play

In Kate's math class, they've been coloring in grids that look like this:

0+0    0+1    0+2    0+3    0+4 ...

1+0    1+1    1+2    1+3    1+4...

2+0    2+1    2+2    2+3    2+4...

to color in all the boxes that sum to, say, 6. Students should (I'm assuming) realize that if 3 + 3 is 6, then so is 4 + 2 (up one, down one)... and so is 2+4 (down one, up one). And so on. and then if they want the ones that sum up to 7, they notice those are always one box below the sum-to-six. Etc. etc. 

But when she "plays" math and gives me a problem to solve, it looks like this (see left) - random addends in random boxes with random rules for coloring: 

She also created a problem for me about 10 cupcakes, and 7 cupcakes went into the cupcakehole. And she knows that's a funny twist on "piehole" (which she knows is one of my favorite words). 

And then this week during her piano lesson, she decided that she wanted to play every piece two ways: the "right" way, and then with her left hand up "up" 4 keys from where it ought to be. (she's only playng the white keys so she's not transposing anything!) And we played it that way and it was fun and at the end of each piece it didn't sound "right" so I would plunk the "C" so that it sounded like an ending!

I want to say that cupcakehole is playing with language in a way that says to me that she "gets" it... or get something. And her piano today was real music-theory play. But her math play isn't math, right? Her inability to play with addition suggests to me (weakly) that she doesn't "get it." She can add and subtract but she doesn't get the patterns of it all and why different sets fo numbers can combine to make the same number. But not that - that's big stuff - she doesn't get the POINT of what she's doing in math.

I think of a paper I just submitted on aesthetics -- I claim that a physics class should give students a new way to play in the world. 

And my students and I are thinking about this sense of play in theory-building ... but mostly I'm just thinking lots about capacity for play as a marker? goal? for learning. And what such play looks like in physics v. other settings. And how much the monks in India were clearly, delightfully playing with their ideas. And where I see Kate playing with ideas v. "just" playing/playing with routines/playing with "school."

springy things.

I've been reading some early physics. Here's Huygens noting that even hard objects are springy - and then he uses this to make speculations about the particles that make up the luminiferous ether: 

"For I have found that on striking with a ball of glass or of agate against a large and quite thick piece of the same substance which had a flat surface, slightly soiled with breath or in some other way, there remained round marks, of smaller or larger size according as the blow had been weak or strong. This makes it evident that these substances yield where they meet, and spring back: and for this time must be required."

have the same kind of experience...

This is from a literary critic, but it could be a little bit about teaching physics I think. Especially the part where your (student) asks you to turn off the music.

... When I write about a novel or a writer, I am essentially bearing witness... It’s like playing, to a friend, a piece of music you really love. There is that moment when you stand next to this person, hopeful and intense as you anxiously scan your friend’s face, to see if he or she is hearing the same thing you heard. How thrilling it is when the confirmation arrives; and how easily disappointed one can be (though we all learn to hide it) when the friend turns after a minute or two and says, ‘You can turn it off, this isn’t doing much for me.’

You are trying to get the listener to hear (or see) the same thing as you, to have the same kind of experience.

Identifying problems and identifying solutions

I'm a little stuck on a paper I want to write, and blogging about it often helps. So here's the story:

- in my research methods course, three students became intrigued by the analemma (which they discovered b/c Boise has an analemmatic sundial, so when we were discussing the motion of the sun and they went to see a sundial, that's what they saw). I want to say that this is the right kind of thing to be intrigued by: it should give most undergrad science majors an intellectual itch that needs scratching. The weird things about it: it says our days are not uniform, despite the fact that the earth's rotation is constant (there is slight variaton - but milliseconds - not minutes). It has two "periods" in a year: in one year, noon is earlier than average, later than average, earlier than average, later than average. But there's just a circle and a tilt - what's the two-ness of this?

so story 1, I think, which is consistent with Anna Phillips's work: the students landed on a real problem that begs explanation.


more interesting for me (for this paper) is the next bit: identifying solutions. (I keep thinking about the Agnes Callard piece on aspirational faith! - it's not the same but there is something there...) how do we think we might make progress, particularly when we don't know what the answer will look like? what kind of explanation will "count" as explanation? what steps did students take, and what did they find satisfying? I want to say that the "math" solution that is (mostly) google-able is not satisfying (nor, really, "understandable" to most of us - including me); the modeling-it solution - both physically and computationally - was only moderately more so; the solution I find most useful (there are two "kinds" of days happening in 24 hours - a rotational day and a revolutional day - and these "days" have different "shapes") feels so SATISFYING.


things I wonder: in some ways, this is a cultivated, aesthetic "sense" - it's like developing someone's taste in classical music or in hip hop or cheese :) - but there's also a sense-of-mechanism-ness to it. there's stuff to say about the affordances of representations, too...

