Posted by: rdkpickle | 02.08.2016


Today I’m moving around the classroom during the warmup and as soon as I kneel down to listen to one group’s conversation, a student stops, points to her work on the first question and asks me “is this right?” All three group members pause and look up expectantly at me. I hedge. I usually hedge.

“Talk me through your process,” I say with that pleasant, unreadable grin.

“That means I’m wrong, doesn’t it?” She’s smiling but she’s creating an out for herself. “I probably messed it up, did I do the whole thing completely wrong?”

“I didn’t say that! You’re the first person I’ve seen to try it this way, speak a bit about choosing this approach.”

Another member of the group laughs. “Have you seen the TV show Parks and Recreation? You know Chris Traeger? He’s so positive and affirming that he broke up with Ann Perkins and she didn’t even know it. Rachel, that’s you, when we explain something.”

I break into genuine, surprised laughter, and the rest of the group follows suit. But it’s true. When students offer to publicly share their attempt at a problem, suggest an idea about how one topic relates to another, or ask a question that sheds new light on the math we’re investigating (for me directly, or in a way that more clearly helps me understand their thinking) – it’s almost always valuable. I’m not faking my reaction, even if their work is way off base: we won’t get nearly as far together unless we are willing to take that risk and forced to articulate and refine our thinking.

I hope my relentless Chris Traeger positivity makes it feel safer to persevere, collaborate, and listen in my classroom. I also hope my students see clearly modeled the habits of building on other people’s ideas and appreciating different ways of being smart.

She launched into explaining her process. The group refocused its attention on her, not me. I moved on.

Posted by: rdkpickle | 01.09.2016


Conversations that get me thinking very deeply about math = A++ way to return from a luxuriously long winter break (spent being sick. Boo sinus infections!)

So. My precalculus team was discussing trig identities today – pacing our unit and then just sharing bits about how we’ve experienced teaching this topic in the past. A colleague brings up the piece about working both sides independently, vs. manipulating the entire equation. He shares an idea I hadn’t considered before, neatly captured here as part of a larger discussion on the issue (click to read entire thread)

Screen Shot 2016-01-08 at 9.18.55 PM.png


I sat at lunch staring into space like a dummy, trying to more clearly parse the discomfort I’m still feeling with this approach. I think the beginnings of my difficulty lie here:

Screen Shot 2016-01-08 at 4.22.18 PM.png

So one place I’m feeling the discomfort is: students could start with a false statement (something that is not an identity) and operate on both sides to produce a true statement. Worrisome, but hopefully they could realize that they couldn’t work backwards, starting with true statement, to produce the false statement. Maybe I’m worried they’ll get so excited about true statement they’ll forget to really justify the proof they’ve GOT by showing it “backwards.” It just leaves me uneasy.

Second place I’m feeling the discomfort: are there true statements – identities – where it’s possible to operate on both sides to get two identical expressions… but then in trying to write the “work backwards” part, run into trouble? I don’t know how to more clearly ask this question. I should probably think about this more when I’ve had some sleep.

Really, you should all just read all of: this

Really, I should appreciate the return to school. These teenagers are endlessly energizing. Their insights surprise me. Their struggles challenge me to adjust my approach.

Really, I should appreciate that I have colleagues who want to dig in so deeply on these ideas. I crave more! More conversation! More chances for me to fail in articulating my questions! More chances for me to refine my thinking about how to engage with students who ask “why can’t I…?”!

Really, I should be sleeping. Happy Friday! Happy weekend! Happy start of 2016.

Posted by: rdkpickle | 12.13.2015

miles and months later

I talk less. I listen more. I laugh plenty. I collaborate with an incredible team of math teachers. I am mentored by colleagues who are generous with their knowledge and time. I have eased into relationships, into community, into my role here. I struggle with balance. I try to be a daughter, a sister, a friend as life changes come fast and furious. I say no to some opportunities, say yes to others, and remind myself that I’m committing myself to this work for years, not months – and it’s okay to have miles left to go.


