The kids are alright

Quelle est une chose qui devrait être interdite à l’école ?

I often start French class with a question. The students reflect and discuss in their table groups, then share their responses with the rest of the class during the whole-group discussion. Yesterday, I opened with the above. In English: “What is one thing that should be banned at school?”

“Littering!” “Homework!” “Vaping in the bathrooms!”, a few students volunteered (in French). Then, a student offered, “Cell phones!” I’m sure you can imagine the disbelief and anger that this response evoked from a class of Grade 9 students, the majority of whom have an iPhone permanently glued into their hand and probably could not imagine a time without them. Once the others died down, I gave the student the floor, who argued with sincerity: “Cell phones are a huge distraction. We’re paid to be here by tax payers, which means we have a responsibility to learn and not waste time on our phones.” Once again, the other students erupted. It took a minute to calm them down.

Finally, a student responded bitterly: “If we’re paid to be here, where’s my money?”

I knew at that moment that French class, strictly speaking, was over. This was going to be something different, and I liked where we were going. Continue reading “The kids are alright”

The absence of number

One of my favorite conversations to have with my students (Grades 9-11) has quickly become centered around the concept of zero.

It first arose naturally last semester, when a Grade 9 student blurted out: “But 0’s not a number, it’s the absence of number!” (I’ve forgotten the context of this remark.) I remember a few other students laughing at this, and I know that this was unfortunately a negative formative experience for her, because she wrote about it in her end-of-year reflection. And yet, when I prodded further at a later point in time, I found that many other students, if not most, held the same belief. We had a whole-group conversation about it, talked about how 0 behaves in a similar way as other numbers in many ways (you can add it, subtract it, multiply it…), but still, I think a lot of students held on to this conception. This was especially clear when the students were solving equations and came to a problem such as this: Continue reading “The absence of number”

On linear patterns and drifting problems

Exactly where [a lesson] moves depends on such complex factors as the structures of those present, the context, and what has been anticipated. It may move toward more formulated understandings, if such formulation is relevant to the play space or if it becomes part of a further exploration. It may simply move to other sorts of activities. This, of course, is not to say that we should just allow whatever might happen to happen, thus abandoning our responsibilities as teachers. Rather, it is to say that we cannot make others think the way we think or know what we know, but we can create those openings where we can interactively and jointly move toward deeper understandings of a shared situation.

(Davis, 1996, p. 238-39)

My Grade 9 students are currently working on recognizing, analyzing, graphing, and solving problems involving linear relations. Linear relations lend themselves so naturally to describing patterns à la www.visualpatterns.org, and this is precisely how we got our toes wet in the topic: For several days, my students had been analyzing, extending, and (productively) arguing about a variety of linear and non-linear patterns. The intention of these first few lessons was to have students develop (or, in some cases, refine) an understanding of constant and non-constant change and to connect patterns in pictures to patterns in tables of values.

As the students began to connect ideas, I looked to develop an activity that gave students an opportunity to apply the generalizations emerging from the phenomena that we were playing with. Continue reading “On linear patterns and drifting problems”

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*:

Screen Shot 2016-09-12 at 7.49.09 PM.png

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.)

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?)”