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I'm reposting Michael Fenton's question here, less because I'm interested in you seeing my answers and more because I'm interested in seeing yours. Ignore his five-year qualification. If your motivations for blogging have changed over any stretch of time at all, let us know why.

In 2009, I blogged because:

  • I wanted a record of what I taught and believed about teaching that I could reflect on and laugh at later in my career.
  • I needed a community. I taught in a rural district with five other math teachers (two of them married). Fine educators, but they were in different stages of their career and had answered a lot of questions I was just starting to ask. I needed people.

In 2014, I blog because:

  • I want more interesting questions. In 2009, I was asking questions about worksheet design, PowerPoint slides, and classroom management. By articulating my questions and noticing which of them created vibrant discussions and which of them fell with a thud on the bottom of an empty comments page, over five years I have moved on to some questions that make my work a joy to wake up to every day. eg. What do computers buy us in curriculum design? What does good online professional development look like? What does it mean for students to think like mathematicians and how do we scaffold that development? What is the "real world" anyway and what does it buy us in math class?
  • I need to stay connected to classroom teachers. I'm fast approaching the date where I'll have been out of the classroom for longer than I was in it. Which scares the hell out of me and keeps me asking for advice from real life classroom teachers on this blog and reading, like, five hundred thousand teacher blogs every day.

A readership is more essential to my goals now than it was then. If you guys aren't tuning in and pushing back at my ideas and offering your own, those ideas get a lot dumber. (In 2009, by contrast, I had 120 students to let me know when my ideas were dumb.)

So a lot of what I do in my blogging lately is try to send you signals that I read and value and act on your responses. (See: the recent confabs; featured comments; putting the word out on Twitter that there's an interesting conversation brewing, etc.)

Perfect encapsulation of all of the above: this week's circle-square confab, which featured 62 comments from a pack of great teachers, creative task designers, and math education researchers.

That's why I blog now. Why do you?

Featured Comments

John Stevens:

I started blogging way back in 2012 because I needed a way to reflect. I was in a very, um, rough patch in my teaching career and needed a way to get some thoughts out there. I was reading all kinds of other blogs and seeing what others were doing, stealing material from people left and right. Therefore, my blog was a way to thank people for giving me cool stuff.

Fast forward to 2014 and things have changed. I’m still reading blogs and stealing left and right, but I’m also trying to give back a little. As information kept pouring in, I started to get some ideas of my own. Sure, some of them are awful, but I’m proud of Barbie Zipline and some others. At this point, it’s still a 70/30 take/receive deal, but I’m all for it.

Bree:

I feel like I’m currently struggling to answer this question – which is probably why my blogging rate has been downwards of around once a month these days.

Shelley:

So many of the good teacher moves are invisible, and as I begin to blog I aim to capture some of the techniques that I have used to engage students. I often pass along worksheets and activities for teachers to use, but sometimes what I really want to pass along are the questioning techniques used throughout the lesson, along with a structure to ensure that students are discussing mathematics instead of working in isolation. Blogging allows for this extra commentary.

Michael Pershan:

When I started blogging, I desperately needed to validate my experiences. I was teaching in big ol’ NYC, but at a private school with just one other math teacher. I needed to know: Was my teaching weird? Was I actually figuring things out about teaching, or just headed down my own idiosyncratic path? I wanted to say things that made sense to other people, so that I could be really sure that they made sense to me.

Also:

My blog is for figuring things out, so that someday I’ll be able to help teachers and kids out in a real way.

Chris Hill:

I used to blog because I felt like I was coming up with some innovative lessons and I was learning some new approaches.

Recently I haven’t blogged because I’ve been handicapped into traditional direct instruction lessons (through resources and student culture). Maybe when I’m not in a different school every year (or when I’m excited about the school where I teach) I’ll start blogging again.

Ask And Ye Shall Receive

So this is fun. Last week at 10:50AM I asked the world to make me two websites:

An hour later the world delivered one of them:

Eleven hours later, the world delivered the other one:

I wired up those domain names to the blogs Rebecca and MathCurmudgeon registered and now we're in business. Two more sites for our pile of awesome single-serving sites:

Be a pal. Subscribe and submit ideas.

Nix The Tricks

Nix The Tricks is simultaneously:

  • a free eBook cataloging many of the rhymes, shortcuts, and mnemonics teachers use (I'm looking at you, FOIL) that rob students of a conceptual understanding of mathematics.
  • a labor of love from editor Tina Cardone.
  • a great example of the deep bench of talent we have in Math Twitter Blogosphere.

It was all sourced from math teachers online. It's all free to you.

Good place we have here.

Geoff Krall:

You’ve seen the tasks. You’ve read the research. You’re basically bought in. But how do you begin?

Almost shockingly free of buzzwords, platitudes, soft descriptions, or anything close to moralizing. Bookmark it and send it around.

Related: Geoff Krall Combs The Internet For Lesson Plans So You Don’t Have To

Christopher Danielson:

School geometry seems to me one of the most lifeless topics in all of mathematics.

Paul Lockhart [pdf]:

All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum.

Proof is part of the problem. There's no mathematical practice with a greater difference between how mathematicians practice it and how it's practiced in schools, between how exhilarating it can be and how inert it is in schools, than proof.

Here's Christopher Danielson offering us a way forward:

… eventually we reach a question that sort of requires proof; it seems true, but is non-obvious, and it has arisen from the questions we have been asking about how properties relate to each other.

Then they prove.

Questions that require proof are hard to create, hard to package in a textbook, and probably impossible to crowdsource. You're trying to nail that point where the seemingly-true hasn't yet turned into the obviously-true and that spot varies by the class and the student.

For example, "Square matrices are always invertible" might strike that enticing balance for one student while for another its truth is too obvious-seeming to be worth the effort of a proof and for others it's too foreign for them to have an opinion on its truth one way or the other.

This is tricky, right? And Danielson offers us a description but not a prescription. He describes the satisfying proof process in his classroom but he doesn't prescribe how to make it happen in ours.

Here's one possible prescription:

  • Ask students to produce something given some simple, loose constraints. Draw any rectangle you want and then draw the diagonals. Choose any three consecutive whole numbers and add them up. Draw a triangle with three side lengths that the class chooses. Add up two odd numbers.
  • Publicly display their productions and ask your students what they notice. The diagonals seem like they're the same length. The sums are always multiples of three. Our triangles all look the same. Our sums are all even.
  • Ask students to tell you why that should be true given what we already know.
  • Ask students what other questions we can ask given our newly proven knowledge.

"You people want students to recreate 10,000 years of mathematical knowledge," says the math reform-critic.

No one I respect thinks students should discover all of geometry deductively. But as Harel, et al, say in a paper that has fast become the most meaningful to my current work:

It is useful for individuals to experience intellectual perturbations that are similar to those that resulted in the discovery of new knowledge.

To motivate a proof, students need to experience that "Wait. What?!" moment of perplexity, the moment where the seemingly-true has revealed itself, a perturbing moment experienced by so many mathematicians before them.

That's more useful and more fun than the alternative:

130927_3

The problem here isn't just the coffin-like two-column stricture. The proof doesn't arise from "a question that requires proof" but from a statement that has been assigned. That statement makes no attempt to nail the gray, truthy area Danielson describes. It informs you in advance of its truth. It's obviously true! You just have to say why. Tell me anything more lifeless than that.

BTW: Ben Orlin is great here also.

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