Posted by: rdkpickle | 06.07.2018

looking back + charging ahead

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.


Posted by: rdkpickle | 08.09.2017

student/parent questionnaire

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.

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Posted by: rdkpickle | 08.09.2017

base eight

#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.


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! 🙂

Posted by: rdkpickle | 08.04.2017

briefly, from the atlanta airport.

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.

Posted by: rdkpickle | 07.31.2017


Is my participation in #mtbos for me, for my students, or for the profession? (or some combination of the three?) Does it matter? Should it matter?

I’m asking this question because my intuition tells me that I need to spend some time being thoughtful about this before I can process any of my thoughts about where our community is, what it could be, and my role in its future.

Right now, my north star as I make choices about how to engage in growing professionally online is *student experience in my classroom*, while attending to personal needs and setting boundaries that allow me to stay happy, brave, curious, and kind.

I suspect this perspective will evolve as my teaching does, and over time I’ll have different goals and desires in participating in/contributing to an online professional learning community.

This post is four sentences (well, five, now) but I’m headed to dinner with Heather and her family (I’ve made very real, lasting friendships through this community) so this is all I have time for. #pushsend. Much love to all of you who are having hard conversations, listening, doing the work.

Posted by: rdkpickle | 05.06.2017

spiraling squares

First, Jamie sees and saves the tweet:

Then, he sends it to me and Molly.

Molly and I spend the end of lunch/beginning of our shared prep block solving the problem (separately) and discussing our solutions and approaches.

We just finished a unit on Sequences and Series in Precalculus, so we decide to use the problem with our classes the next day.

I’ve gotten slightly better at framing stuff like this. I didn’t start with the problem. I started by having my (only 10 remaining with Seniors gone on projects) students count off into groups of 3’s. Move seats. *The mystery! The drama! What is Rachel going to have us do?*

Next I gave verbal instructions – get out a piece of paper and draw a (not too small) square. Then divide sides into thirds, draw next square. Shade. Etc. Students drew about 4-5 levels in and we paused.

Then I gave the question.

They started in seats on paper. Honestly, I think I could have left the room for 20 minutes and come back to find them still intently focused – I don’t think I’ve ever had a class quite like this before. After about 5 minutes, I made them get vertical and sketch ideas on the whiteboards. Here are some work-in-progress shots:

(The third group got bogged down with some algebraic/arithmetic mistakes. The black stuff got added as a student tried to reverse-engineer the math after knowing the answer.)

The engagement around the room was pretty great. I interacted with various individuals, groups, and students added notes and made comments as they took breaks from their work to observe others’ process.

The addendum, of course, is that after I tweeted out these WIP shots, Dan Anderson steps into the thread with an awesome OpenProcessing interactive that I just had to email out to my class this morning, even though it’s Saturday and it’s pretty unlikely any of them woke up thinking about this problem.

(I think I dreamed about this problem last night. Sorry, William – I’m still not dreaming in four dimensions. But for now, dreams about great days in class will do.)

Posted by: rdkpickle | 04.08.2017

log properties

Just wrapped up a unit on logarithms in Algebra 2 Honors. (p.s. It’s Friday and I’m officially on spring break!!!) [note: I didn’t finish this post when I started it, and now it’s Saturday and my break is officially almost over!!!!] In teaching logarithms for what is maybe the 8th year in a row, I managed to stumble on a different way to talk about the log properties that was like, okay, duh.

Let me preface this by saying I do think the way we talk about mathematics out loud can create or reinforce misconceptions for students about how math works. The best example I can point to is using “cancel” as an all-purpose term that students interpret as “these things disappear!” rather than taking the time and care to point out when inverse operations undo each other (“divides to one” or “adds to zero”). [See Nix the Tricks for more]

I feel the same way about sloppily using the word “distribute” when I’m not talking about the distributive property – especially given how quickly students make the mistake of trying to “distribute” operations. (i.e. log(X+Y) = log(X) + log(Y))

So, this year when I started talking about log properties, I was more careful about the way I spoke. After first noticing and then proving the properties by making the connection to exponent properties, I fell into a habit of describing them the same way I describe the exponent ones. That is, if we expanded log(XY) to log(X) + log(Y), I’d say “because when you multiply two powers, you add their exponents.” Ditto log(X/Y) = log(X) – log(Y) (“when you divide two powers, you subtract the exponents”) and log(A^C) = C*log(A) (“when you raise a power to a power, you multiply the exponents”).

Might seem like a small shift, but I caught myself a time or two reverting back to really imprecise language like “so the multiplication here becomes addition of the two logs” and realized how irritating and confusing this sounds. What’s happening with these log properties isn’t a magical swap of one operation for another, and these aren’t algebraic rules that students should feel like they are memorizing. Instead, these properties are a natural extension of ideas the students are really familiar and comfortable with – exponents.

Posted by: rdkpickle | 03.23.2017

today, the future

Got to do some fun things in class today. Credit to Jamie for curating these (and every other element of the awesome, so fun and challenging A2H curriculum):

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In addition to the mathematical challenges the day posed, I felt challenged by the time of year and all of the time-sensitive, human needs I ought to be attending to as we send home feedback in the form of grades and comments to our students as well as recommendations for courses for next year.

