sonata mathematique

I am no longer a classroom teacher. Surprisingly, I am still working at MA! More on that in a different post.

We’re in the beginning stages of defining our next 10-year strategic plan. We’re also at the start of the self-study process for CAIS accreditation.

Driving across the Golden Gate Bridge today thinking about institutional change and leadership, my brain stumbled upon a memory from one of my first few years of teaching at Flint Hill, when I was part of a small group providing feedback to a draft of the school’s strategic plan. I remember being fired up enough about the discussions I was a part of (the buzzword then was “innovation”) that I wrote a long, rambling document of thoughts about schools and change.

I’m posting it here, with slight edits, and emphasis on parts that feel most resonant today.

I’m struck by the thoughts and themes here that have remained present in my perspective on teaching, leading, and institutional change, over a decade later.

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Instruction vs. curriculum – our maps right now focus on content/skills, the change we are talking about is more about instruction… delivery, experiences we create for our students, and how we shape habits of mind.

Breaking down walls: rounds, blogs, videos. We need to know what others are doing. It builds into the bigger picture of the school’s vision/direction and it helps create change from bottom up (not just top-down implementations)

In class – in instruction – we MUST tap into what is special about having 20 humans occupying the same room. Think bigger. Think backwards.  Think about this CONSTANTLY when designing lessons. It should be the benchmark… if students could do it alone (ex: watch playback of a lecture-style lesson, read silently, work problems silently) then it’s not right for in-class time. (note: that doesn’t mean it’s not good or worthwhile.)

PLAY: create experiences for students to engage with content and get out of the way. Be comfortable with more open-ended, messy process (Grades get in the way of this?)

Class should have more: Making, touching, talking! DO something.

Students don’t all have to get the same thing out of these experiences.

“you need to be intentional about designing different tasks for different strengths.”

No more “those teachers” or “they” talk. Make decisions about how to be the best school possible, clearly communicate vision and direction to everyone (be specific – just like we would do for our students) and then build space for faculty to own it. If certain teachers aren’t doing their job (especially as it continues to evolve), point them to the specifics, help them, or help them leave. But don’t discount teachers before including everyone in the process of changing the culture.

There is a lot of our self-worth wrapped in our ability to be effective educators and we need to respect other people’s lifetime of work – listen to their ideas and value their experience. There can’t be an “in-group” and an “out-group.”

There is a feeling that some in administration who would like us to adopt new ideas don’t understand the reality of how those decisions impact the day-to-day workload for teachers. Sometimes it can just feel like “one more thing we have to do.” It becomes an easy way for faculty to write off new ideas or initiatives from above if we can say “they have no idea how much they are actually asking us to do, and they aren’t giving us the time or tools to do it.”

We need to be convinced that the work we do to innovate will be supported by administration and our time will be respected. All of us are at different places in this journey of reconceptualizing what education can look like, so meet us there… know what we’re already doing and help us grow.

This is true of most teachers: “I think they want to do the right thing, they just don’t know how yet”

“every person you meet knows/can do something you can’t.” this is true even of those “stodgy, traditional, change-resistant” (I’m saying this sarcastically) teachers. don’t toss experience!

Nobody likes to feel undervalued… tap into the experience of veteran teachers and open them up to change and you might be surprised by how far they will go… and what they might bring to the table that others would miss.

Enlist and encourage faculty members to be positive change agents without creating an in-group (like Emily said – making a personal connection with another person and drawing on what they already do is a more effective way to create change on a micro level than just saying from above “here’s the next thing, do it.”)

If you feel understood, you’re more likely to listen when someone is trying to help you grow.

Tap faculty members and task them with being change-agents – breeding goodwill for new initiatives by setting the example in their own class – then using their interpersonal skills/interconnectedness to have positive ripple effects on other faculty members.

We (classroom teachers) sometimes feel like change is just happening “around” us – (as Andrew said) …”reading tea leaves” about what the school is looking for or where we’re headed.

Some classroom teachers are left trying to bridge the gap between those who are already doing something dramatically different in their own classroom (but we feel out of the loop – are those teachers in the know and we’re not? Is what they are doing effective? Should I be trying the same things?) and the force of traditional expectations (what do they “need” for the next course, student/parent ideas about how classes are supposed to be structured, course name, college prep expectations, etc.)

