Paul Salomon’s “imbalance problems”. You know how I love a thought-provoking picture.
Sh*t I F*cking Love (Wherein I Am Moved to Profanity by Enthusiasm) Friday, Apr 5 2013
Some Miscellaneous Awesomeness Wednesday, Jul 18 2012
Just some awesome stuff I feel like pointing out:
Vi Hart does it again. That young woman has created a new art form.
Terry Tao’s airport puzzle. If you have to get from one end of the airport to the other to catch a plane, but you really need to stop for a minute to tie your shoe, is it best to do it while you’re on the moving walkway or not? (I learned this problem from Tim Gowers’ blog.)
Paul Salomon quotes Vi Hart quoting Edmund Snow Carpenter, and the quote is absolutely worth me quoting yet again:
The trouble with knowing what to say and saying it clearly and fully, is that clear speaking is generally obsolete thinking. Clear statement is like an art object: it is the afterlife of the process which called it into being.
Dan Goldner is doing my job for me. The original purpose of this blog was to read writing about math education, and to summarize and discuss it. I don’t do this very much any more (although expect summaries of a couple articles from the current JRME in the next few
weeks months), but I do have a long list of things I wanted to read and discuss here but figured I’d probably never get to. On this list was the 1938 NCTM Yearbook, The Nature of Proof, by Harold Fawcett. But I’m taking it off; Dan’s got it covered.
Another One to Keep Your Eye On: Anna Weltman Saturday, Jun 23 2012
Here’s another blog to keep an eye on:
Recipes for Pi, by Anna Weltman.
I know Anna IRL. In fact, both of us have seen the other one teach. Thus prior to discovering her blog I already knew her as mathematically thought-provoking, endlessly creative, and deeply tuned in to student experience, not to mention a total sweetheart.
So I was excited to learn that she had started blogging in February, and her writing hasn’t disappointed. It’s sporadic, but who am I to complain about that, and more importantly it’s characterized by that same deep thinking about math and student experience that marks her teaching. Check it out.
Justin Lanier Thursday, Apr 26 2012
P.s. Japheth Wood Is My Dude Friday, Mar 2 2012
Never Be Wobbly Friday, Sep 16 2011
Having learning as a full-time job is really, really delicious. But tonight when I stopped mathing and engaged the edublogosphere it felt like a relief to read about classrooms, populated by humans. (To my fellow humans: I love the differentiable manifolds but I love you more.) Thanks Jesse Johnson, Dan Goldner, and Kate No Wackness for your continuing dedication to learning (your kids’, yours and ours).
This is my favorite thing ever.
The particular thought that was driving me crazy at least from 7pm to 10pm, not that you care, was: if is any surjective continuous function between topological spaces that maps open sets to open sets, then I can prove that the inverse image of a compact set is compact. I studied a converse if and happen to be smooth manifolds and happens to be an injective immersion. But these are very very strong assumptions. How much can they be weakened?
Kate, this is A’s name for you. (An homage to your no bullsh*t approach.)
Dan Goldner Thursday, Mar 31 2011
This is a shout out.
Dan Goldner came on my screen last summer during Riley’s soft skills conference. My impression was that he was a bright-eyed bushy-tailed newbie (just off the student teaching year) with a surprising amount of classroom insight considering this.
At the end of the summer I met him IRL in a miscellaneously awesome context and have been following his blog Work in Pencil since then. In the fall of his first full-time year in the classroom, he didn’t produce a lot of content. (No surprise.) 2 posts in the early fall, 2 right before Christmas, then nothing for months. (I guess I’m not one to talk.)
But now he’s back, and I feel that my initial impression last summer, while quite positive, was actually an underestimate. I didn’t anticipate all this maturity. I want to let you read for yourself, so I’m going to minimize the endorsement verbiage. I will say this: disconcerting forthrightness and vulnerability combined with some real writing craft. Keep your eye on this one.
The Math Wizard Tuesday, Sep 21 2010
Okay, one more shout out.
My colleague Japheth Wood (News from the Math Wizard), with whom I’m delighted to be co-teaching a class for preservice teachers, is an awesome problem composer. He’s also been dipping into the sea of math and math ed blogging, one toe at a time. He’s finally got one whole foot in:
In particular, check out that image.
