Integrating Sound with Math

Time to rethink my integration of science with math. My attempts to connect proportions of the human body with measurement went down in flames in my entry last year, so I’m focusing on Systems, Order, and Organization related to sound this time.

I know sound, math, and science are all suuuuuuper tight. What I don’t know is how to adequately organize my sound unit so it includes great inquiry-based investigations. My guiding framework is an annnnncient curriculum from the National Science Resources Center (published when I was in junior high) that has such profound extension activities as the one featured below:

Ugh. Not helpful. It’s worth noting that there are a whopping two math extension activities in this entire unit.

The wise and enthusiastic Katie Weichert gave me some great ideas to chew on and think about. I wish I saw her more often. But in her absence, I had to get a move on.

So I started trolling the Internet.

This Aztec music lesson seems compelling.

I’m also interested in harmonics, but I don’t know how to build this into a full lesson. My students already use harmonic series as a procedure to line up from music class, so I wouldn’t need to go over the basic musical idea of third and fifth intervals.

THIS could be useful. It appears to be a sound generator. Could I have kids compose a song using fractions and then convert them to their frequencies? Speaking of composing music…

I imagine I could show snippets from Donald in Mathmagic Land and have students generate questions from that? Yesssssss, I could totally do that… That way the learning would be authentic and related to the curriculum we already have in place!

My only concern remains starting with a video. I want to make sure I’m looking for an introduction that inspires perplexity, not just engagement. After the 27-minute video was released in 1959, Walt Disney admitted:

“The cartoon is a good medium to stimulate interest. We have recently explained mathematics in a film and in that way excited public interest in this very important subject.”

(emphasis is my own) Now in looking at moving from merely interest to investigation…… I suppose that recording student questions will take care of that fear, right? Then having their questions shape the following lessons?

Hmmmmm. Of course, there are a wealth of videos available on sound and math, but much of the information is so complex that I can’t figure out how to simplify it.



I’m also interested in looking at the materials used in instrument strings and the number of strings included in different instruments. How do the number of notes an instrument is capable of producing related to its system? Can systems be different sizes? Is a larger system necessarily “better” or more “complete?”

Anyway. Let’s see how this goes.

Rigorous Math Every Day

The open-ended math from the Wall Street Journal a week or so ago was pretty rad. But lessons like those are admittedly woefully rare in my classroom. It’s a huge shame, right? Learning like that shouldn’t just be a once-a-month or even (eep) once-a-semester event.

So I started pondering why doesn’t math look like this in our classroom every day. I needed to keep myself real. Here’s what I came up with:

I’ve purposely chosen those phrases because I think we teachers sometimes use them as ultra-self-deprecating or unproductive language and the conversation just stops there. But I want to explain why these really are often valid concerns (or at least, valid-feeling concerns) and then focus on how I’m personally working to move past them.

Perhaps you’ve already heard me rail against people who say “I’m just not a math person” and seen me express frustration that the idea “math is sooo hard” is a bunch of bunk. That said, I’m still thoroughly unconfident in my own math abilities. I was mortified when I transposed two numbers in our soccer math. I freaked out when Mr. Brown informed me I HAVE BEEN DOING ORDER OF OPERATIONS TOTALLY WRONG. So it’s fair to say that when I deviate from our district frameworks, it’s a little stressful.

I’m moving past this excuse by being willing to really lean on my secondary-level colleagues. I love collaborating, but I don’t particularly love admitting that I need help. So this is a huge area of growth for me. Also, taking the leap to put detailed lessons online has given me a chance for feedback from folks from across the nation, like from my favorite ladies in the Midwest.

I was euphoric when our class completed its project last week. I was also exhausted. I can get sucked into manic cycles really easily. Although spinning my way into a cycle can be absolutely exhilarating. I need to be honest with my body and realize that it’s not healthy for extended periods of time.

“The management is hard.” That’s what people tell me when I share our latest project. I agree, but not in the way they intended. Teachers often mean, “I’m going to have children stringing stuffed monkeys from the room if I open the lesson to exploration.” I share with my kids the explanation from Twyla Tharp’s book The Creative Habit that in order for creativity to take place, it happens within a system of order. A dance studio is essentially a bare floor and mirrors. An artist can’t create a masterpiece if she can’t dig out the right paints in her chaotic mess. And we can’t have deep, meaningful conversations about math in our lives if we’re not already solid in our class expectations.

So, the management I’m talking about isn’t the student-secretly-reading-under-the-table-instead-of-doing-math business. And it’s not because issues like that don’t exist in our classroom — the aforementioned situation actually happened last week and was dealt with swiftly. I’m talking about the mental gymnastics I put myself through as I’m wandering about the classroom facilitating conversations. Although the brain only takes up 2% of our body weight, it uses 20% of our energy, according to Bill Bryson‘s A Short History of Nearly Everything.

So I’ve gotta keep myself mentally in shape. That means reading tons of books I love even when other teachers tease me. That means blowing off grading homework for a night to paint my nails. That means making time for my physical health and not necessarily devoting hours of lesson planning each day.

