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in which I recommend classroom origami September 16, 2013

Posted by Ashli in Math Art, Teaching Thoughts.
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My old classroom held relics from the students I taught each year. The day before winter break was one that I always took to talk about origami, show some clips from an awesome documentary, and teach the kids a few basic things. Recently on twitter some folding pictures happened which spawned me to fold which lead to classroom origami talk. I’ve shared this a bit before over at Global Math, but thought I would document a bit here.

PHiZZ 105 torus

Exhibit A

Every piece in this was done by a student of mine. Not all the kiddos signed their pieces, but many did. There are 5 of these in my old classroom–one for every year I taught at the school except for the first one due to a storm canceling school the day before winter break (I know, right?). I did, however, put it together. I’ve found few kids have the manual dexterity + patience needed to assemble a large one of these so I do that myself over the break. Here’s what it looked like before I started:

box of PHiZZ pieces

box of PHiZZ pieces

If this project looks huge (100+ pieces?!), never fear. Part of the beauty of the PHiZZ model is that there are various sizes you can make with the same module. Kiddos who get into origami often like to start with the 12-unit (cube!). You can also do 30-unit or 90-unit versions. And yes, you can go higher then those.

where to learn
I learned how to make the PHiZZ Units from this website back in college. Now we have the benefit of Tom Hull himself instructing how to make the unit in a youtube video.  I don’t show videos on how to fold in class since I like to go at the pace the class needs (and the pace a precalc class needs is much different than the pace of an algebra 1 class) and use the document camera. Now, the above torus is a variation on the typical balls people make.

Many of the books I have are well out of print and inherited from my grandmother who taught me how to fold when I was very young. I mostly do modular origami and I like pretty much anything by Tomoko Fuse. There are lots of rubbish websites, but OrigamiUSA has some free patterns and links to local origami organizations.

One of my favorite things about the PHiZZ model beyond the lovely creation at the end is that you can use paper from Staples Memo Cubes to make them. I actually don’t like PHiZZ models made with origami paper as most origami paper is either too slick, to thin, or both. Good washi paper would work, but it’s not worth the cost. I would typically purchase 2-3 of these cubes at the start of the school year and use them to teach some basic origami as well as using them for student reminders (they are bright).

other thoughts
As i was working on this last night30 pieces

I started wondering how do you teach this type of patience? In college I thought nothing of spending the 2-3 hours focus and make a 90 piece PHiZZ model. I find the process completely absorbing and satisfying in the way working a big math problem and coming up with an elegant solution is. How much of the origami side of my nature has influenced the math? How much more accepting am I that good things (beautiful things!) take patience, trial-and-error, puzzling over directions (sometimes in Japanese, which I do not read even a little bit), struggling and putting them down for a breather lest I rip them in half so I can come back later with fresh eyes.

More importantly, how much can teaching students origami help them build up those traits? Listening carefully. Immediate feedback. Attend to precision.

Start with the figures that only take a dozen folds. Do the ones that move or jump because those are so satisfying. Then do harder ones. Make origami a warm up one day a week. Smile with thanks at the kids leaning over to help their neighbors. Congratulate the ones that struggled last week but get this weeks’ figure. Encourage the ones growling in frustration to keep trying and slip them an extra sheet before they leave in case they want to try again later on their own without peer eyes on them.

Tonight I’ll be working on this module pattern. Happy folding :]

in which I plot in origami with friends #TMC13 July 23, 2013

Posted by Ashli in Math Art.
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Hey all! Heading to TMC13? Like art? How about origami? Have some time on the plane/train to do some folding? Awesome. Let’s begin!

The Inspiration: Madamoiselle Maurice and an image to honor our hosts

Colors: blues and yellows (Drexel colors–don’t stress about the shade as some variety will be nice). Shoot for a 4:1 ratio of blue to yellow.

Figures: Birds (in blue, because it’s Twitter Math Camp) and pinwheels (in yellow)

Sizes: Try to keep the paper under 7″. Like shade variations, size variations will also be cool.

I’ll be working with some inside sources to find a good spot for the final project. The goal here is a group art project that’s mathy, a homage to our hosts and something to visually capture what I feel is one of the themes of the Mathtwitterblogosphere: that together we create an awesome, giving community.

Q & A:

But, Ashli, I really love to make this other type of bird. Could I fold those blue birds instead of the design you suggest?
Of course. Like cranes? Fold cranes. Just keep in mind that you want a design that lays relatively flat to make it easy to affix to the wall.

What about butterflies? can I make blue butterflies?
Just make sure it has wings, people. We need some cohesion with this design.

Can the yellow ones be other shapes? Like hats or little tshirts?
If the power of Gauss compels you, then you go for it. But try to stick to un-organic things for the yellow.

