

These constraints on attention provide some useful questions to ask. Are students paying attention? If not, how can I facilitate an environment that helps them direct and sustain attention? Are students paying attention to the right stuff? If not, how can I design activities that will help them do so? Are students overwhelmed by the demands on their attention? If they are, how can I reduce the cognitive load of the activity to help them learn effectively?

Responding to Student Struggle

I’m still unpacking Lani Horn’s awesome talk on an asset-orientation that you can watch here, and I began exploring a few days ago here.

Ambitious Instruction

I want to explore the idea of ambitious instruction and the teacher actions connected to this idea. For a more academic read, this paper outlines the term ambitious instruction. Lani uses a much simpler representation to get across the key ideas:

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I really like this contrast. Ambitious instruction takes typical practice and sets higher goals that are focused on student thinking and an expansive view of what it means to do mathematics.

Slipping Away From Ambitious Instruction

Lani talks about a result from the MIST study where many teachers were aiming for the ambitious instruction, but slipped back to the left side of the chart when students struggled. A number of teachers viewed the struggles as intractable because they focused on students’ deficits and shortcomings. This is a clear problem; if teachers’ conceptions of students cause us to think, implicitly or explicitly, that they aren’t capable of engaging with meaningful mathematics, we’re stuck.

Even tougher was that a larger group of teachers, even if they didn’t use deficit language to characterize students, still moved away from ambitious instruction when students struggled. They were trying, but when things got hard they slipped back and reduced the cognitive demands for students.

I can see myself in both of these examples. I’ve been guilty of using a deficit framing of struggling students, and I’ve been guilty of lowering the cognitive demand of tasks when the going gets tough. Both actions can seem benign on the surface, whether I’m describing a student as unmotivated or making a choice that a certain task isn’t appropriate for that class that day. But in practice, these actions functioned in a way that lowered expectations and denied opportunities to learners.

Moving Forward

One solution Lani offers is teacher education and ongoing professional development that focus on ability, bias, and an asset-orientation to counter deficit thinking. I want to continue thinking about how to build this habit: to catch myself in instances of deficit thinking, to educate myself in ways of seeing strengths in all students, and to surface and address my own biases.

At the same time, I think there’s an important instructional piece. I can enact high expectations for students by challenging them with high cognitive demand tasks and having scaffolds ready if they are necessary. I can practice the course corrections I need when I realize a class is not ready for a demanding task, step back to build the foundation, and return to an opportunity to challenge students with meaningful mathematics.

I see these as two different skills I can work to improve to support my practice:

  • An asset-oriented approach to framing and talking about students that frames challenges as solvable and values students for what they bring to the classroom
  • A focus on adjusting the scaffolds and supports rather than the rigor and expectations of demanding tasks that students struggle with

This still feels a little fuzzy to me, and I’m left with the same question Lani ends her talk with: what structures help teachers sustain this work and this practice on a day-to-day and a year-to-year basis?

Lani Horn on an Asset-Orientation

Lani Horn gave a great talk at the University of Utah earlier this year that I just stumbled across a video of on Twitter. The title of the talk is, “An Asset-Orientation is Everything: How Strengths-Based Approaches to Math Teaching Help Teachers and Students. The heart of the talk is about 40 minutes and it is absolutely worth watching. I want to pick on one small element of what she said that resonated for me, and also poke at it a little bit.

In her talk, Lani focuses on the challenges of ambitious teaching in math and the influence an asset-orientation has on teachers’ ability to improve their practice. More specifically, she makes this claim:

An asset-orientation is necessary (but not sufficient) for math teachers to improve their practice.

If you’d like to see her reasoning and the breadth of research she cites to back up this claim, go ahead and watch the talk. In this post I want to focus on exploring what an asset-orientation is and also what I think it is not.


Lani defines an asset-orientation in her talk:

When teachers take an asset-orientation toward students, they seek to understand their strengths and value them as whole people.

She then offers a contrast between two ways of talking about a student:

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It’s worth unpacking the first image, because those phrases and similar phrases can seem benign on the surface, but function in ways that perpetuate deficit thinking. Things that seem descriptive, like “a C student” can actually essentialize that student’s capabilities. Even when we mean well, phrases like “at-risk” can surface a deficit framing for a student that assumes they are less capable, assumptions that are likely to play out in practice.

An asset-orientation focuses on strengths and values students as whole people. Here’s another quote from Lani:

Doesn’t mean I’ve given up on her as a student, though. Doesn’t mean that I’ve excused her or written her off. I am going to work with her. to figure out how she’s going to develop her student skills, despite the challenges that she has, building off of the strengths I see in her.

Lani addresses a misconception I had about deficit thinking. Lani is talking about a shift in language from looking backwards — at prior performance, at demographics, at other things that are currently out of that student’s control — to looking forwards at the work that is necessary to help that student reach their potential. The purpose is not to pretend that deficits don’t exist. Instead, the purpose is to frame problems of teaching practice in ways that are solution-oriented and value what students bring to our classrooms.  Deficits do exist, but focusing on deficits and framing problems around deficits makes them suddenly intractable. An asset-orientation is solution-oriented and focuses on where the work forward begins — building off of student strengths and capabilities.

In the past I’ve felt a bit queasy about some of the language I hear teachers use when they chide others for using deficit framing. If deficit framing is being replaced with fluffy language that just replaces a deficit with a euphemism and offers no path forward, that’s not a useful change. If avoiding deficit framing is only focused on language and not what teachers do next, it’s just semantics. That’s why I think Lani’s conception of an asset-orientation is so important. It’s focused less on eliminating deficit framing — necessary, but not sufficient — and more on the language we should be using and the influence that language has on everyday practice.

If you’re interested in another thought-provoking talk from Lani, check out this video on what it means to have the knowledge one needs to be a teacher.