This Week at the Global Math Department

Edited By Nate Goza  @thegozaway
View this email in your browser

Online Professional Development Sessions


Strengths-Based Mathematics Teaching and Learning: 5 Teaching Turnarounds to Build Student Success

Presented by Beth Kobett

Explore teaching turnaround strategies that can reframe and open up students’ mathematical learning opportunities. Learn to identify and leverage students’ strengths to develop powerful and strategic learning moments that recognize and bolster students’ strengths to build mathematical success.

To join us at 9:00 PM EST for this webinar click here!

Next Week

SmartSlides for Engaging Students

Presented by Lynda Moore

In this session, you will see how Lynda Moore (teacher of 30 years) uses hyperslides to engage her students and build confidence and ownership in their learning. She uses live data, immediate feedback and self assessment to teach HS Geometry. The use of Teacher Time, Think Pair Share and looping of content are some of the tools that you will learn in this webinar. Math can be paperless, Math can be engaging, and Math is AMAZING, and Learn to KnowMooreMath with Lynda Moore.

Register ahead of time by clicking here!

You can always check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

From the World of Math Ed


As teachers who believe that equity is a central concern in math education, we are always looking beyond ourselves but also within ourselves, adopting a critical lens toward the systems, practices, and institutions that marginalize and harm certain mathematics students, but also turning that lens back onto ourselves to see how we are implicated in those same systems. I’d like to share the powerful stories and advice from two math teachers who have applied this duality of extra- and introspection in their practice.

Idil (@Idil_A_) has written an incredible post on self-study. It may be tempting to think that self-study is simple and straightforward, but as she points out, it raises deep questions about the nature of what counts as knowledge. Do we tacitly organize knowledge in a hierarchy? Do we place our own particular experiences below the “generalizable knowledge” developed in academia? These are some of the questions I found myself asking as I read her post. Beyond the what of self-study, Idil also engages in the how by giving five pieces of advice. I’ll outline them here, but please read her words to see how she elaborates on each one.

  1. Have a clear focus
  2. Be systematic
  3. Be honest
  4. Include feedback on others and external artifacts
  5. Result in professional and personal change

Finally, she concludes with perhaps her most important point: the question is not if we are part of the problem, but how.

The honesty with which Idil approaches her practice is equally evident in Esther Song’s (@eugoogleypart 1 and part 2 in the Nepantla Teachers Community (@NepantlaTC). First, a word on the community. Read what they’re about and then subscribe if you haven’t already done so. It’s a mind-blowing organization of teachers committed to social justice mathematics education. I’ve learned so much from them.

Esther’s two pieces are a demonstration of vulnerability, reflection, and growth. Her dilemma is one that likely resonates with many of us: perceived math apathy among students. Like the Nepantla Teachers Community state in their norms, I’d suggest sitting and reflecting on the first piece before moving on to the second. But do read the second piece. It’s so beautifully written. And I’ll just leave it at that.


How do people think about “teacher learning” and why does it matter?

We know a lot about different ways teachers are supposed to learn: we have credentialing programs, where teachers typically take coursework and earn their certification. As a part of that, we have student teaching, where pre-service teachers interact with students in classrooms and do the challenging and exciting work of trying to help other people (some of whom are reluctant to engage) to learn. Once teachers are certified, they participate in professional development, that highly variable “system” of workshops and inservices that offer them new ideas, tools, techniques, or opportunities to reflect on instruction. Some teachers learn from colleagues, with whom they can share ideas and resources, or maybe even consult with about challenging situations.

But all of these primarily describe situations that purport to help teachers learn. None of them actually describe how teachers go from one understanding to another, one form of practice to another, changing what they do from day to day in their classrooms.

In research, a lot of accounts of teacher learning focus on changes in instructional practice. For instance, maybe a teacher starts out, say, giving a lecture and using their whiteboard ineffectively, with notes scattered around without a clear sequence. We then give them feedback about how to organize that information so students can follow the lecture’s logic. Then, if the next time we watch them lecture and we see improved whiteboard use, we can say that they have learned.

But eventually, the notion of change in practice as a way to describe teacher learning falls short. How we draw a boundary around where an instructional practice begins and ends, especially when its success is not entirely up to the teacher? In the whiteboard example, the teacher has a lot of control around their board use, organization, diagraming, color coding, and the relationship between their spoken words and scribblings. If we think of more interactive practices, however, that depend more on student inputs, the situation becomes more complex. Even in the whiteboard example, we can extend our consideration to how the teacher annotates the whiteboard to account for students’ ideas and questions. In this case, the expanded view of whiteboard practice no longer only comes down to the teacher’s actions; it also involves the students around them, how they engage with students’ ideas, making the practice variable from class to class.

Most of the instructional practices that we promote in mathematics education are more interactive than whiteboard use, and thus more contingent on teaching situations. As a consequence, the boundary of instructional practice becomes even more complicated. For instance, say that a teacher went to a professional development workshop on using a Notice and Wonder conversation structure in the classroom. They work through some examples with their colleagues, identify what kinds of tasks might lend themselves to a rich Notice and Wonder discussion, and even get some examples from teachers who have used them a lot. They have learned some useful things.

Maybe then our hypothetical teacher tries Notice and Wonder in their first period class and has a dynamic discussion. Students make good observations. They raise interesting (and even amusing) questions. So we ask: has the teacher learned the practice?

What if we extend the story to the teacher’s next class? They try the same activity second period. Students stare the teacher down. After an uncomfortable amount of silence, one student, out of pity, volunteers something that kind of misses the point. In short, the Notice and Wonder activity bombs. Do we change our assessment? Has the teacher learned the practice?

In my research project Supporting Instructional Growth in Mathematics (Project SIGMa), we are pursuing questions about teacher learning by looking not only at teachers’ changes in practice, but also their sensemaking about their work. All teachers know that not every practice works equally well all the time. So the ways teachers make sense of the problems of practice that arise as they take on these complex, interactive practices may matter almost as much as whether they can recite the steps of the routine or do it unproblematically some of the time. For their understanding to be robust, they have to understand the elements of their teaching situation that may impede the practice’s successful execution and, relatedly, how to troubleshoot the practice.. When things work well, how do they think about it? When things don’t work as well, what conclusions do they draw? What evidence do they marshal to warrant their interpretations? What does that tell them about how to adjust the practice in the future?

Since so much of what happens with interactive instructional practices depends on the particularities of classrooms, students, and content, in our view, it is not sensible to say that teachers learn an interactive practice through one (or even five or ten) successful executions. Instead, we view teachers as learning these interactive practices when they know the routines, can bring them to life with different groups of students, adjust sensibly in response to a range of  student inputs –– and have productive ways to interpret what happens when things do not go as expected. This means that instead of concluding simply, “That practice doesn’t work” or, even, “That practice doesn’t work with my students,” they consider the variables that make one lesson, one class, or one day different from another. Their adaptations consider the goal of the practice, and they adjust it to make sense of the teaching situation while keeping those goals in mind. They think ecologically about how these differences might affect students’ participation and sensemaking. This kind of robust understanding takes time to develop, and it requires high quality feedback to support the teacher’s interpretation of what is happening in the classroom.

Written by Ilana Horn (@ilana_horn)

Follow us on Twitter
Visit our Website
Copyright © 2019 Global Math Department, All rights reserved.

Email us at:

unsubscribe from this list    update subscription preferences

Email Marketing Powered by Mailchimp


Leave a Reply

Your email address will not be published. Required fields are marked *