Note: Today’s post uses each of the Standards of Mathematical Practice, or SMP.
I threw a temper tantrum, dear reader.
Back in 1997, I learned about base 2 notation. Mr. Konrad Dzwonkiewicz, taught MST’sÂ introductory computer science class, where we learned the Pascal programming language, introduced us to the language of 1s and 0s that make up all our work with computers. (SMP 7:Â Look for and make use of structure)
Through Mathematics in Civilization, I’ve learned that in every single major civilization from antiquity onward, the development of a number system preceded any written language. In this sense, then, learning mathematics can be considered studying the roots of our language system, English. (SMP 8:Â Look for and express regularity in repeated reasoning)
We consider the alphabet as being the building blocks of our language. But I’m quickly learning that math holds many pre-language building blocks that our kids need. (SMP 2:Â Reason abstractly and quantitatively)
That doesn’t mean teaching toward this idea is easy. In fact, I straight-up threw a temper tantrum when I hit a tough spot (and I’m still in Chapter 1, sooo it’s probably going to get crazier).Â What did this grown-up temper tantrum look like? Welp, IÂ scribbled and tore the paper like many of our young mathematicians would in a similar situation. I’m not perfect.
But just like we encourage our students to make sense of problems and persevere in solving them (SMP 1), I carried on. And if you’re thinking, as I did, that familiarity with the duodecimal system (a counting system based on using the digits 0-9, then T and E to represent 10 and 11) is a silly obscure skill, consider that our time system is based on 12 and, to a greater extent, the Babylonian Base 60 notation.
Speaking of the Babylonians, after I regrouped, I looked more closelyÂ at my work, and corrected my errors (SMP 3:Â Construct viable arguments and critique the reasoning of others andÂ SMP 6: Attend to precision). And then I got caught up in the aforementioned Babylonian Base-60 math. This time, I was able to control my rage, but not my confusion.
Those trumpet-and-rewind marks on the righthand page are the symbols (SMP 4:Â Model with mathematics)Â used by the Sumerians and Babylonians because they were the only two symbols thatÂ could clearly be etched into tablets (The symbols look remarkablyÂ like the iconography used in The Crying of Lot 49 (There’s a ton ofÂ ELA standardsÂ and social studies crossover here; I’m not going to list out all the standards for this cross-curricular extension).
Looking at my work, I was able to convert from base 10 (our decimal system) into base 60 for numbers that were smaller than 100. Anything beyond that was largely out of my control. But I remembered Chip Brock telling me that even if we can’t complete a problem, we should write out the solution so we can perhaps gain additional insight. I tried that, but it still didn’t provide any clues.
You can see my highlighted bits remind me that I need to sally back online and find some videos that explained things more clearly. (SMP 5:Â Use appropriate tools strategically)
I returned to Khan Academy because of their ease of searchability, but there wasn’t much available. I found this and it’s quite nice and has a lovely, lush green background.
Worth noting: This video never explicitly tells me **how to do the problem I was working on,** but it does give me a broader understanding of the context of the problem I’m working on, which provides additional entry points for students (me) who have shut down. (SMP 1)
More later, once I muster up the energy to view aforementioned video.
I reached the end of the first chapter in Mathematics in Civilization only to be greeted by a practice set at the end. I know practice sets are usedÂ inappropriately in many contexts, often only seeking level 1 information from kids, but in this case this practice setÂ served as a formative assessment of my comprehension.
This is interesting for me as a teacher, because as adults, we don’t often encounted what we refer to as “instructional level text.” I might even be willing to wager that, given the idea that instructional texts are supposed to be read with 95% fluency, that this book is a frustrational book for me.
So what am I doing for myself so I can have a deeper understanding of this text? Well, in class we often encourage kids to draw from a bank of resources (in ELA, this often includes a teacher-or-team-vettedÂ stack of books at a variety of levels on the same topic).
Unfortunately, part of the struggle I had in teaching math is that for many years I didn’t feel like I had access to resources that could help **me** in my elementary math **instruction,**Â so this text is really instructional or frustrational level for me. Deeply understanding this book and its concepts are partly hampered by my lack of experience in reading dense // technical texts.
I know it’s difficult to picture my work without seeing the book, but here are my notes for the first section of the first chapter and the practice set (which is really enough for me to chew on for basically the past week). For context, this is considered pre-algebra and is explored in 5th grade Eureka math curriculum.
I got stuck on base 2 and base 8 expression, andÂ so I went to Khan Academy. I was fairly sure that I’d find a video that would fit my specific needs. I discovered that the Khan Academy was great for specific skills, and this one featured a history lesson before jumping straight into the binary lesson system.