To ease transition into a new vision: we can start by creating structural changes that are smaller in their scope. For example: setting aside intentional time for departmental collaboration, cultivating a virtual filing cabinet for course resources, putting together specific teams tasked with designing projects/interdisciplinary courses that break out of our current “silos”…

All this is preferable to just saying “hey everyone, from now on we don’t have exams, everything is project based, there are no bells or closed classrooms, okay ready set go”

And also, it makes it clear that we will be thoughtful about change – WHAT we change AND how to implement it. It puts power in the right place – otherwise teachers who want to try something “new” feel like “they are getting away with something” (as Andrew noted re: makers.) We will feel empowered if we feel like everyone is in the loop on the way we are adapting our courses/instruction

When it comes to change, “slow is fast and fast is slow.” (Henri Picciotto)

If you adopt so much NEW at once without time to prepare for effective implementation of the NEW, and it doesn’t “take”… it burns the political capital of the leadership team… it feels like wasted time… and it will become rational for teachers to resist any future change.

There seems to be a major need for clarification of roles for ALL faculty/staff members, from the top down to the bottom. We need to get rid of the resentment that breeds when we don’t understand others’ roles – everyone at this school works hard. We need to know what they are doing, though, to see how we fit in the big picture.

We also need to trust in admin and see that there are consequences for not being a team player: that if someone does not do their job, it gets noticed and fixed.

It is possible for a teacher to be incredibly effective in the classroom and drop the ball in other areas. We have a LOT of duties that aren’t just instructional – and we all have strengths and weaknesses. How do we hold faculty accountable for all of the pieces (especially the unglamorous but important ones) in our teacher evaluation system? Too many times quiet rule-followers are left to pick up the slack on these duties – and it takes away from time they could be growing in other areas. (they get left behind on innovation because they are drowning in the paperwork.)

Feeling “seen” by our administrators and colleagues matters. Breaking down walls (again.) share successes! Both inside and outside the school community!! The individual successes of our teachers and their own initiatives and accomplishments ARE good for our branding!

As a teacher: how we work, how we structure our school day as professionals – what is this supposed to look like? How do I balance the needs of instruction (academic facetime with students), mentoring (other facetime with students), curriculum design (usually done on our own time and in isolation), grading/record-keeping, communicating with parents/students/colleagues, coaching, etc. while STILL finding time to grow?

How does Flint Hill support me in that? How does the school want me to prioritize my time?

Sometimes what I do in my classroom feels invisible. Is it seen? Does it matter? Where does it fit into the big picture of Flint Hill?

We have to feel the work we are doing matters and lasts for more than just the “now.” We have to SEE (not just hear) how new initiatives/projects (e.g. curriculum mapping, Folio) actually help build a cohesive, stronger program schoolwide – Otherwise all of the busy feels fleeting and exhausting.

Unifying all initiatives, inspiration, etc. under a clearly articulated vision.

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Like I said — everything old is new again.

Hi folks.

It’s been a while.

Since I last wrote – well, first and most obviously, Covid happened. I made it through the quick pivot to remote teaching in the spring of 2020 one day at a time, like everyone else. I survived the wacky 2020-2021 school year: part remote, part in-person, all socially distanced, all exhausting. (We had something like 7 different schedules that year!) I didn’t write much about my tenure as department chair which began back in the fall of 2018, and after four years in that role, I stepped back at the end of the 2021-2022 school year. I spent two years from 2021-2023 serving on the MA Board of Trustees, providing me with both a birds-eye view of independent school governance and an up-close look at the reality of that work. I began mentoring a teacher fellow through Penn GSE’s Independent School Teaching Residency program in the fall of 2022 and am now in my second year in this role. I have been grateful for the intentional time to connect with an early career teacher about the practice and problems of teaching. In some ways, it connects me back to the younger me – the one who started this blog over a decade ago.

There are highlights and lowlights and learnings and stories from the last few years of my career that I feel some small regret not to have documented here.

Here is a very small sampler of what I have been doing since the last time I wrote.

