Never mind that the school year ended almost two months ago. Never mind that the summer program I worked for ended yesterday (edit: a week ago. Sigh.).

Here are the last few photos of the 2012-2013 school year. Most have little to do with math and more with closing down the year.

(edit the second: I am unable to make the images align nicely with the text. Apologies for the formatting but I am 1 parts frustrated and 3 parts trying to make my flight, so this will have to do for now!)

Day 172: Using diamonds and rectangles to review factoring polynomials. My supervisor and I sometimes talk about how effective this is. It is (like many things) not how I learned to factor (which I used to do mostly by trial and error) but I do think it helps students look at the procedure a little more systematically. I don’t know how clearly that came across in my explanation. Unfortunately, I erased the work before taking a photo.

Diamonds and Rectangles

Day 173: Using generic rectangles to factor polynomials. This time, I left the work in.

Generic Rectangle for Factoring Polynomials

Day 174: Different teachers at our school use different programs to create exams (and graphics for said exams). As a result, I had to redraw a trapezoid for the final. I can’t tell whether this is an example of me trying to be precise or me being OCD. A friend has suggested that I use Geogebra. I think I really just want a free copy of Geometer’s Sketchpad.

Trapezoid for Final Exam

Day 175: Final days, yo. This is a written reminder, both for the students and for myself, that this really is their last chance to turn in all the things. Surprisingly, some of them do not turn in everything. I’m still trying to figure out if this is forgetfulness or something else.

Last Days

Day 176: During quizzes and exams, we’ll generally leave some of the important formulas on the board. At first, I was a bit puzzled by this – we didn’t do this when I was growing up (and yes, 18-year old me can’t believe I just said that). But it’s helped me think about what things are important for students to memorize (not everything) and to see that, even with the formula, that doesn’t mean that students will remember concepts or know how to apply them.

Notes for the Final

Day 177: Last real day with students. My primary class took its final today. We still do some things with objectives and expectations, but hopefully they’re ready to go at this point. In retrospect, students seemed to do better on their unit quizzes. I wonder if that’s a sign of forgetting (which is interesting, since we gave them several days to prepare/study specific things for the final).

Day 178: Finals Expectations

Day 178: Students do say the funniest things. We have them do a quick evaluation of the course at the end of the year. I’m posting a few of them (technically without permission and focusing on the funny rather than the mathematical). Overall, students felt supported, though I need to work on discipline and classroom management (especially with a few tough cookies). I was pleasantly surprised by what they said they learned from this class.

Student Evaluations

Day 179: Grades due today. Students generally don’t attend class. A few showed up to grab work and clean out their binders. We recycled the rest of the work.

Day 179: Binders

Day 180: Clean slate. At this point, I’m so use to coming in, writing objectives and expectations and then figuring out how to communicate math (whether it be by speaking or on the board). It’s weird to see the board empty.

Day 180: Empty Boards


Math as Blog Post

This post is Reflection the Fourth for “Math is Personal”. It is largely a response to Justin Lanier’s post “In What Ways Can Math be a Part of Your Life” which looks at some of the ways that people can use math in their life. My students from last year ALWAYS asked “When am I ever going to use this?”, so this post caught my eye.

Justin’s post looks at 4 ways people use math:

  • Math as Everyday Activity: Calculating tips, figuring out how much bacon you can afford with your monthly paycheck, etc.
  • Math as Social Token: : How other people perceive your knowledge of math. For example: whether your friends consider you a “math” person, whether your GPA/courseload/SAT scores are strong.
  • Math as Investigatory Tool: Using math to access other areas of knowledge, especially science and history.
  • Math as Source of Enjoyment: Enjoying math. Doing math of your own volition. Think Rubik’s Cubes

So here’s what I’m thinking:

Math as Everyday Activity
As a teacher, I try to think about Math as Everyday Activity often. I feel like students buy into Math As Everyday Activity…sometimes. They seemed more responsive when I was able to show them an authentic connection. Making the connection is definitely easier for some topics (statistics, solving for unknowns) than for others (triangle congruence shortcuts) and I feel like students can tell when the connection is forced.