I don’t have any paper, but I’d be into folding when I arrive at TMC13. Will there be any paper I can use there?
Currently working on acquiring some to have in stacks for people who want to help out with this. I’ll also have some boxes to put finished projects in. If anyone has spare paper and wants to bring it along, that would also be cool.
[Update: Thanks to a speedy Amazon order, a bunch of 6" origami paper is getting delivered to The Math Forum offices on Wednesday, July 24th. I'll have it out somewhere obvious during the opener so you can grab some and fold while you listen.]

Is this something that I’ll be able to take an epic nerd-photo in front of?
Yes, yes it is. Not that I would ever get 100+ people to fold paper in order to assemble an epic backdrop for math-nerd photos *cough*

Thanks for reading! Super excited to meet you all at TMC13!

in which I watch too many Ignite talks June 8, 2013

Posted by Ashli in General, Prof. Development.
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Though I wonder if that’s actually possible.

This post is more me curating Ignite talks for future reference than anything. If you have a 5 minute chunk of time and want to watch something mathy/educationy/awesome, click one of the links below, arranged in no particular order:

Avery Pickford, CMC-North, A Humble Proof (if there’s room in the margins)

Max Ray, NCSM 2013, Tweet Me, Maybe?

Annie Fetter, NCSM 2013, Hidden Decision-Making in the Math Classroom (Everybody’s doing it. Why shouldn’t you?)

Eleanor Terry, NCSM 2013, Increasing Our Confidence (Intervals)

Karim Kai Ani, NCSM 2013, Mathalicious: Real-World Math

Patrick Callahan, NCSM, A Modest Proposal

Bill McCallum, NCSM 2011, A Tale of Two Triangles

Dan Meyer, CMC-South 2011, When Will I Ever Use This In Real Life


This is by no means a complete list, so please post in the comments below some of your favorites!

in which I relearn some things about function notation March 17, 2013

Posted by Ashli in General, Mathematics.
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I can get lazy with my language around mathematics. I try not to, but I know it slips through.

My personal biggest challenge in this regard is statistics. Stats demands precision, and I’m just not there with it yet. It’s a work in progress. If I am every talking about you with stats and I say something ridiculous, please feel free to correct me. I will appreciate it.

Beyond stats, function notation is one of those things that I know a lot of people are very casual about. I see teachers and students (and I know I’ve done it when talking) swapping between f and f(x) as though they are the same thing. To help with clarity, and the seed that made this post happen, here is a nice discussion about function notation that I am blogging about so I have it easily in reach and I thought some of you would also find interesting.


Oh, and there’s that Podcast thing that is now up. There will be a new one up this Thursday, 3/21 that’s a shorter format focused on a prompt, what to do about GReader, and other news of the online math world.

in which I cross-post about the podcast March 8, 2013

Posted by Ashli in Teaching Thoughts.
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For all interested parties, I am starting a podcast called Infinite Tangents. The focus of the podcast will be teachers stories, specifically those around the mathematics classroom.

To listen to Episode 0: An Introduction and learn more about the podcast, click here. Thanks, and please share!

In which I read research articles with interesting contrasts January 14, 2013

Posted by Ashli in Teaching Thoughts, VAM.
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Since acronyms seem to be a part of any profession, we have the delight of two MET’s in math education. One is the Mathematical Education of Teachers, which just came out with their second version that I am working my way through. The other is the Measures of Effective Teaching project that the Gates Foundation has been putting on the past three years. Today is about the latter.

You can go and read the whole thing here. If you skip to page 20 you can read their “What We Know” conclusions from the 3 year study. I like a lot of what the report has to say about how to use classroom observation, rigorously training observers, taking a balanced approach, etc. I have a hard time with a standardized test being the end-all measurement and I don’t trust student surveys for an accurate portrayal of a teacher’s abilities.

Interestingly, right after finishing the Gates report I was given a link to this abstract from a paper issued in December of 2012 by C. Kirabo Jackson:

I present a model where students have cognitive and non-cognitive ability and a teacher’s effect on long-run outcomes is a combination of her effect on both ability types. Conditional on cognitive scores, an underlying noncognitive factor associated with student absences, suspensions, grades, and grade progression, is strongly correlated with long-run educational attainment, arrests, and earnings in survey data. In administrative data teachers have meaningful causal effects on both test-scores and this non-cognitive factor. Calculations indicate that teacher effects based on test scores alone fail to identify many excellent teachers, and may greatly understate the importance of teachers on adult outcomes.

I am interested in the idea of a teacher’s outcome on “non-cognitive ability”. How do you measure a teacher’s ability to help kids throw off the fear they all seem to exist in during adolescence as they work to figure out who they are and who they want to be? I don’t think a standardized test measures that well and there is something powerful about realizing you have the respect of an adult who is not your relative and who shows passion for life.


[UPDATE 01/17/2013]

Two new articles have come out that chime in about the statistics (or lack thereof) in the Gates Foundation article. Good reads. And if you teach stats they are rather applicable.

