The Global Math Department Newsletter

#GMDReflects:

An Invitation to a Year-Long Community of Reflective Practice

Some years ago I read a study about teacher-student contact in the classroom that had a powerful impact on my practice in the classroom. The findings weren’t new to me, but unlike most research that I had been reading at the time, the data came from Ontario classrooms like mine. The study found the following:

Teachers talk to boys more than girls
Teachers discipline Black boys most often
White, middle-class boys get more positive contact with a teacher than any other group

I read the paper while I was out of the classroom, working on my Masters degree, but it was still on my mind when I returned to teaching the following September. I wanted to see if I would have the same dynamic in my high school math classroom, so I engaged in self-study — a research methodology that I also learned about during my studies — to examine my practice. Engaging in an intentional self-study process, more formal than my usual professional reflection, was a profound experience. The things that I learned about myself, my practice, and the difference between my intentions and actions that semester have shaped much of my life as an educator since.

I am inviting you on a reflective journey into your own practice through the Global Math Department Newsletter this school year. Each month I will share reflections, ideas and prompts to guide our self-study here, and on Twitter with the hashtag #GMDReflects. There are so many wonderful professional learning communities online, but my hope is to create a reflective practice community. #GMDReflects will be a space to connect with other math educators on a reflective journey throughout the school year, with the goal of better aligning our actions with our values.

As for what to study about your own practice, that is up to you. If you're new to reflective practice, starting with teacher-student contact could share some powerful insights. It is fairly easy to observe and track (great for you in an already challenging year) and, with respect to examining the difference between our values and actions, it is a very revealing area of observation. That being said, focus on what you care about at this moment, the monthly prompts will be general in nature, not tied to any particular topic.

And with that, here is Part 1 of our self-study journey together!

Getting Started: Self-Study as a research methodology

Teachers are used to assessing and responding to the needs, patterns and gaps that we observe in our students. Self-study is different. When we engage in self-study we ask questions like: what am I doing, why am I doing it, what do my actions mean, what do those actions create/perpetuate for my students or in the world. Self-study as a research practice is rooted in teacher inquiry, reflective practice, and action research. That is to say: it is done without an outside researcher, it encourages us to be reflective and critical of our own practice, and it is aimed at solving problems.

I have been using self-study as my primary tool to engage in equity work in the classroom. When I learn about larger patterns of injustice and inequitable distribution of resources in schools — specifically time, attention, and opportunities — I ask “how am I part of this problem?”

The How

There are many ways to engage in self-study. No matter what the execution looks like for you, I think any effective self-study process should:

have a clear focus: address 1 specific practice/dynamic
be systematic: observe, reflect, change, reflect, repeat
be honest: you will learn difficult things about yourself, that is precisely the point
include feedback from others and external artifacts
result in professional and personal change

A clear focus: What is the question that you want to answer? For me, self-study is always about how I am implicated in a larger, systemic problem (because we all are). If I am thinking about academic streaming/tracking and know that students from particular groups are disproportionately streamed away from higher levels of mathematics, I ask “who am I recommending for each stream?”

The question is not “am I discriminating?” or “am I a bad person”. The question is always “what am I doing?”

Be systematic: Your inquiry should begin with an observation phase. Track your behaviour in any way that is natural to you and suitable for the question at hand. I would not recommend walking around with a clipboard and tallying throughout the day or anything that would disrupt your normal practice. When I was tracking teacher-student contact, I spent some time at the beginning of each break (prep period, lunch, after school) running through the interactions that I had and mentally noting patterns. This process may have been aided by note-taking but I know myself, I don’t like to journal or write down my reflections with any kind of regularity. Requiring this would have deterred me from engaging in the process. I do, as a habit, take quiet moments to mentally reflect throughout the day, so I built self-study into that practice.

I observe myself for about 1 week. I reflect on what I have observed to determine 2 or 3 changes in my behaviour (actions, speech, routines) that I could make to address the issue, then I commit to those changes for another two weeks. After I have incorporated the new behaviours and they stop feeling like a conscious effort, I observe myself and my classroom with new eyes. Are these actions addressing the issue? How do I feel? What changes do I notice in myself in relation to my students? What changes do I notice in my students in relation to my new behaviour?

If I don’t know how to address the issue, I ask other teachers for their best practices or resources.