Reflections on teaching in a Tibetan Monastery

I’ve been wanting to write a reflection - but the past two weeks have been a blur: we left the monastery, arrived in Mumbai, and then on a string of flights back to Minnesota - and to Richard’s family’s lake house, to a wedding, and then a road trip back to Boise, where I've been teaching and preparing for more teaching. The longer I’m home the more slippery my thoughts.

I also find that the reflections I find myself thinking about the most are more personal than I might have anticipated - which is why they are here and not on the more advertised blog. That is, less about “what it’s like to teach in a Tibetan Buddhist Monastery” and more about “what it was like for me to teach in a Tibetan Buddhist Monastery for two weeks, far from home, with a theoretical physicist.”

I thought I would have a lot to say about what it’s like to teach physics to such a different population, and I do, but what I really found unsettling were the ways in which it was similar. That is, my anticipation of difference felt unhelpful. In trying to imagine their worldview (I read books on Tibetan Buddhism this past semester and tried out some language instruction on YouTube) I had exoticized my students and, in some ways, was afraid to teach. I find humility and empathy important in teaching; fear sounds like it might engender humility and empathy but I don’t think it does. At least not for me. (I can imagine that some colleagues and friends who work in this space - around questions of equity - who have a better sense of the harm that science and science education in the presence of colonialism have done - would say that, no, I should be afraid and even abstain from teaching entirely.) I could write a ton about this, and I’m sure most of it would, to some, reveal my naïveté and not any great insights — but I’ll save that for another post. Or a conversation over coffee. Or beer. 

There are, of course a few things that were striking about the difference. Most of all is the tradition of debate. The consistent - and, yes, cultural, religious - training in debate that supports them in constructing ideas together in richly playful, fun, but sincere (no pulling punches, so to speak) ways. It makes me think that, in our efforts to make curriculum accessible to all students we strip it of the particularly rich, cultural ways in which scientists argue and make meaning (ways that are embedded in western, masculine culture to be sure and definitely not perfect). Which is not to say that there aren’t other ways- this Buddhist tradition is, perhaps, particularly well suited for learning science. But physics is a cultural practice. I run into this a lot as I think about physics.

Also striking was being paired with Ilya as a co-teacher. I have cotaught with Kim (English), Irene (biology), Joe (math), Steve (philosophy), Michele (math ed), Matty (science ed), Lindsey (math ed), Paul (science ed), Stamatis (physics), Rachel (physics), and a host of grad students. But none practicing theorists (though Stamatis has that background; as does my husband). And in my research and teaching I make a lot of claims about what practicing science is like (often as a contrast to school-science); but really what do I know? I know that there are ways in which my approach to physics (even when I was more of a physicist) is pretty idiosyncratic. I think those idiosyncrasies are rooted in my work-arounds (I am not a good programmer; I met limits in my math abilities that I never pushed through) and less about what it really means to do physics - but that may be naive. The partnership particularly pushed on my sense of the role of math, prediction and experiment in physics. (I might not have been particularly humble in my pushing back on his ideas! - there’s a part of me that - even still - thinks perhaps we aren’t a trustworthy eyewitness to our own practices; that he doesn't know what he's actually thinking when he does physics. Aren’t I a bit of an ass?) 

And then there was the way in which the monks approached my information and teaching. It felt different. I'll just sketch quickly a few of those ways. (1) they treated, it seemed, the ideas as things to take into consideration - things they may or may not agree with. they vetted the ideas. found inconsistencies and asked me about them. disagreed. I have a million thoughts about this. (2) they tracked my arguments as my arguments; when Ilya spoke they would question his line of reasoning to him and not to me -- it was not like there was monolithic science ideas, but particular (and perhaps idiosyncratic) arguments. also a lot to say about this. and (3) everyone commented on this: it didn't feel sexist - I didn't feel like they interacted with me differently because I was a woman -- which is weird since they are deliberately isolated from women.