Some moments:

  • Reconsidering and deepening my knowledge of trigonometry based on a sequencing that forced new approaches to concepts, and colleagues who thoughtfully construct student-centered explorations into big ideas
  • H’s question when we were studying Law of Sines about where, exactly, this sinA/a ratio showed up on the physical dimensions of the triangle itself, which led to this new discovery about the circumcircle and its diameter
  • Dance Dance Transversal. Will always remind me of something else, now, something about how the best way to honor someone else’s life is to keep living yours.
  • S’s observation about exterior angles summing to 360 – completely unprompted – in Geometry after discussing exterior angle theorem
  • My Algebra 2 crew. Alternating between amazing days and days that make me want to pull out my hair, this class is never boring. They’ve worked so hard all semester and many of my standout moments have been with them. From Bucky the Badger to sweet sweet Desmos activity builder love, they have come a long way since Day 1.
  • Interleaved homework in Algebra 2. This team is 4 strong, and I follow the lead of my colleagues for the most part on pacing, sequencing, and homework. Nice to see topics spiral back again.
  • Navigating 3 teams with 3 very different personalities and approaches to collaboration. Mostly this just leaves me appreciative of experience and a diversity of teaching styles. “There is no one way.”
  • Desmos activity builder! and Desmos activity builder! and more Desmos activity builder!


As the semester wraps, trying to honor and celebrate the good things that have happened. I’ll have more time to dive back into Global Math, attend conferences, and hang out with Bay Area tweeps at our meetups soon. These first few months were what they needed to be.

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Posted by: rdkpickle | 10.08.2015

looping loops

“The newspapers, even some in France, said it was the marvel of the age; better than the Eiffel tower – and it was a Ferris wheel.

That almost mundane sensation we have now of looking down from above and moving through space, up and out and down and around again, no one had ever felt those things before, and of course now we can’t really feel those things again. We’ve gone around too many times. We’ve looped too many loops.”

High Above Lake Michigan – The Memory Palace

There’s something profound here about rhythm and routine vs. the novel and once remarkable. There’s a transition from terrifying and thrilling to comfort and confidence. I have a few more loops to loops, but I’m getting closer.

(We listened to this episode in Precalculus this week: working on circular motion, angles, linear and angular velocity, etc.)

Turns out other folks have been thinking about loop-de-loops lately:

Posted by: rdkpickle | 09.09.2015


One wonderful thing about my new setting is that I live close enough to school to walk to work each day. My morning commute has thus been transformed from the quiet 395-to-66 D.C. carpool, with quick stopover in the short solo suburban pre-dawn drive, to (now) a nice 12-15 minute walk downhill in the brisk California morning air. I find myself listening to podcasts of every variety to pass the time, and the confluence of physical and mental activity starting my day means I arrive awake and a bit more at ease with the transition from slumber-self to work-self.

It also means a lot of my footwear is no longer appropriate for daily wear. In my first year of teaching, I invested in a couple of awesome, neutral, comfortable heels that I generally relied on to set off a maybe-not-quite-fashionable-or-even-close-to-matching outfit. It also lent me the advantage of height over my students in early years – those heels meant “I’m the teacher, you’re the student; I’m tall and I know what I’m doing.”

Here, I’m wearing flats. As I work hard (and it’s hard work!) to move into a much more student-centered space, I find it doesn’t make sense to rely on those extra 3 inches of height, literally or metaphorically. As groups of 3 or 4 students work together to puzzle through warmups, groupwork, or homework review, the better move is to get close, crouch down to desk level, wait a bit, and listen. It’s a blessing that I can see this modeled by colleagues who are experienced and thoughtful, and that students coming to me from others’ classrooms are used to looking to each other as they grapple with new ideas instead of turning to the tallest voice in the room.

There’s still more nuance here. I’m working to establish classroom norms that were hard to talk about upfront as a newcomer to the community. Every one of my classes is in a different place in terms of what parts of class are working well and what parts need work. And yet, every day feels like forward motion. One step at a time, one (comfortably outfitted) foot in front of the other.