Be honest: The most difficult and important part of the initial observation phase is being honest while withholding judgment. For any kind of growth or change to happen, we must have a clear picture of our current state. Just watch yourself and, as much as you can, don’t deconstruct your behaviour yet. Negative or troubling patterns will emerge. The presupposition of self-study is that there are ways that you can improve and, friends, not every improvement is about moving from good to great. Be open to the reality that your actions may betray your values or best intentions.

Value judgments about your actions come in the reflection phase. Lean on your support networks. Fight defensiveness, fight shame, fight ego.

This is where we will pause for Part 1. Good luck in your first month on this journey!

I look forward to connecting with you at #GMDReflects. - Idil Abdulkadir (@idil_a_)

Get Outside and Touch Some Math

In elementary school, I struggled with mathematics. In the margins of my workbooks, I remember scribbling bigger dreams, a distraction from the symbols and numbers begging rigid responses.

By the end of high school, I experienced a shift - I became enamored with the math of the unknown - imaginary numbers, hiding behind the horizon of reality, the mysteries held in multiple infinities. I wanted to bring the beauty and wonder of mathematics to young children, and more importantly, I wanted to learn how they make sense of mathematics.

As I transitioned from student teaching to teaching in my own classroom, I felt the pressure of curricular restrictions increasing. I attempted to push back in ways I had learned from mentors and colleagues - to bring in more student-led mathematical experiences. But fundamentally, in school, math is two volumes per year, red ink on quizzes, after reading, but before science. It is words muttered by a handful of students as they reluctantly take out their workbook and turn to page 36...“I hate math”.

But how can you hate math when math is everything?

Curriculum gives structure, consistency, predictability, and a standardized experience - but even the best curricula position teachers as the leaders of a classroom - the ones with the presumed ability to interpret what’s being asked of students and assess whether they’ve reached the intended goal.

"Turn to page 36, and complete the exercises. First an addition problem, then a word problem.
oh, and be sure to show your work."

The more pressure I felt to standardize the math experience my students received, the less I wanted to use standardized curricula. The more I used exercises from page 36, the more it made me want to push my students' ideas about mathematics off the page and into the open air.

One of the rich, student-led math activities I’ve used in my classroom since I first started teaching is counting collections, where two students count a bag of objects and record their thinking. It was important to me to give students ample opportunities to count, especially at the beginning of this unusual school year. Given current social-distancing requirements, I sought the advice of the MTBoS for how we could adjust this activity.

My former professor, Elham Kazemi (@ekazemi) responded with the suggestion to have students see what they could count in the classroom from where they were sitting - or maybe even take them outside to find things to count.

Students began counting all kinds of collections inside as they noticed that math was EVERYWHERE around us. We counted notebooks, pencils, desks, chair legs, everything we could. After discovering and recording things inside the classroom we could count, we went to the field behind our portable - notebooks and pencils in hand, on a mission to see what we could find outside to count. The excitement was palpable, because how often do we get to really have the freedom to explore at school? Students ran around, excitedly gathering flowers, mushrooms, fistfulls of dry grass - carefully sketching how many portables and windows they saw.

The unusual excitement I saw in the students came, I believe, as a little taste of something we can’t replicate with curriculum books and classroom activities, worksheets and manipulatives - discovery is the part that makes math come alive. The unforeseen of, “What will we find?” in a space that is unknown takes mathematics from a defined page into the open air, into every space and place that we enter. It turns mathematics into a mystery worthy of discovering.

When math curriculum drives math learning, it not only deprofessionalizes teachers, but also desensitizes students to the mathematics that exists in the world - the big, expansive, beautiful, messy, unexpected mathematics. The mathematics that is worth discovering, unlike the “discovery mathematics” we find in math classrooms that starts with a problem worth thinking about but always ends tied up in a really pretty bow. When in the real world has a math problem worth doing resolved so nicely, in perfect integers, in rationalizable fractions, or the ever rare check & tip that ends in $.00?

When students explore the math around them, digging into the messiness of mathematics, I don’t know what they’re going to find, and that is thrilling. I don’t know what they are going to bring. I am no longer in control of the students’ every exploration or expression. I become an observer, someone who moves alongside students, finding joy and curiosity in whatever they are drawn to, whatever they are discovering.

Math curriculum can create a sense of false confidence in both teachers and students - teachers know what to expect from students, and the students know what to expect from the questions, what they need to do or show to be successful. It wraps us in the security of being able to delineate right from wrong - but at what cost?