• Hired and onboarded 7 folks during my tenure as chair (2 in permanent positions, 4 temporary hires covering leaves, 1 Penn Fellow)
• Learned about Observational vs. evaluative feedback
• Observed every member of the department multiple times (I learned something new about the practice of teaching every single time, and the debrief conversations were always enriching and valuable for me. I work with some great folks.)
• Thought a lot about placement and tracking (intentionally planting the seeds for programmatic changes we implemented this year)
• Developed our MA Math Department Competencies (I was quite proud of this work, and if feeling inspired, may share in a future post)
• Math Night 2020 (Covid!)
• Taught a bunch of 9th graders starting high school on Zoom – Advanced Algebra I classes fall 2020 (Covid!)
• Asked students for more feedback at the end of each unit via Google forms and wondered why I hadn’t been doing that always as a teacher (Covid! Also, kids will remind you that they are funny and earnest and always paying attention if you give them an outlet to share.)
• Take Me To the Good Times – Thanksgiving “Assembly” 2020 (Covid!)
• Frank’s trivia questions with Justine – December 2020 (and every year since)
• A truly memorable PC class in Foster Hall (Ethan – “Thank you very much!”)
• Attendance posters & Dolly Parton fandom (Covid!)
• Taught an overload in the 2021-2022 school year (while chairing and serving on the board… the year of “too many plates”)
• Planned and hosted Math Blast with Brizendine funds (April 2022)
• Connected 1:1 with about a quarter of all incoming families each spring around placement decisions and follow up (RingCentral from the back patio of the new-new apartment, emailing from a Jason Isbell concert, and so. many. phone. calls.)
• Learned how to smile and start with connection, enter any tough parent conversation with curiosity and empathy – while still being clear and direct AND not underselling my expertise (see also: how to talk to Dads who think their son should be in Honors math)
• Spent 6 months during the 2021-2022 school year as the only woman in the math department.
• Planned PC with Anya 2022-2023 – Fishbowl, Beyond Precalculus, and the Martian Habitat Project (“Every day’s a good day in math class!”)
• (Currently) enjoying my silly class of sophomores in Algebra 2 and our go-to-excuse (“It’s Kevin’s fault!”)

During these past few years as this job asked more and more of me, I have experimented with where and how to draw the kind of boundaries that allow me to live a happy and full life outside of work and my identity as a teacher.

I moved 3 times, became an aunt 4x over, officiated my best friend’s wedding, and got married. Lots of love. Lots of change. Lots more on the horizon.

More on that, soon enough.

[this was in my drafts from a year ago, i found it and decided to hit publish.]

i hated how much doubt i felt this year, but i feel grateful to know that most leaders feel a hell of a lot more self-doubt than they let on.

healthy teams don’t appear magically and avoiding conflict isn’t a sign that a team is functioning well. healthy teams disagree in a way that doesn’t feel personal – it’s about trust.

feeling seen = specificity, observational, details, not vague praise. “you’re doing a great job” is easy to reject but i notice the way you __ and naming the impact is meaningful.

i feel a renewed sense of purpose about my goals as a teacher/our work as a school – helping students develop as humans and young adults, especially against a rising tide of pressure to be overly academically/goal/outcome-focused

I’m inspired by students (several) who found an innovative and ingenious way to approach a problem on a recent quiz. They are so used to being stretched that it feels maybe a bit natural to them that on problem #1, they’d need to do something they hadn’t done before and just move right on.

I’m inspired (and humbled) by colleagues who are well-read, thoughtful, and brilliant – unafraid to take a risk, challenge an idea, propose something new.

I’m inspired by the lengthening days, the light on my walk to work and the light that squints through the office window in the mornings.

I’m reading you, and you, and you, and not reading enough, and forgiving myself for not reading enough because I am making time for myself in the spaces between things and I’m just forgiving myself in general.

Anticipating a quiet Friday morning, a packed day, rain.

Oh hi! School starts tomorrow, which I guess is the best time to be blogging? Sure.

What I’ve been reading:

• I’m about a chapter into Inventing the Mathematician: Gender, Race, and Our Cultural Understanding of Mathematics by Sara N. Hottinger. This was a recommendation from Nicole Hansen, and we’ve committed to being email pen-pals as we dive into this one together.

“…our perception of natural ability versus hard work is gendered, especially in mathematics. Female students claim that they are not really good at mathematics because they always have to work so hard to succeed. Male students do not discuss how hard they work; instead they claim their success in mathematics just comes naturally.”

• I just started White Fragility by Robin DiAngelo and plan to participate in the #ClearTheAir chats starting this Wednesday at 7:30 EST, thanks to the generous and gentle nudging of the wonderful Marian Dingle.

“The key to moving forward is what we do with our discomfort. We can use it as a door out – blame the messenger and disregard the message. Or we can use it as a door in by asking, Why does this unsettle me? What would it mean for me if this were true? How does this lens change my understanding of racial dynamics? How can my unease help reveal the unexamined assumptions I have been making? Is it possible that because I am white, there are some racial dynamics that I can’t see?”