Posted by: rdkpickle | 09.03.2015

short + sweet

From beginning of the year student survey:

“I fall behind when i don’t ask questions. It’s a pride thing. Pride isn’t very compatible with learning.

Oh, how I’m feeling that last sentence. Growing quickly under the guidance of incredibly supportive, welcoming, thoughtful colleagues. Loving my new classes, new students, new environment. Working hard.

Starting over is humbling, but I’m strong and incredibly fortunate for the opportunity.

Much love to all of you as you journey through first days and weeks.

Posted by: rdkpickle | 08.29.2015

summer recapitulation

What a fantastic, and fantastically long summer. This summer, I:

  • Drove across the country – twice
  • Drove through 22 states + D.C. (South Carolina was accidental.)
  • Attended Brentwood High School and Flint Hill graduation ceremonies
  • Visited the Museum of Mathematics in NYC
  • Saw Sol LeWitt, Richard Serra, and more at Dia: Beacon
  • Went to two weddings
  • Hiked. Mountains! Alpine lakes! Wildflowers! Geysers! Bison! Elk! Yellow bellied marmots! (No bears.) ((That we saw. Fairly positive plenty saw – or heard – us as we sang our way through Black Hills, Grand Tetons, Yellowstone, Sawtooth, Tahoe, and more.))
  • Played the license plate game and found every state except Rhode Island. Come on, Rhode Island.
  • Hung out with @sarcasymptote in Yellowstone National Park
  • Read How Children LearnMake Just One Change, and Eleanor and Park
  • Listened to a lot of great new music: recent faves include Tyler Lyle, Jason Isbell, Liza Anne, Lucy Rose, Best Coast
  • Attended #tmc15 in Claremont, CA
  • Gave my first-ever conference presentation at #tmc15 on Better Questions
  • Wrote and performed another “camp song” with Sweens and @calcdave
  • Oh, and moved to California.

dream team

grand prismatic

grand canyon of yellowstone

mt washburn wildflowers


The hiking, driving, on-the-road summer gave me plenty of opportunities to be quiet and feel connected to nature. I embraced my in-between state, enjoying both solitude and simple times with friends and family across the country.

Summer has ended but its spirit lingers. Happy 2015-2016 school year, all!


Posted by: rdkpickle | 06.08.2015


“The spirit behind such games should be a spirit of joy, foolishness, exuberance, like the spirit behind all good games, including the game of trying to find out how the world works, which we call education.”

– John Holt, How Children Learn

Beyond its utility or beauty, mathematics – and the teaching of math – grips me with the promise of joyful discovery. All of my most meaningful mathematical memories have been less about competition and more about connection. Filling a whiteboard with invented notation that makes us laugh on an extension that has our hearts pounding, a tiny notepad whipped out past midnight to share a favorite proof with a tired/huddled/eager group of math teachers, a student who walks laps with me around the B-hall to discuss his mathematical wonderings, posing puzzler after puzzler at red lights during a city bike ride (shouting hints while avoiding train tracks), waiting patiently for the visible “aha” to light in the eyes of a student at work – once-timid, now powerful problem solver.

It’s in this spirit of joyful curiosity that I close one chapter of my teaching career and begin another. I spent two years nestled in my childhood home, teaching at the high school I attended as an awkward teenage daydreamer. I grew closer to my sisters. I said goodbye to my grandfather. I struggled in a way I hadn’t before, and learned I have worth – I am worthy – full stop. I learned just a bit more about building a positive classroom culture with classes of 30. I fell in love with all species of freshmen – loud, angsty, serious, eager, anxious, silly – all endlessly surprising. I adjusted to the grind of daily 47 minute classes and developed routines and procedures that maximized most of the minutes we spent together. I was welcomed as a colleague by former teachers, chaperoned trips I used to participate in, and on Fridays wore a T-shirt that said “Bruin for Life” on my 7 minute commute to work down the same streets where I learned to drive.