Finally, I thought I would miss my family - especially Kate. A friend who teaches in Dharamsala in the summers and I talked a lot about the decision to leave for two weeks. She said that she finds it’s important to be a kind of role model - that her daughter might know that there are professional lives that are so enriching and rewarding that you could really love going to work every day. In the end I find that this still makes the decision to go or not related to its impact on Kate - and, ultimately, I was delighted to find out that I wanted to be there simply because I wanted to be there. I didn’t have to justify the trip to myself by its impact on her, but simply its impact on me. Had it been really hard on her for me to be away I would have felt sad about that, or guilty even, but not thought “I wish I hadn’t gone.” But it wasn’t hard on her; and it wasn’t hard on me - I am going to seek out opportunities to do this kind of thing (novel, work-related, extensive travel? - I don't know exactly what I mean in trying to replicate this feeling) more often.

My equity lesson and students' questions

We've been using these resources this week in my methods course:
http://stemteachingtools.org/pd/sessiong

Today I wanted to highlight that what we're asking -- hearing and attending to the resources that students bring to class -- isn't easy.

I began by sharing a book Kate (age 4) wrote last week with her babysitter (a professor's son). Making books is something we do together a lot -- Kate loves it. She'll look up pictures online sometimes as she makes her stories and has me draw those. Sometimes she draws the pictures. The words are all hers.

I read them Kate's story (below is one of two books I shared), including the "About the Authors" on back, and asked them, at their tables, to discuss what cultural resources they saw. I was worried they would have a hard time seeing the "invisible" white culture, but they didn't - we kept track of it all on the board: it reads like a typical book: sequentially, with an introduction of characters, a dilemma (will you play tomorrow?) and a resolution. The first page is the cover. We note the authors of the book. The images relate to exactly what's happening in the story (no additional information). She has good penmanship (one dad, in particular, was like, "this is better handwriting than I have..."). She clearly reads stories like this, in books like this, and is reproducing her own. She has access to paper, markers, and staplers and is allowed to use them as she sees fit.



I then asked them to read a story told by Leona - a first grader - as recorded in a classroom near Boston, and - again - at their table they should discuss Leona's cultural resources.

Today, it’s Friday the 13th an’ it’s bad luck day, an’ my grandmother’s birthday is on bad luck day. An’ my mother’s baking’ a cake. An’ I went up my grandmother’s house while my mother’s bakin’ a cake, an’ my mother was bakin’ a cheese cake, my grandmother was bakin’ a whipped cream cup cakes an’ we both went over my mother’s house an’ then my grandmother had made a chocolate cake an’ then we went over my aunt’s house an’ she had make a cake an’ everybody had made a cake for nana — so we came out with six cakes last night. my grandmother snuck out an’ she ate all the cake, an’ we hadda make more an’ we was sleepin’ an’ she went in the room an’ gobbled ‘em up an’ we hadda bake a whole bunch more. she said mmmm she had all chocolate on her face, cream, strawberries. she said mmmm that was good. an’ then an’ then all came out, an’ my grandmother had ate all of it. she said, “what’s this cheese cake doin’ here” – she didn’t like cheese cakes - an’ she told everybody that she didn’t like cheese cakes. an’ we kept makin’ cakes, an’ she kept eatin’ ‘em. an’ we finally got tired of makin’ cakes - an’ so we all ate ‘em.

An’ now, today’s my grandmother’s birthday - an’ a lot o’ people’s makin’ a cake again but my grandmother is going’ t’get her own cake at her bakery. an’ she’s gonna come out with a cake that we didn’t make. cause she likes chocolate cream  - an’ I went t’the bakery with her. an my grandmother ate cup cakes.  an’ an’ she finally got sick on today. an’ she was growling like a dog ‘cause she ate so many cakes. an’ I finally told her that it was - it was Friday the thirteenth bad luck day!

As expected they struggled (for the most part). Resources included: she has a family. [pause] Then: "her story isn't in sentences, it's kind of a run-on sentence." So I asked "is there a structure in her run-on sentence?" One student noted that she starts on Friday the 13th, goes back in time, and ends on Friday the 13th again  - that it's kind of a circle, like Quentin Tarantino films. (We laughed.) He noted that there's also a lot of "cakes" like it's a motif (we unpacked "motif" - "it's like the flame in Lord of the Flies - the flame shows up over and over again, and means something") - "so what does the motif represent, then?" we chatted - no great answers. One student noted the hyperbole - the one (obvious) person of color in my class said "I don't like the word hyperbole. I think that sounds like she's lying or stretching the truth. I think she's just being really funny." We discussed whether or not "lying" even applies to Leona's story - if that judgment makes sense in the context of her story.