Don’t move past it to the text (mine or Japheth’s) until you’ve sat with it long enough to absorb everything. If you find yourself with a mathematical question, don’t move on till you’ve tried to answer it.
Seriously; stop reading and go look.
There’s a lot of difference, pedagogically and content-wise, between this image and Dan’s boat-in-the-river video but there’s something very important and very exciting in common. Both manage to ask a very specific and mathematically rich question without whispering a single word. I think the natural current could be strengthened a bit by putting little venus flytraps on top of the square numbers, but that’s the only improvement I can think of.
So, questions for you:
a) What question, if any, does that image leave you with? (Am I right that there is a natural question you can’t help but have once you’ve absorbed the image?)
b) What are the features of the image that lead to the question? Given a mathematical question, how do we go about turning it into a wordless image that asks it?
Japheth and I passed out slips of paper to our class of preservice math teachers a week ago. On the slips were either Japheth’s original image, or tieandjeans’ modification. We asked them to write down a mathematical question that the paper provoked, and then try to answer it. We didn’t give them a ton of time. (Less than 10 min.) Interestingly, while I thought the sense of danger in the modification would make the gravitational pull toward our intended question (will the grasshopper manage to avoid all the squares?) greater, our students’ knowledge of Super Mario Bros was a distraction, because the up/down motion of the plants, and the question of Mario’s specific trajectory, became relevant considerations. (You can see below that one group, perhaps reading what we were going for, explicitly ruled out those considerations.) So I think the students that got the original grasshopper image actually gravitated toward the intended question more predictably. I still think the sense of danger would help, but maybe we just keep the grasshopper and add venus flytraps that appear static and aren’t close to the trajectory?
Anyway, here’s what they came up with. As you can see, for all of the above, the natural current is still pretty strong.
Grasshopper / Mario Problems
If the placement of fly traps continues, and Mario times his jumps so the trajectory never hits the plant, will he ever land on a fly trap and die?
Does Jiminy land on a box?
When does Mario’s jump not clear the venus fly trap?
Will the grasshopper land on one of the empty boxes (perfect squares)?
Hopping by 4. What is the mathematical formula to determine where Mario lands?
Mario will never land on a perfect square.
How many times will the grasshopper land between consecutive perfect squares?
For # between , , if odd then , if even then .
Will he ever land on a perfect square?
Can the grasshopper keep jumping without hitting the black box? If no, then when will he hit the black box?
Grey boxes increase by +4
Black boxes increase by consecutive odd #s, +3, +5, +7, +9
Do you notice a pattern between the grey boxes? How about the black? Can you predict what # Mario will land on next?
The next plant will appear at 36. Mario will land at 26, then 30.
When will Mario land on a flower (perfect square)?
Will Mario die and when?
When will Mario land on a plant?
Can he change the size of his jumps and still ensure he will not land on a plant?
Will the grasshopper ever land on a black square?
Can (4n-2) be a perfect square?
Will the grasshopper land on a boxed number (i.e. a perfect square)?
Sum of squares must be a multiple of 4 or odd.
(Ed. note: they’re misquoting a result they found the previous week. The result was about the difference of squares.)
Kate Nowak Is Such a MF Bad*ss and Other Stories Friday, Sep 17 2010
And writing about it, which, because it’s Kate, means she’s writing about what makes it hard, which means she’s putting into words the core of maybe the biggest obstacle I can see to the improvement of math education in this country.
I haven’t used the Regents exam as a threat, not one time. I casually mentioned it on day 1. I’m doing my best to ignore it.
Problems like Solve: x + |2x – 4| = 4x – 8 just piss me off to an alarming degree. Only if you tell me what x represents and what relationship those expressions describe and why you think they are equivalent, NYSED. Then maybe I’ll solve your equation, but right now I think it’s too uninteresting.
Nothing about what I just wrote does not provoke anxiety.
And then she’s tying her thoughts together with a nautical metaphor?
Oh right. She used to be in the navy.
* * * * *
I am working on the Talent Lie series but I don’t think I’ll have anything up for a good long while. I’m teaching two courses for teachers this fall, one for inservice folks and one for preservice folks, and I foresee a need to actively reflect on those courses, so if you hear anything from me in the next month it’ll probably be about that.