Up next is a new adventure, vividly imagined but far from begun. What I’d like: to root myself in my new community. To be more focused in my professional growth. To collaborate with and learn from colleagues who bring vastly different experiences to our meeting. To walk alongside my students as we try to find out how the world works.

“I never want to be where I cannot see it. All that energy and foolishness, all that curiosity, questions, talk, all those fierce passions, inconsolable sorrows, immoderate joys…”

How I hope as I journey forth that joy remains central to my approach of the teaching of mathematics, and the being of human.

Posted by: rdkpickle | 04.15.2015


There are some things about fear and bravery and teaching that I still haven’t completely ironed out.

A zillion quotes from John Holt’s How Children Fail to get things started, here:

“I asked them why they felt gulpish. They said they were afraid of failing, afraid of being kept back, afraid of being called stupid, afraid of feeling themselves stupid.”

“We adults destroy most of the intellectual and creative capacity of children by the things we do to them or make them do. We destroy this capacity above all by making them afraid, afraid of not doing what other people want, of not pleasing, of making mistakes, of failing, of being wrong.”

“I am horrified to realize how much I myself use fear and anxiety as instruments of control. I think, or at least hope, that the kids in my class are somewhat more free of fear than they have been in previous classes, or than most children are in most classes.”

“I had not lost all of my distrust in myself or fear of the world, but I had lost enough so that I could see the trials and failures of the classroom not as threats to my authority or sense of personal worth but only as interesting problems to think about and try to solve.”

As someone who has been (at times) held hostage by her own anxiety, teaching daily forces me to face my own vulnerabilities. I understand how important it is for me to feel comfortable in my own classroom. I understand how important it is for me to create a classroom where students feel comfortable, open to making mistakes in service of making meaning out of mathematics.

I’m still unsure about how to remove my sense of personal worth from the equation here. I know that if I dwell on every small failure, I will drain what little energy remains at the end of each day when I need those reserves to plan the next. Teaching problems – the trials, the failures – are interesting problems to think about and try to solve, but the breakneck pace at which those problems crop up often leaves me reeling. How do I face each student interaction with the patience and sensitivity it deserves? How do I set my own [ego, distractions, stressors] aside and allow myself to experience struggle as a part of professional growth?

Contributing to the growth of these gulpish teenagers into confident young adults is an important, consuming task. Some days, when I have slept fewer than 6 hours as a result of some crazy attempt to have a personal life in addition to a professional one, it can feel easier to wield fear as an instrument of control rather than bringing my calm, laughing, messy best to my students. Just a reminder to set my ego aside. Just a reminder that my best is enough.

While I’m posting: some odds and ends.

1) Yesterday in study hall, I was busily typing on my computer while a student looking over my shoulder out the window asked me if it was currently raining. The sad part is I immediately stopped what I was doing, flipped around, looked out the window, and nearly answered his question before I stopped myself to exclaim “are. you. kidding. me.”

2) I have spent a lot lot lot of time lately researching whatever I can dig up about the new standardized tests slated for 2015-2016 school year in Tennessee. I am sitting with ears perked listening to stories of SBAC and PARCC test administrations in other states.

3) I teach all freshmen classes this year, which is a first for me. I started my first year of teaching with mostly seniors, and have kind of inched my way down to these needy, wonderful 9th graders who are equal parts exhausting and energizing. As the spring weather creeps in and summer looms large, I’ve had so many friendly conversations with students ready to share their thousand thoughts with someone who will listen. It matters for students to have an adult in the building who they feel cares about them.

4) It is an unwritten law that if you plan a lesson requiring laptops and internet access, inevitably a cable in the county will get cut (?), knocking out all internet other than networked attendance and email clients. (Today.)

5) Teacher appreciation lunches this week have gifted me 5 extra minutes in the morning that I’m not spending packing my lunch, and a couple hundred extra calories each day in the way of delicious desserts. Thank you so much to the parents who are supporting us with their time, service, and yummy food.

6) I love working one-on-one with students, and I’ve gotten a ton of it this week. A few years in and there is _still_ nothing like the push and pull of working with a student – wherever they happen to be in their current grasp of a topic – to reach new levels of understanding. Those small victories, unique to each individual I’m working alongside, are a purely joyful experience.