Then to debrief, I shared that I grew up in the south. My high school was half black, half white. We began as freshmen with 750 students, and 400 graduated, mostly white. And that Leona's story sounded like stories I had heard growing up and that I found them hard to follow and unfocused and frankly not that smart. And that when I read Jim Gee's analysis I was totally humbled. So then we read Jim Gee's analysis.

She's BRILLIANT, right? It makes Kate's story look so boring! so unimaginative! there's no hidden meaning or representation, no play with time, no patterns that exist over stanzas, no humor.

I asked them to write on a notecard something they wondered about, bothered them, or were puzzled by. Here they are:

- Where can we find resources to learn about our students? I'm worried I'll have a Leona in my class but won't be able to understand her in the way James Gee is able to.

- This makes me wonder how I'll be able to distinguish between a student who is just rambling without much meaning behind it and a student who is actually making sense of something in a way that is unfamiliar to me. What should I be looking for in student work and discussions?

- How does this look for older science students? I know the blue pie/brown pie example. More important, how do I incorporate it. I can't even imagine what it'd look like, so how can I put it into practice?

- I wonder what are good practices and methods to include everyone and yet speed up the process? Should you try to help rephrase to a more western-culture story or move the western culture to a different way to view things, or both?

- I wonder why it's so hard to recognize good story telling just because it's different.

- In a western style education system, how do we make sure all cultural styles can exist? Mostly, how do I make sure I don't fall into this same trap?

- I wonder how as a teacher do we recognize the uniqueness in her story to "praise/recognize her" during the class rather than just pushing her [Leona] aside?

- I wonder now, in hindsight, if I've missed opportunities to understand a student's insight because I didn't take the time to recognize cultural differences.

- I want to hear "jumbled" stories like Leona's and be able to follow along while understanding her purpose. However, this structure is not common in my culture. What should I do to become a better listener?

- It makes we wonder why we put so much emphasis on writing to fit a mold (copying sentence starters) when clearly students can develop and understand more at a deeper level?

- How do these different ways of talking affect students from various cultural backgrounds? With more exposure to different cultures, will students recognize elements of a story better?

- I grew up absolutely everywhere in this country and in others - so often I say the wrong thing. I got so much flack for calling it "pop" instead of soda. So sometimes the cultural barrier isn't a huge one but it's enough to feel insignificant. 

- It makes me want to learn more about different cultures.

- Going throughout the education program,  I have taken note of many things that I know will be a disadvantage to the students I would one day like to teach. There are strategies and techniques we are taught to use that I know will be difficult to use in cultural classrooms - not because the students aren't smart enough, but because they do not have the resources that are required or demanded when using that strategy or technique. I fear that I am requiring my students to assimilate to western ways of learning, but I recognize the society we live in. It is a hard thing to realize and battle.

- There is no distinct one culture in the US. This US is made up of 11 different distinct overarching cultures. [I think they're referring to this.] that will come at problems differently or think differently so you can't think or teach to only dominant culture. 

- English when written is and can be inexact, because much of the meaning is carried with tone/volume, while other languages use exact words to describe exact situations. Why do we not use those in science? i.e., Spanish, German, French [will acknowledge some confusion here from me]

- Isn't it possible Leona was just telling an exaggerated story about cake and we are assigning credit where it isn't necessarily due? I've had experiences where I was given an answer that I believe was really insightful but when I asked them about it, it turned out there wasn't quite the same reasoning going on that I had interpreted and they actually just stumbled into a good answer. [this one is hard for me]

- How do you embrace cultures that you are not familiar with? Even research could be misleading and result in insulting the culture.

I recently looked for  - and found - my creative writing literary magazine from 1986 (4th grade). I was looking for it b/c a friend - Mitzi - has become a famous artist and she has artwork in it :) 

Here are the winners of the magazine's awards: 

Three of the six awards were to the Atkins girls. And for years I thought of myself as a particularly good writer because of these awards. And I went back to read my writing: it's terrible! One student - Azra - wrote a poem about how "sadness tastes like rubber." I wrote "the old clock on the classroom wall/ told its time to one and all." craziness.

pulling teeth

I am WORKING HARD to get students interested in trying to figure out how clocks work.

I feel like someone is doing magic RIGHT  IN FRONT of them -- completely transparently there is magic happening, and no one is at all interested in how the magic trick works.  Isn't that impossible? Don't we want to know? What is going on?