Some relevant quotes that I think show good direct instructional practice:
“And to solve this, (finding a way to move on from primitive counting methods such as using tally marks, etc) human beings have invented number systems. And it’s something that we take for granted. You might say, ‘Oh, isn’t that the way you’veÂ always counted?’, but hopefully over the course of this video you’ll start to appreciate the beauty of a number system and to realize that our number system isn’t the only number system that’s around.”
There, the instructor shares his learning outcomes so students will know theÂ teacher’s goal for this lesson,Â which will provide students with historical context to broaden understanding of number sense, and will hopefully help them manage numbers in base 10.
The thing that’s interesting to me is that the learning goal ISN’T “learn how to write in base 2.” The learning goal is broader, and it reaches out to work in other disciplines civilization, economics, language standards here), but it’s still grounded in one specific aspect of mathematics: being able to “see” numbers in both base 10 and base 2.
This video was enough for me to better understand what I needed to do that I didn’t need too look at other number systems videos (there were a great number at first glance), and these additional videos could provide both extension support as well as RTI.
It took me perseverance to make it through the whole video, because honestly, a part of me thought it wasn’t going to deliver. So here’s an example of the next video I had lined up in case this video didn’t meet my needs.
This video is more of a practice set. I had it going in the background while I returned to my practice set and finished it. I appreciated that the faceless Khan Academy voice spoke to me using an informalÂ tone to invite me into the learning, saying things like,Â “I’m assuming you have at least tried, and we can work on it together.”
Upon reflection of my own work, I realized the biggest stumbling block in my way of learning mathematics is that often times I can’t “see” how numbers fit together. You know how in your brain you can just KNOW that 1+4 = 5 ANDÂ that 2+3 also equals five? I don’t yet have that kind of automaticity in this kind of number sensepractice.
I’ve had enough “we do it” practice, so it’s time for me to try again on my own.
Chris Turnham is a great artist. We have three of his screenprints in our bedroom, and another one in our family room.* I wish teachers could afford his pieces to display in their classrooms. That’s his work to the left there, a print I’d love to use during our plant growth and development unit.
Lately, I’ve been thinking about how many schools have outdated, cliched books that don’t facilitate pushing students’ thinking. So I wondered what we could do to turn these stereotypical texts on their head and make totally standards-aligned lessons and units of study that view issues through a critical, social justice-minded lens. My goal is to create un-bannable lesson plans that explicitly address past widely-held beliefs.
My first introduction to Chris’ work coincided with discovering a great show in LA that highlighted RetroFuturist designs. This, combined with multiple conversations with picture book author and illustrator Julian Hector about the futurist movement, has led me to an exciting announcement for our class website.
Each week, in celebration of Throwback Thursday, I will be posting what I am calling:
Aesthetically pleasing retro futurist lesson planning for social justice.
We’ll be looking at how vintage documents and books give us a chance to reflect on our past as a nation, as well as looking into the future to see how we can help make the world a better place.
You’re invited to join in! You can e-mail our design team right here. If you’re looking to get a sense of theÂ kind of documents we’re seeking, troll around the Library of Congress digital collection.
This whole endeavor is also inspired by Bellevue teacher leader Kristin Leong, whose Mostly Appropriate Resources push the envelope as to what’s an acceptable “text” for our students. I love her work and would give just about anything to coteach with her.
“It’s a Southside revival, put your hands high
Let your arms be the pillars that be holding up the sky
I heard a few heads say that hip hop is dead?
No it’s not, it’s just malnourished and underfed.”
“Southside Revival,” Blue Scholars, 2005
Seattle is changing.
I’m from metro Detroit and I saw what happened to the region in the 1980s and 1990s. Nobody in my circle of friends and family really talked about it, except to express some amount of disappointment and regret.
Now I’m seeing some of the same patterns in Seattle, and again, nobodyÂ in the publications I follow seems to be addressing a big, underbelly-style demographic shift, a shift I’m calling the Brown Shove.
The Seattle I moved to in 2005 was a vibrant place with lots of quirky individuals. I worked at Display and Costume and met lots of artists and creative folks who saw their efforts reapÂ great success.
But then theyÂ startedÂ moving from Seattle. The rent prices are insane here, driven by the influx of tech people (briefly: Amazon) moving into the area. Based on the demographics of my friends who have moved away, I’ve been referring to this as the Brown Shove. I’m acutely aware that the only reason we haven’t been priced out is because my husband is a software engineer. And I’m acutely aware that the reason he’s a software engineer, despite having a background in music, is at least in part because he fits the #seattlestereotypes of a charming technology fellow.
