Some days

Here’s something you already knew: Some days are really hard. Some days weigh heavy on your shoulders as you leave your classroom, feeling defeated. If I’m honest, some days feel like this*:

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What’s your point, Ilona?

I’m not sure. I guess I just needed to look at those emotions square in the face. Tomorrow, I will try again, hopefully a little wiser. And the next day. And the day after that.

 

*(Sam assured us that he feels much better now.)

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How to sabotage your classroom culture in 5 seconds

“What you do speaks so loud that I cannot hear what you say.” ― Ralph Waldo Emerson

Since the first day of school, I’ve been working hard to try to establish a classroom culture where students feel comfortable taking risks, asking questions, sharing and building on each others’ fully-formed and partial ideas, and acknowledging and correcting their mistakes; where all students feel that their contributions and questions are valuable and worthy of consideration. I have tried to do so by pointing out (less often than I should) when a student or a group is exemplifying one of these norms, by waiting (again, less often than I should) after questions and contributions to give more students the time they need formulate and share their ideas, by giving tasks that are accessible to a wide range of students and can be tackled with a variety of strategies, by eliciting and celebrating different solution paths, by highlighting different kinds of mathematical smartness (h/t Ilana Horn)…

And then, I proceeded to potentially sabotage it all with an inexcusable split-second decision. Continue reading “How to sabotage your classroom culture in 5 seconds”

“When I see the word ‘mathematics’…”

In our division, classes on the first day of school are only 15 minutes long. By the time students settle in and introductions are made, there is hardly enough time to wrestle and play with an interesting math problem. I saved that for the second day. Instead of going through the syllabus, however, I gave the time over to my students to reflect on the following questions:

  • When I see the word ‘mathematics,’ I think of…
  • A good experience with mathematics was when…
  • A bad experience with mathematics was when…
  • This semester, I expect to…

(The students completed the prompts in their new math journals, which I will hopefully get a chance to write about once the routine is more firmly established.) Continue reading ““When I see the word ‘mathematics’…””

The sub trick that kills (On engagement)

I’ve been substitute teaching for about a month now, which has been a roller-coaster ride (the fun kind). On a few of those days, I was left a lesson or activity to facilitate, but most days I’m not so lucky. Understandably, most teachers prefer to leave substitutes with a work period (alright, let’s call it what it is – glorified babysitting). However, I really enjoy engaging with students, especially when math is involved, and so I usually can’t resist showing the students a mathematical “magic” trick that I leave as a challenge for them to figure out during the period. I now have a small collection of tried and true “tricks” that I like to pull out at the beginning of class, but there’s one in particular that kills every. single. time, no matter the age group (although it will likely need to be adapted for grades below 6; I haven’t tried it). Continue reading “The sub trick that kills (On engagement)”

Card Auction (Introducing dependence)

Last month, Nat Banting described a fantastic task on his website called the Dice Auction. You should really just read the original post, but I will summarize it as best as I can here.

Cfh3p4sUsAEk2Wj.jpg_largeThe premise is that you are invited to an auction, and given a budget of $10 [I changed the budget to $15 for my students to encourage a bit more risk taking]. Everyone at the auction has the same budget. The participants are all bidding on certain events that may occur when two 6-sided dice are rolled (e.g., both numbers are greater or equal to 5; a single 2 is rolled; both numbers are odd; etc.). After all the events have been auctioned off to the highest bidders, the two dice are rolled 20 times. Each time the event that you purchased occurs, you collect a prize. Bidding always begins at $1 and goes up in increments of $1. You cannot bid against yourself. The order of the events up for auction is known beforehand. If you choose not to spend (some, or all of) your money, the auctioneer will sell you prizes at a cost of $2 per prize after the bidding has ended. Your task is to get as many prizes as possible.
Continue reading “Card Auction (Introducing dependence)”

What Hacker got right

I won’t lie: The release of Hacker’s new book, The Math Myth (And Other STEM Delusions), struck a sensitive nerve. I read and listened to Hacker’s interviews with a vengeance, and then I tweeted about them with (somewhat restrained) fury:

Continue reading “What Hacker got right”

Against complacency (What have we learned, and where do we need to go from here?)

"If someone says it’s simple, they’re selling you something." - Dan Meyer
“If someone says it’s simple, they’re selling you something.” – Dan Meyer

Last week, Dan Meyer wrote a brief reflection on Ed Beagle’s First and Second Laws of Mathematics Education:

  1. The validity of an idea about mathematics education and the plausibility of that idea are uncorrelated.
  2. Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.

The second law particularly resonated with me, a soon-to-be teacher. The more I learn about mathematics education, the more I realize that there is still so much to learn, and that anyone who says it’s simple is selling you something (Dan Meyer). My to-read list is growing longer and longer, even as I realize more and more fully that what matters most is not what I read, but what I do at the ground level with my students. (Side note: Last week I also began my foray into John Mason’s work – thanks, Danny Brown.)

Continue reading “Against complacency (What have we learned, and where do we need to go from here?)”

“MY numbers!” (On the ownership of knowledge)

The other day, I presented some students with the following game:

Last cookie is a game for two players. In this game, a number of cookies are divided between two cookie jars, and each jar has at least one cookie. Each player can take cookie in one of two ways:

  1. By taking any number they like from just one jar or
  2. By taking the same amount from both jar.

The winner is the person who takes the last cookie(s).

Some of you may recognize this as Wythoff’s game; on the NRICH website, which has a great online version of the game, it’s called Last Biscuit (I modified the name for a Canadian audience). If you aren’t familiar with the problem, I highly encourage you to give it a go – very easy to understand and play, but the optimal strategy is not particularly obvious.

I assigned this game as homeplay (get it?? because it’s a game… terrible, I know). Then, the other day, we picked it up again after about a week of rumination.

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Continue reading ““MY numbers!” (On the ownership of knowledge)”

My math elevator pitch

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Last week, some incredibly talented students at our high school put on an evening of one-act plays. I was particularly excited to see A Charlie Brown Christmas,  and I was not disappointed – I was so impressed by how well the kids brought the classic cartoon to life. However, the play that really gave me some food for thought that night was A Straight Skinny: a story about a high school algebra class that had been caught cheating on a midterm exam.

Continue reading “My math elevator pitch”

On McNugget math (and being less helpful)

Another great Pi Club (still a working title) meeting.

Today, we worked on the McNugget problem (a case of the Frobenius/coin problem), which goes something like this:

Chicken McNuggets come in packages of 6, 9, and 20. Assuming money is not a factor and that you can only buy full packages, what is the largest number of Chicken McNuggets that you cannot buy?

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(Of course, I brought McNuggets for the occasion. You know, as manipulatives…)

Continue reading “On McNugget math (and being less helpful)”