• Dan Meyer’s post “Drill Based Math Instruction Diminishes the Math Teacher as Well” which is a good starting point for folks who didn’t read the NYTimes op-ed “Make Your Daughter Practice Math. She’ll Thank You Later” or follow the many, many reactions on twitter. Also, this quote speaks to where a lot of my thoughts are at, presently:

“I’m absolutely convinced that a) we act ourselves into belief rather than believing our way into acting, and b) actions and beliefs will accumulate over a career like rust and either inhibit or enhance our potential as teachers.”

• Michael Pershan’s awesome blog post for the Virtual Conference of Mathematical Flavors called “I Don’t Focus My Classroom on Solving Problems” that also includes this great quote from Bill Thurston:

“Mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians.

Tomorrow’s the first day of classes. I know that my students will come to understand what I value by the way I work with them every day, not just on the first day. Still, there are some things I don’t want them to have to read between the lines to see. Like,

You get messages all the time about who is or who can be “good at math.” (Not to mention the messages you get about what math is, and who gets credit for its construction.) I want to let you know that one of my fundamental beliefs as a teacher is that your mathematical ideas are valuable. I will learn from you, you will learn from me, we will build something together in this space, and we will leave changed by each other.

I am excited to see where this year takes me.

I’ve been staring at this blinking cursor for over 15 minutes now, and I promised myself I’d write something today, so I’m typing this sentence to get things started.

It’s not really that I don’t have anything to say, it’s that I have too much to say – a feeling of overflowing fullness following a week of learning at #tmc18, coupled with a yearning to dig in to so much more I can’t believe I haven’t learned yet. I’ve been reading a lot. I have a lot on my list left to read, and some partners committed to processing things with me so that I am held accountable to move beyond thought to dialogue, action, fighting for a better and more equitable future for all.

The enormity of the work we have ahead of us is daunting. So for tonight, as the hour gets later and I anticipate another full day tomorrow, I will take the advice of Chris Nho:

“Come to a stopping point. Maybe you just learned some things about the problem. That’s fine.”

More soon.

I sit on the precipice of summer break — today was my final day of meetings before what will hopefully be both an adventurous and restorative several weeks away from the classroom. Year 3 at Marin Academy and in California was full of so many highlights, both personal and professional. It was a year in which I experienced relative stability (no new preps or major life changes) and was able to get more settled into the routine and rhythm of the work here, while also realizing that I must seek out new challenges to remain propelled towards growth going forward. This week I’ve had to say farewell to beloved colleagues, friends, and administrators, while also taking the first steps into my new role as math department chair. What a strange time – busy, busy, busy, and then the great spaciousness of summer.

I didn’t blog much (read: at all) this year, but earlier today I found myself flipping through photos from the year and felt compelled to post at least a small glimpse of some of the highlights from the 2017-2018 school year in this space. Here’s hoping that the coming weeks allow me time to process and incorporate my learnings from the year that has ended as well as space to tend to my renewed sense of purpose as I prepare for the coming school year and all that’s ahead.

 

Several folks have been tweeting and blogging about what they do in the first few days of school, so I thought I’d blog about something I’ve given out every year on the first day.

(I’m days away from my ninth year of teaching, and in that time I’ve been at three different schools, taught 11 different classes, and never taught the same class more than 2 years in a row, so consistency hasn’t exactly been on my side. So, this may be the ONE AND ONLY thing I use in my class that has stayed the same in all of that time. So I definitely have a little bit of an attachment to it!)

I know at some point I got the first version of this from someone else – either online or a colleague. So credit goes to whoever inspired this idea! I hand this out on the first day of class and ask for it to be returned the next class (we’re on a block schedule, so that gives students two days to get it done). I always really enjoy the bits from the parents especially, as it often gives me a lot of insight that I don’t necessarily get from the students’ answers alone.

#tmc17 has come and gone. I traveled from Nashville to Atlanta with Molly, spent five great days at Holy Innocents Episcopal School thinking about math and teaching, and journeyed on to Hilton Head for a post-tmc-vaca with Heather. I began writing this post from the airplane back to California after nearly 3 weeks of travel and am sitting here finishing it from my couch back in my apartment. I’m grateful for a few days before school starts back to read, reflect, and catch up on personal things before school starts back soon.

Anyway.