The 50 Million Dollar Lie, by Gary Rubinstein

Gates Foundation Wastes More Money Pushing VAM, by Gene V. Glass

in which I hear from a former student December 10, 2012

Posted by Ashli in Reflection, Teaching Philosophy, Teaching Thoughts.
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Like many teachers, I occasionally get notes or drop-ins from former students. And I don’t care how old they are; they will always be my kids. With the advent of the Facebooks, I have several that I occasionally hear from after they’ve graduated. I especially like the ones that apologize to me for not taking more math in college. Kinda adorable.

Last night I got a missive from one of my darlings worried about her math final. If she doesn’t pass it, she’ll fail the class. This is her first semester in college. The note was short, and she ended it with

Why am I so bad at the maths?! D:

I wrote back the following:

For me, maths was more about accepting a different way of thinking than anything else and that can be the hard part. We’re not brought up in a logic-based society. So much of high school math is focused on procedural thinking–if A, then do B & C, and ta-da! And that’s not really math. That’s more like advanced baking. Useful, to be sure, but not a way of thinking. Since I don’t use those types of problems as my main push in classes it’s also why the typical A-maths kids don’t like me for a few months–they’ve never really had to think for understanding before.

And that right there is the key. Maths makes sense. It’s the Queen of Science for a reason. If you think what you are doing in math does not make sense or is magical, than we need to figure out a different way for you to think about it. Luckily, there are a lot of ways to think about maths that are successful. Unluckily, finding the way that works for your brain can be grueling.
I got through high school using procedural skill (the If A, then do B stuff). I hit a brick wall in my first maths class in college because it didn’t work with that professor. I had to show him how I was making sense of the maths and since I wasn’t really making any sense I didn’t have anything to give him. There were a lot of nights spent in the math study room and I didn’t really get the thinking needed to understand, but I was moving that way. Slowly.
Sophomore year was when it was finally clicking that I needed to build my own understanding so I could stop playing the memorization game (it wasn’t possible to pass some of my classes via pure-memorization as no ones memory is that good. And I was taking Latin at the time so my memory banks were full up with vocabulary).
So yeah, maths is hard if you’re taking the memorize ever permutation of a problem and how to solve it route. Figuring out the patterns behind the maths is a challenge, but it pays a lot of dividends. If you ever want to chat about your stuff, just let me know. I have skype and I use google hangouts quite a bit for my work. Just remember: I am 3 hours ahead of you :)

What I did in class wasn’t enough to get her to where she needed to be to be successful in college maths. I still focus too much on the procedural at times, but every year I moved more and more away from that as I built up skills toward a teaching style I never saw in high school maths. I’m curious to see how much my classroom skills will atrophe while I am out of one or if the level of ed-research, blogs, and consulting work I do will help me hold steady. One can only hope.

I miss my kids.

in which I send you to a research survey October 29, 2012

Posted by Ashli in Uncategorized.
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If you follow me on the twitters, they you have already seen this link. At NCTM Hartford (which I’ll be blogging about, just not when my power may fail at any moment), I got to meet a delightful Math Ed doctoral student who is taking a look at Math modeling. If you have some time and could fill out her survey, it would be much appreciated. Support the community!

To take this survey, you need to be in the US and a 7-12th grade math teacher.

click here to go to the survey.

Thanks for your support in this. As a consumer of math ed research, I feel I should try to give back to it whenever I can.

in which i give a talk on the profession of teaching October 19, 2012

Posted by Ashli in Prof. Development, Teaching Philosophy.

IM&E hosted a thing at Berkeley October 12-14. I was working with middle grades folks and asked to give the final plenary talk entitled ‘Call to Action’. I chose to talk about the profession of teaching and how I think we get more teachers engaging with teaching as professionals. I’ve tried to type up what I said in the talk based on my copious notes, powerpoint, and memory below the cut. I know it’s not exact and I suspect my memory is editing to make me sound better, but I don’t have a video recording (thank Gauss) so it will have to do. I’ll warn you it’s longish, but I would love to hear your thoughts on professionalize and education in the comments.

Oh, and this is the tweet that spurred much of my ideas for the talk. Or rather, had me re-writing much of my ideas for the talk.


in which 3d graphing is explored September 28, 2012

Posted by Ashli in Math Art, Precalculus.
While I’m not sure about all school districts, in mine there is this awkward time after the seniors have graduated but before the rest of the school gets out. In classes where all the kiddos are in the same grade, this isn’t a problem. I have never taught a math class where every kid was in the same grade. Since I taught some (technically) 4th year classes, however, I do my finals during the ‘senior’ finals time and that leaves me a week or so with the students who remain. Typically I like to spend time covering a special topic.  I chose to explore 3d graphing and had them make these in 2011:
y = sin(x)*cos(z)
And this in 2012:

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