The following excerpt from this article, which I read to prep for a Strategic Plan working group meeting last week, felt especially timely:

The same principle applies: Do whatever you can to take instinct out of consideration and rely on hard data. That means, for instance, basing promotions on someone’s objectively measured performance rather than the boss’s feeling about them. That seems obvious, but it’s still surprisingly rare. Be careful about the data you use, however. Using the wrong data can be as bad as using no data. Let me give you an example. Many managers ask their reports to do self-evaluations, which they then use as part of their performance appraisal. But if employees differ in how self-confident they are—in how comfortable they are with bragging—this will bias the manager’s evaluations. The more self-promoting ones will give themselves better ratings. There’s a lot of research on the anchoring effect, which shows that we can’t help but be influenced by numbers thrown at us, whether in negotiations or performance appraisals. So if managers see inflated ratings on a self-evaluation, they tend to unconsciously adjust their appraisal up a bit. Likewise, poorer self-appraisals, even if they’re inaccurate, skew managers’ ratings downward. This is a real problem, because there are clear gender (and also cross-cultural) differences in self-confidence. To put it bluntly, men tend to be more overconfident than women—more likely to sing their own praises. One meta-analysis involving nearly 100 independent samples found that men perceived themselves as significantly more effective leaders than women did when, actually, they were rated by others as significantly less effective. Women, on the other hand, are more likely to underestimate their capabilities. For example, in studies, they underestimate how good they are at math and think they need to be better than they are to succeed in higher-level math courses. And female students are more likely than male students to drop courses in which their grades don’t meet their own expectations. The point is, do not share self-evaluations with managers before they have made up their minds. They’re likely to be skewed, and I don’t know of any evidence that having people share self-ratings yields any benefits for employees or their organizations.

[emphasis mine]

Designing a Bias Free Organization, Harvard Business Review

I want my students to know I see them and value the ways they give themselves to our mathematical endeavors each day. I worry about recommendations (Honors, not Honors) and the messages they send to students, intended or not. I worry about the different ways in which different student groups receive these messages, based on internalized oppression and a lifetime of being told they probably won’t measure up.

My day ended with two other colleagues – sharing, venting, laughing, and making ourselves wholly vulnerable over drinks and dinner. Our upcoming spring break will be energizing and so needed. The work will continue, soon enough.

Posted by: rdkpickle | 03.13.2017

favorite problems 3 – dartboard

[previously: favorite problems 1 – pirates, favorite problems 2 – triangles]

This one came from the “#MTBoS,” before it was named such a thing.

These were early days, when I was still kinda geeking out over the fact that I was tweeting with k8, and Dan, and Sam. There was this energy about the whole thing for me – I’m a competitive person, and realizing there was this group of whip-smart, motivated, brilliant teachers to learn from and look up to – I wanted to impress, to be impressive.

I’m pretty sure I could use my internet skills to figure out who first posed the square dartboard problem, but it’s a Monday night with a long week ahead and you’ll forgive my delinquency, here. What’s more important is what I haven’t forgotten – that I spent a long Greyhound bus ride to New York City sketching notes in a small Moleskine notebook (the same one I used to sketch tiny maps of Metro stops + the cross streets I’d find upon riding the escalator up up up and emerging onto the D.C. sidewalk). The problem posed was a challenge. I wanted to be in with the in crowd, wanted to solve the problem and share that I’d done so. Brain buzzing, headphones on, I jotted down my ideas, ignoring the seatmate eyeing my mathematical scribbles with furtive, skeptical glances.

The question: “There is a square dartboard, and a dart has equal probability to land anywhere on the board. What is the probability that the dart will land closer to the center than to the edges?”

It wasn’t until the ride back that I solved the thing. I don’t think I tweeted about it. I did, however, save the work. It was posted proudly in the “cubes” at my first school, traveled with me to Nashville to get laminated and hung near my desk. Still have it, somewhere. Years and miles separate me from the girl who experienced this problem as a test of her authenticity as a math nerd, who saw a solution as signal that I was worth being invited to the table.

Still something kinda magical about it, though.

So. Scrolling down invites spoilers.



[Worth mentioning – I posed this problem to students, years ago. Kids I didn’t even teach, who hung out in my room to talk math and after an hour or so filled my whiteboard with the work below. None of us back down from a challenge. All of us want to feel like we earned our way to the table.]


[[edit: @dandersod points me to the original question, as posed by infinigons. his work: here. “you were the nerds i wanted to accept me!”]]

[context: I moved back to my hometown of Brentwood, TN in 2013 to teach at the public high school I attended. I probably shouldn’t post this to my professional blog, but I’m 3 years removed and so much happier now. If this makes one teacher laugh or feel less alone, then okay.]

“i am so tired too. i slept 14 hours on friday, 8 hours on saturday, 8 hours last night, and then took a 2 hour nap this afternoon. it’s not good or healthy it’s like a HEAVY tired like someone is SITTING ON ME”

“i had a shit day yesterday and shit night last night and i’m having another shit day today. i feel like an actual crazy person. i am close to tears.”