Curriculum isn’t going anywhere, but what happens when we let our students (and ourselves) dig our hands into the messy mathematical sandbox? In those moments, students have discovered the beauty and wonder they find in the mathematics around them - and I realized it is not up to me to show it to them, but for us as teachers to let them find it for themselves.

Written by Janaki Nagarajan (@janaki_aleena) and Lauren Baucom (@LBmathemagician)

A CULTURE OF HELPING

As teachers, we are inclined to think of ourselves as helpers. When I talk to educators about why they teach, responses are often some form of “helping kids”. Helping is something that as math educators, we talk about often.

What is the right amount of help to find that elusive zone of productive struggle?
What is the right amount of scaffolding that will help lead students to a solution path?
How much help should be provided when assessing a student’s understanding?
Which feedback could we provide that would help students clarify or extend their thinking?
How can I position a student’s ideas to help them cultivate a positive mathematical identity?
How can we help students help themselves, in other words, become lifelong learners?

It’s not an easy feat to answer these questions, which is what truly makes teaching an art. With all this thinking about helping, we position ourselves as the ones offering, or at least facilitating, the help. Because this is wrapped up in our identities as teachers, I have found myself struggling sometimes to accept help. Culturally, as a math teacher, I am expected to have answers. I am expected to know algorithms, procedures, and solution paths. I encourage students to seek help when they need it, yet have tremendous difficulty following my own advice. Seeking help feels like an imposition. Ironically, every day we offer help to others and are delighted when we are taken up. As an educator, I thrive on helping others, but struggle to seek help for myself.

Creating a culture of help-seeking amongst adults in education can be a tough, but necessary road to pursue, especially this school year. With staff shortages, quarantines, and a host of other factors that are currently straining the system in novel ways, we will need each other for support more than ever before.

A first step for me personally, will be to accept help when it is offered. As an educator, I offer help all of the time. These are sincere offers because helping others is what drives me. But my acceptance rate for help is very low. The reasons for declining are many and varied: I don’t want to impose, I don’t want to seem unknowledgeable, I’m not sure what I even need, I feel like there are other places where I could seek help, and so on. In an effort to rationalize how accepting help could benefit others, I’m working on trying to find the benefits to accepting help beyond myself. This includes thinking about how diverse strengths are given opportunities to come to light when there is a culture of mutual assistance in a school, PLC, or team. These could be strengths in technological knowledge, teaching resources, or building relationships. When each of us is given a chance to pitch in with our strengths, the whole group is better off. And one thing that I’ve learned from connecting with so many great teachers through Twitter and the Global Math Department is that not everyone is aware of all of the amazing things that math teachers are doing to connect with students and content.

A second step for me will be to stop making assumptions about those offering help. In the recent past, I’ve declined help because I figured the person offering help had a schedule that was equally hectic, they were equally stressed, and equally incapable of serving anyone besides themselves at this chaotic moment in time. But the ebbs and flows of this year have shown me that capacity to assist is not a constant. Just because I am overwhelmed at a particular point in time does not mean that everyone else is. Instead of viewing an offer of assistance with assumptions that surround my current state, I will try to move past those assumptions to an understanding that someone else’s circumstances could have their capacity to help in an improved disposition. I say this about places where my relationships are strong, where trust is high, and communication is clear. For relationships where this might not be the case, accepting help will be more difficult.

Lastly, I am going to pay it forward. When my ability to aid others exists, when I am not in a panic or highly stressed moment, returning the favor and taking something off of someone else’s plate will be my go to. Whether planning a lesson, covering a class, providing technical assistance, creating a common assessment, or providing a space to listen to a colleague’s complete humanity, my goal is to put out the strengths I have, when I have the energy to capitalize on them. I will gently insist that other educators also work toward accepting help, with the goal that we strengthen our communities.

I’m hopeful that I can stick with these goals this year. Talking with some colleagues a few weeks ago, we realized we shared the trait of too often letting our pride impede acceptance of assistance. But now is the time to examine our internalized individualism and paternalism, to face the discomfort of admitting vulnerability, to reach out and embrace our full humanity, with its desire for community, belonging, and learning together. This is the year to make asking for and accepting help, the norm for educators.

Written by Brett Parker (@parkermathed)

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