One of my favorite sessions I got to experience at #tmc17 was Kent Haines‘s session exploring numbers in base eight. Here’s the description:

I was excited about the opportunity to do “math for its own sake,” as I’ve found that these kinds of sessions get my wheels spinning with ideas for my classes, often in surprising ways. I also really enjoy learning from watching other fantastic teachers facilitate a session that is a bit closer to a classroom experience.

Kent’s session didn’t disappoint. We were a small group, anxious to get going by starting discussion even before the session officially began. Kent started with a quick intro (we’re aliens with 8 fingers, base 8 numbers will be green on the whiteboard to make things easier, we’ll still read the numbers aloud using the English words we’re used to so “21” is still pronounced “twenty-one” even though it means “two eights and one one”) and we jumped into things.

First, we counted up to 40, with some quick chats about efficiency. Then we filled out our hundred chart. (Yes, still a hundred chart. Not a sixty-four chart. Hmmmm…) We talked about movement on the hundred chart – how left and right are still subtracting/adding one but up and down movement is now by eights.

Next we moved into doing some operations with our base eight numbers, and this is where things got really fun! My notes are pretty messy here, and I know I’ll fail to capture all of the great insights we had as we were playing… but have a look and I’ll try my best to capture as much as I can below the images.

So first off, it was very cool to be put in a position of “disequilibrium” (as Kent named it) and have to slow down and think about addition and subtraction in a way I just don’t do anymore in our base ten number system. I’ve never taught elementary school and have very little experience with how young learners might think about addition or subtraction (these basic facts being mostly memorization to me at this point), and I definitely haven’t thought about the variety of strategies for two digit addition or subtraction problems outside the standard algorithm. So needless to say I was totally hooked as I started to realize how many different strategies the participants in the session were using to make sense of the problems and the connections between the different ways of thinking through, for example, 55 – 37.

You can see a few of the different strategies folks used on the bottom right-hand side of my work, under the words “some ways”. Luckily, I was sitting at a table with Nicole Hansen (@nleehansen) who has experience as a K-2 math coach and we had a really interesting chat about the different strategies she’s familiar with and how they might translate in base eight. Definitely inspired me to learn more from my elementary teacher friends! One really nice moment from this conversation is kind of cut off in the picture above, but Kent was using the hundred chart (projected on the board) to talk through the subtraction problem 55 – 37, doing so by starting at 55 on the chart, and moving “up” once (subtracting one group of eight), again (another group of eight), a third time (another group of eight), and once more. Then, because that was a subtraction of four groups of eight, he moved to the right to “add one back”. The realization that you only have to add one back to move from subtracting 40 to subtracting 37 actually got an out-loud exclamation from Nicole!

Kent also directed us to notice which problems had the same (apparent) answer in base eight as in base ten, and try to explain why. (Circled on my notes page.)

We then moved on to filling out a multiplication chart. Nicole and I both tried to slow down and focus on making sense of any patterns we noticed, or reason through individual facts by transferring strategies we might use in base ten multiplication. (For example, noticing that multiplying by 4 in base eight feels like multiplying by 5 in base ten. And – what’s up with multiplying by 7? Why does it work like multiplying by 9 in base ten?) There were moments where I felt myself engaging in something similar to “mental math Monday”-type-thinking to compute some of the math facts in this new, unfamiliar landscape and that was pretty cool!

David Petersen (@calcdave) and Jamie Collie (@jcollie44) were also in the session and were inspired by the numbers in the multiplication chart that have the same (apparent) answer as they would in base ten, and decided to hunt for patterns by getting all fancy and color coding those values in Excel. Here’s a zoomed out image from their work (and if you want the file, hit them up on twitter).

I definitely left the session convinced that I wanted to spend a little more time in the alien universe of base eight.

And then a few days later, twitter wowed me even more me by informing me that Fibonacci base exists. COME ON, Y’ALL!! Too much cool! Not enough time!

Definitely a fun hour+ of playing, and a highlight session of my #tmc17 experience. Thanks, Kent! 🙂

I suppose it’s strange, at the end of a long summer full of trips, beautiful hikes, family time, various opportunities for learning, and time to reconnect with myself — to say that I am ready for summer to end and to get back to work.

But I miss my students. I miss my colleagues. I miss the challenges and constant struggle – the laughter, the frustration, the growth.

As I posted to twitter yesterday:

“one of my favorite things about being a teacher that i didn’t expect when i decided to become one: the journey to be a better teacher is bound up in learning how to be a more compassionate, curious human.”

Oh boy, I’m excited to get back to that journey.

More soon.