“whip yo hair, girl. i killed a spider in 1st pd crawling across the floor while i was teaching. cool”

“This is the day from hell seriously. I am so bored and all I’ve done all day is take attendance and be a cattle hearder. And get mad at kids for doing dumb and disrespectful things. Soooo much less organized than our senior day, which is the only thing I can compare it to. Chaos!!!!!!

Also during one of the homecoming skits a white kid had on fake dreadlocks and said his name was obamaniqua. I was not amused.”

“oh my god i just remembered that snow days exist”

“i cried a little on the flight home yesterday feeling overwhelmed about life again, and i read the book mom gave me from cover to cover. it did provide some comfort, although there were parts that (i thought) were cheesy. overall i feel better – last night i didn’t panic and today i didn’t panic. it wasn’t a great afternoon, but it was ok. i can doooo this

i’ve decided the thing i hate most about this job is the grading, especially when kids fail. it gives me hives. i still don’t mind lesson planning, except my brain has been too cloudy to make good decisions without feeling overwhelmed by options/not sure how things will work in a class of 30.

random rachel update of the night”

“i’m thinking about quitting again today… i need to stop fantasizing about it, i think. but today’s it’s not desperate or anxious thinking, just like “when will this year be over” thinking.

we can do it though…. 5 weeks until thanksgiving… we can do it…..”

“i don’t understand how i’m going to have energy to write college recs or teach for this whole year or do anything else when this year is over…. all i want is to be in bed forever and eat until i weigh 200 pounds or more, and read and watch movies”

“i just taught the MOST BORING CLASS of my life. seriously. no joke. it was bad.”

“I feel like someone is going to walk through my door at any moment and announce, “you’re fired!”

Which I guess actually wouldn’t even be all that bad. I don’t know what I’m worried about. I mean truly. I just hate feeling like I’m not doing things as good as I should be.”

“i took my first dose of antidepressants last night and don’t really feel anything (not that i was expecting to.) we’ll see what happens as it builds up in my system. i’m hoping no side effects, only taking the edge off my sadness/anxiety. we’ll see.

i woke up today at 4 and couldn’t go back to sleep. just laid in bed and was uncomfortable/worried. tried not to be. i hate feeling like this.

in the shower i thought about quitting at christmas. it’s just so hard to imagine doing this for the whole year.

haven’t been observed yet. i honestly don’t even give a shit at this point. if i’m crappy, whatever.

i can’t believe i have to be here until 9 pm.”

“i 100% agree. if i make it through this year i’m NEVER looking back.”

“how many hours is too many hours to spend in bed? how do normal people do stuff like garden and run errands and clean house and pay bills on the weekends? i loveeeee lying down and being a blob in my beddd”

“i haven’t slept more than an hour straight in 2 nights. i am exhausted. i keep waking up and clenching and unclenching my muscles and worrying deliriously about school. when it got to be 5 this morning i went into my mom and woke her up and laid on the bed whining about how much i hate working and didn’t want to go to school. it’s always better once i get here, but getting up each morning has actually become the hardest thing in the world… it’s taking herculean efforts to get me in the shower and dressed.”

“so, helping with model un was actually really really fun and i’m so glad i did it. i absolutely love belinda wade. it was great to get to talk to her and hang out with her, and to see the kids in a non stressful non school environment. it reminded me that kids are smart and fun and sweet and a lot of times eager to please you/earn your respect. it also reminded me that the first year at a new school is supposed to be fucking hard!! it’s supposed to take a while to feel comfortable. i know this year i’ve had extra on top of that with my anxiety and depression, but it helps me to let go the worry of feeling like i’m not living up to people’s expectations of being a good teacher. they all KNOW it’s supposed to take time.”

“guess what??? when i’m in a good mood, i’m a good teacher! no joke. i’m in a good mood today and the whole day has just gone sooo much better. i think it has to do with confidence – being able to face the teenagers without wishing i were invisible. 4th period is my super shitty class and yesterday it sucked, and today it was great!!!!!!”

“ughhhh finally finished my 3 algebra class marathon and i have lost my voice and am exhausted. i have been my old teaching self ALL week though, i mean confidence level wise and clearer directions and not forgetting things. i’m sure it’s my mood and the meds and the rest from break.

but again it makes me think HOW does ANYONE who is less organized or, to be blunt, smart as us, DO THIS JOB???”

“an actual miracle has just occurred. i copied ALL of the worksheets for AAT next week. normally i’m scrambling the MORNING OF. oh happy day!!!!”

“i am feeling like 87% normal today.”

“just used the bathroom for the first time since i got to work… WHYYY IS THIS JOB SO HARD?!?!?” [sent at 2:27 pm]

“i wish you WERE here. i would go with you. i’m trying to live a more full and meaningful life. like, read more, learn more, care more. all of that. none of the stuff that doesn’t matter. i don’t know what that means exactly but i guess i’m just feeling *hungry* about life again… for the first time in a while. which is GOOD!”

“i know right!!!! give me liberty or give me summer!!! (or something…. you know”

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