Seattle has a lot of nicknames, but the three that come to mind related to this Brown Shove are as follows:
The Emerald City
None of these labels are inherently bad; I’m not looking to pick a fight there. And I’m not the first to bring up these nicknames and their relationship to a changing city. In a piece published on February 18, 2014, John Cook, editor and co-founder of Geek Wire, examined these dynamics:
A nickname can say a lot about a community â€” where it has been and where it is going. There’s a new Seattle emerging â€” one which is far distant from â€œJet Cityâ€ or â€œQueen Cityâ€ or â€œEmerald City.â€ None of those really work so much anymore.
Also in February 2014,Â Knute BergerÂ wrote about Seattle needing a new nickname, and he examined our history of nicknamesÂ in an excellent piece:
One hundred and fifty years ago, our sawmill town on Elliott Bay saw events that portended huge changes. In May 1864, a â€œcargo of bridesâ€ called the Mercer Girls arrived as potential mates for the male settlers, so the city could become self-propagating.
In October of that year, Western Union â€” the Comcast of its time â€” brought the telegraph to Seattle, connecting us with the newly wired world.
Our city is built on immigration and technology, and rapid changes have regularly turned over our collective identity.
TheÂ three names I pulled from Seattle’s nickname history strike me as particularly relevant because taken together, they help break down some of the pigeon-holes that we’ve been putting residents into. Rather than blaming techbros or hipsters, I think it would be useful for us to examine when we can actually fall into differentÂ categories at different points in our lives, or even different points in our day.
Emerald City residents: These might includeÂ folks who genuinely love Seattle at its core. This could be folks who love the natural wonders the PNWonderland provides, or people who enjoy seeing renewed vitality in the area. It includes people like me, who love the Emerald City, while still acknowledging there are manyÂ folks (read: our insanely huge, underserved homeless population, and other people slipping through the cracks) who might claim that this is nobody’s Emerald City.
“What does a town that’s been to hell and back know about the finer things in life?”
Jet City residents: These are folks who move into and out of our city. It could include people traveling a lot for their profession, or people who see Seattle as a stopping point on their travel routes. These folks often help me realize what an exciting, unique place we live in; how lucky I am to be alive right now.
“What does this city know about luxury, hmmm?”
Rat City residents: These are folks who might only see the bad parts of Seattle’s growth and change. This category would also include folks with self-serving interests who are pushing out families and children (have you READ the Seattle Public Schools news lately?) who don’t match up with their views of a new urban paradise. This label could also apply to the erased and marginalized populations that Seattle’s civic policies seem to be working to quash even more. (Ask your friends who have moved to Burien, Tacoma, or Marysville)
“It’s the hottest fires that make the strongest steel.”
For the record, I consider myself as belonging to different groups depending on the day, maybe even on the hour, so this reflection isÂ by no means comprehensive. (TBH I could write a whole book just about the lessons in the Imported from Detroit commercial) (I have written a lesson plan about it, FWIW) (It’s totes Common Core aligned)
So I’ve been thinking a lot about how my background growing up in metro Detroit plays into all this. I’ve been thinking about Ken Jennings’ reflection on being beaten by Watson on Jeopardy, where he said he “felt like a Detroit Auto Worker in the 1980s.”
We need to know who we are and what we value so that we can ensure this city is a vibrant, exciting place for generations to come. We need to approach our residents’ needs from different angles.
I saw what happened in Detroit. I’m sick at the prospect of what thingsÂ would look like if it happened here.
I’ll end with another quote from the Geekwire piece as well as Chrysler’s now-classic ImportedÂ from Detroit ad, which features a shoutout to the Emerald City.
I’m writing this morning to share a little bit more about my recent hospitalization, my resignation from classroom teaching, and my dancing-around-the-issue label of “chronic health issues”. I hope you’ll understand I’m mainly sharing this because I’m desperate for other folks to be equipped if they ever have to deal with a similar situation.
Back in February, I was briefly hospitalized for a manic episode (props toÂ Siobhan Chan for her kindness). In a diagnosis that is no surprise to anyone, least of all me, it seems I have Bipolar I disorder. I tweaked my meds (I’ve been on Prozac for years, so we added in a mood stabilizer), and thought the worst was over.
A few weeks ago, I broke with reality and on Good Friday, Toby McKesÂ took me to the emergency room again. I lost three days to effed up dreams, and when I woke, I learned I had been involuntarily transferred to Fairfax, a private hospital. (More on that later; Toby and I are planning to write a series of pieces around navigating mental health care in Seattle.)
On the positive side I received tremendous care from the folks at Sound Mental Health, Seattle Counseling Service, ABH Seattle, and Kristin Andrews at the Polyclinic. My experience in the emergency room (“Now which patient are you?”) was scary, and Fairfax was frankly, the stuff of nightmares, but I’m encouraged by folks working tirelessly within a broken system.