Not enough hours in the day. I’m, frankly, super-pissy when I hear teachers say this, and then five minutes later I’m nodding at the truth in it. Because yes, our job is impossible and yes, there are insane demands coming at us from all angles. But I feel like you can’t automatically default to complaining about time without carefully looking at how you currently do spend your time.

For me, this has meant a intentional devotion to super-quick transition times and an up-tick in the priority I make in keeping my room clean so I don’t have to scrounge for materials. Now, my goal is shifting to providing great math instruction by still letting me be a human.

Among neuronormative folks, the general consensus is I’m an overachiever. *I* don’t feel that way, but apparently the speed with which my brain works and the resulting efficiency I have in completing mental tasks makes me one. When I think of overachievers in my mind, I definitely don’t want to be someone who spends hours constructing the perfect math centers that can only be used for a week or two. I’m certainly not that extreme, but I admit I’m still working on this. Mainly because I get sucked into interesting information online and can’t pull myself out. But limiting myself to a half-hour of prep time before class begins seems to have been a good boundary to set.

I want a system, whether it just be an internal mental process or a procedure I can use in my classroom, to ensure that I’m pursuing great math with my kids but I’m not spending hours in the staff lounge or on the Internet to do it. I suppose a time-hog that others might forgo would be the time I spend documenting my process and further questions I have through blog posts here, but the writing-about-it part is just fun.

I could continue writing, I suppose. But I’m off to redo my nails. Because I’m only going to really be a good teacher if I know when it’s time to let go.

NBPTS Reflections

I didn’t pass my National Boards.

So there’s that.

Welp, I think I’m finally ready to start reflecting on not passing. I’ve also registered to resubmit my portfolio, so I guess I’m also ready to GET BACK ON THAT HAWS.

Not to complain, but I wish people had told me “this is a three-year process” earlier in the game. It seemed like people started saying that around February or March, but by then I had already worked myself into a lather of my own view of what the certification process was. And my view did not involve my 2012-2013 school year looking like this:


There are, of course, a few positives to be found in this situation. Number one: the lovely, talented, and charming Liz Willard is now a NBCT.

Congrats, Liz! She’s in the middle, in black. Kimmie Choi, second from the right, is also a NBCT.

She joins the ranks of several other respectable colleagues who are also certified. When people found out I didn’t pass, I received many (well-meaning) comments to the effect of “You’re a badass teacher; if you didn’t pass, the process is broken.”

I disagree. I had no freaking clue what I was doing through most of the past year, despite fearless cohort leadership by straight-shooting, no-holds-barred NBCT Diane McSweeney. I’m bummed, but I’m TOTALLY FINE with the fact that I didn’t play the game the way it was meant to be played. In many ways, I respect the process MORE because I don’t feel like I just got a free pass. Besides, I got a perfect 4.0 on my documented accomplishments entry, so I must’ve done SOMETHING right, no?

Many people also said, “Wow. If YOU couldn’t pass, I don’t even think I’m going to TRY.” or “I don’t know how you’re managing to redo everything all over again.” Come now. I know you think you’re complimenting me, but you’re notttttttt.

I’ll tell you what WAS a big motivating factor when I was feeling terrible after learning my results. The response of NBCTs. I wasn’t entirely convinced before, but now I know this is a community I very much want to be a part of. Every single person I know who is National Board certified has offered to help me redo my portfolio. EVERY SINGLE ONE, even if I haven’t talked to them in two years. Well, Rob hasn’t offered yet, but he was busy getting engaged, so I’ll forgive him.

NBCT Rob Stearns, marrying us the day after he submitted his portfolio in 2011.

The National Board folks themselves could have been a squeak more helpful, I suppose. This is what I saw when I accessed my scores last week (actually, it’s not EXACTLY what I saw because when I logged in today to get a screenshot I couldn’t see what I saw before, so this is the closest I could get):

Wat. I couldn’t remember the cut score for passing, and nowhere on the main page did it say “YOU TOTALLY PASSED” or “YOU TOTALLY BOMBED,” which was probably intentional, but it made me panic for a minute. Until I realized my fate. My crappy, crappy fate.

The feedback I received on the entries I didn’t pass was taken directly off the NBPTS four-point rubric. So it was directly aligned to the scoring, which was helpful, but it wasn’t terribly specific, which was not helpful. It also did not help my soul to read that my entries indicated I wasn’t reflective and wasn’t knowledgable about my content areas, the two areas I thought I was strongest.

So here I go. But it’s not just me this time through. Garrett, who was in my cohort last year, is trying again as well. So is one of my favorite Seattle U cohort members, Adrienne. And a few other folks are trying their luck at National Boards the first time around, including a few other Seattle U MITFEEs, like Melinda and Julia.

Me and Julia at graduation, June 2007.

I’ll be in good company if I pass next time, but it’s nice to know I’m in good company even though I didn’t pass this time. Thank you all for your continued support.