7) I have a lot of thoughts about how to make my school a better place for new teachers. I hope my thoughts translate into concrete action, and that I follow through on the responsibility I feel to leave this place better than I found it.

7) I need to learn how to listen better. My voice takes up a lot of space in my classroom, and in my conversations with colleagues. Suggestions?

Have fun at NCTM Boston this week, friends. Think of me in my classroom in Tennessee, dangerously near the downhill slide to summer, fighting small battles every day to make my classroom, school, and community a place I am proud of.

Posted by: rdkpickle | 03.29.2015


First full week of classes since the week before Valentine’s day! (No joke.) We just got back from spring break and finished up our unit on quadratics with graphing and applications.

Some good stuff:

MondayDesmos Polygraph!

I knew this would be a total blast, and it was. For those unfamiliar with the activity, it’s essentially a computerized “Guess Who” style partner game with a set of 16 parabolas. (Desmos has done some really smart things here, like starting off the activity with a practice round against the computer to see how the game works, and inserting questions between each round so that students can build vocabulary and get better at asking questions.) Other folks have done a great job writing up their experience leading this activity (see Dylan’s post here, which I now realize I should have reread Sunday night when I was prepping, oops) so I won’t go into details. For laughs, though, here was my favorite question asked throughout the day. Brilliant. :)

outsmarting the system

For homework, I asked students to read through some of the sections in their book on graphing quadratics and create a one-page “cheat sheet” synthesizing the important ideas and vocabulary. Here is one of my faves:

parabolas cheat sheet

Tuesday – WODB and Graphing Quadratics foldable

For Bellwork on Tuesday, I used a “Which One Doesn’t Belong?” question from the brand new, awesome site created a couple of weeks ago by Mary Bourassa. We had done one of these style questions before, and I’ve noticed that a wide range of students are eager to offer suggestions for why each one is different – not just the students who typically speak up in class.

wobd parabolas

After the bellwork, we made a foldable to organize all of the info about graphing quadratics that students had read about the night before. I had photocopied some of the info on already to save time, and called on students in the class to help us fill in definitions and work examples as we went.

graphing quad foldable 1

graphing quad foldable 2

graphing quad foldable 3

graphing quad foldable 4

Finally, we practiced graphing quadratics by hand, from start to finish by finding opening direction, width, axis of symmetry, vertex, y-intercept, and x-intercepts.

graphing quad class practice

Wednesday“Make these Parabolas” and groupwork

In our Algebra 1 course we don’t go into vertex form for a quadratic, but I thought my Honors students would pick it up pretty quickly based on their prior work with transformations and absolute value functions. So, I used this Henri Picciotto task “Make these Parabolas” as bellwork – first showing students a bit about vertex form with sliders on Desmos, then writing one equation of a graph as a class.

Screen Shot 2015-03-29 at 12.33.53 PMI turned them loose for about 5 minutes, and was super excited to see how many students were able to create the designs without any other instruction or help from me. (I even had a student ask me after class if there were more graphing challenges like this he could try. Don’t worry, I pointed him straight to Daily Desmos. :) )

make these parabolas 2

make these parabolas 1

make these parabolas 3

make these parabolas 4

make these parabolas 5

make these parabolas 6

After the bellwork, students worked in groups of three on a packet with some questions about graphs of quadratics that came from the textbook. This included some of the skills we had worked on the day before, some questions where they were given the graphs and asked to write the zeros, vertex, axis of symmetry, domain and range, and some pretty straightforward application problems.

On the homework for my Honors class, I included a couple of challenge problems I was hoping would help them to connect what we already studied with quadratic formula and the discriminant to the graphs of quadratics.

quad challenge

Thursday – Review (entire quadratics unit, including solving equations)

Friday – Test

It was a good week. Only a few weeks of instruction remain before we begin preparing for the Algebra 1 End of Course Test. I’m grateful for sunny days and renewed energy to tackle the last few topics in the course.

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