Again, I’m nervous about going all “One Flew Over the Cuckoo’s Nest” (my favorite book in HS) on you all, but I’m hopeful that sharing my story will not be perceived as grandstanding, but will instead be useful to others. Here’s the information to Seattle Counseling Services, if you’re looking for someone to reach out to.
If you follow me on Twitter (@MsHoughton) or Instagram (@beforetoday7), you may have seen me using the hashtag #seattlestereotypes both for positive and negative behaviors, comments, and practices I observe in the Emerald City. I found one today when I unearthed this Pagliacci ad. Pagliacci’s is one of our local pizza jointsÂ (We are fortunate that there are many! BTW, I need to give a shout out to two that just recently opened, Dino’s Tomato PieÂ and Meltdown Pizza Co).
Here’s the front of their ad, designed (IMHO) to resemble the Trader Joe’s Frequent Flyers that we often receive.
Cute, right? Comics and graphic novels are a pretty big deal around here. But here’s where it gets super-Seattle-y.
WHY YES THAT IS A BOOK SUGGESTION LIST ON THE BACK PAGE OF THE PIZZA AD.
We tell our students of the importance of maintaining a safe, long-view oriented presence online, but what would happen if our phones were taken or observed by someone who didn’t know us? What would give them clues?
I wanted to find out, so I’ve uploaded a few screenshots from my phone yesterday. I’ll post them as a gallery so if you want to use them without my commentary, you can. (Thanks to Morten Hendrickson for introducing me to galleries at WCNYC’14)
Let’s start with my lock screen.
I’m pretty much perpetually running in low battery mode, because I go to plug in my phone and get away from it for a while, but then I think of something I want to look up or get others’ perspectives on, and then I head back into the bedroom to unplug it.
((Irene I am Sherlocked pic))
Depending on your schema, you might also recognize the art as the Blessing of Worlds emblem from the video game Destiny. It’s been my lock screen for as long as I can remember, which supports the idea that I’m not much invested in the visual aesthetics of my phone. I couldn’t get a shot of my phone case to deduce from that (because I’m too wimpy-fingered to prise it off), but I’m definitely not one of those people who have a dozen or more cases (tho I wish I were).
From my home screen, you can see I’ve kept the default Apple background, which perhaps is an indicator that I’m not deeply invested in the aesthetics of my iphone in the same way that, say, I was obsessed in the late 90s/early aughts with crafting the perfect AIM combination of text font, size, and color (Times New Roman bold in a deep green color, in case you were curious).
From this second of two homescreen pages,Â I’m VERY interested in what you think of my app downloading habits.
(Irene adler in white dress and phone smiling))
Selfieeeeee. It’s taken on the porch, which if you know me, means I’m writing in my journal and probably sipping some tea. (I’ve had to cut out all but decaf coffee because of med interactions)
Clothing is a costume for me.
((Image of Sherlock in firefighter costume in bedroom)
This is the screenshot that made me really start getting excited about this post. You want to talk about elevator pitches? I feel like people can get a pretty clear picture of who I am and what I value just from this one image.
Marie Curie? Bucky Fuller? Splitting my time between Seattle and Michigan (no one’s emerald city)? It’s all there in one portrait-rotated image. “No matter the costume, it’s always a self-portrait.”
This is my about page on Facebook. I feel like it speaks for itself, which is kind of the point. The fact that I didn’t “write about myself” there speaks to my reticence toward being too self-promoting in my work and my life.
((John Watson “nothing ever happens to me”))
You may notice that there’s only one quote that isn’t attributed. The person who said it was Dr. Stephens, who for many, many years was both my mom’s and my OB/GYN. He’s the man who managed my parents’ care while they tried for a decade to conceive yours truly. I was hesitant to post his name because I didn’t want people to think that I was Â bragging about a PhD fellow thinking I can have and do whatever I want, because that sounded grandiose to the extreme.
The funny thing is that now, in 2016 (he passed in 2005), rereading this quote makes me think immediately of Teachers Who Game. “The world is yours to play with.” Isn’t that lovely? Life is our most important game.
Here’s hoping this has been an enjoyable endeavor!
This is a first, ladies and gentlemen. Today, I had the opportunity to witness a “math person” saying he “failed” at “art.” We know how rare this instance is, given that if you replace the previous sentence with “artistic human” “failed” “math,” we’d have approximately one majillion examples to point to.
Dan Meyer compiled a collection here, and I know the FW folks actually have used it quite a bit.
Anywayzzz, I’m trying to live that Guide on teh Side lyyyfe, so I’ll just share the screenshots and let you comment below or on Twitters.