Math as Investigatory Tool
I feel like I believe strongly in Math as Investigatory Tool as a result of student teaching last year. As my definition of math begins to extend beyond merely using numbers to measure things, I begin to realize how much math is about understanding and communicating about the world around us. I was not as aware of Math as Investigatory Tool prior to my student teaching/grad skool year.

I especially see Math as Investigatory Tool in Common Core Practices (persevering, making sense of problems, making arguments, etc), which I want to promote even more in the years to come (speaking of, check out this amazing paraphrase of the Mathematical Practice Standards). While I didn’t appreciate Geometry’s abstract nature in high school, the idea of having to logically prove something (rather than just saying “they look about equal” or “because you told me to write it down”) stands out to me as useful, important and intriguing. I am also trying to figure out how to teach proofs in a way that’s intuitive and not just 2 column based (re: 2 columns: so much writing, so little interest).

Math as Social Token
I’m honestly not sure how I feel about Math as Social Token. I’m not sure how I used to feel about it, I’m not sure how I feel about it now and I can’t even fathom how I’ll feel about it in December (4 months into the school year), let alone next year, let alone in a few years.

"Just call me Mr. 800...said no one ever"I know that Math as Social Token is heavily in my favor as an individual. A lot of my high school friends were strong math students and while that encouraged me to engage with math and cast it in a more positive light, it also exposed me to the way that your average high school student generally thinks about math (“More homework? Boo. When am I ever going to need to know how to do this?”). My SAT scores (which fall solidly into the category of “just good enough”) and psuedo-engineering major also play into this. So I’ve benefitted a lot from mathematical social status, even if I don’t consider myself “a math person”.

But here’s the thing: I want my students to be accepted (or have status; however you’d like to call it) regardless of their relationship with math. In an ideal world, yeah, they’d all love math, pass all their tests (standardized or otherwise) and dance through fields of gold with rainbows and butterflies. But I suspect that many of my students will struggle with math and, while I want them to persevere and overcome those struggles, I don’t want those struggles (which may reflect negatively on GPAs, SAT scores, etc) to hold them back. Right now, I feel like status is conferred for having the right answers, not for struggling to make sense of problems or asking clarifying questions (or any of the Math as Investigatory Tool practices). More to the point, indicators such as GPA, SAT scores and even the courses you take (or are allowed to take) aren’t always indicators of mathematical ability or disposition. And despite the fact that I’m committing to teaching math for the foreseeable future, it’s probably more important to me that my students are good people. Or creative problem solvers. Or persevere when the track is tough and the hill is rough (and I fully agree that you can do all of these while still being a strong mathematician). Or maybe I’m just irritated by status issues, mathematical or otherwise.

Math as a Source of Enjoyment
I need to think on this one. I believe it’s important, but am currently trying to figure out how I can authentically convince students that they can enjoy math and that it’s not just a required subject . Also, I worry that students (especially those who have struggled in the past) may not buy into this as quickly as others. There are certainly things I can do to encourage this, such as finding interesting, complex problems (hit me up if you’ve got any?) and helping to scaffold student knowledge in a way that makes it accessible to students who may not consider themselves math students. Like I said, I’ll be thinking about this more.

I’ll close with a quote from an email from one of my grad school instructors, writing about something called “productive disposition”, which is basically the belief that math is useful (side note: I spent most of the year referring to this as “positive” disposition. #FacePalm I am also quoting this email without permission. #DoubleFacePalm)

Quote: “But productive disposition is about having the ‘inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s on efficacy’. Useful (or worthwhile) could mean useful in solving real world problems, but useful could also mean useful for solving more complicated math problems that are not set in context. Additionally, ‘sensible’ is about students seeing math as something to make sense of rather than as something to be memorized.”


As part of the sMOOC/online course I’m taking, we’re all reflecting on a site called Math Munch.

Every week, they (it?) post(s) on 3 mathematical topics. This week, it was the Coastline Paradox, Clueless Puzzles and Beach Art. Last week, it was honeycombs, a polyhedron called the rhombic dodecahedron and a game called Microtone.

And now, an unrelated image (’cause: child of the 80s):


What I like about Math Munch

  • Extra resources. I’m liking the resources and background information that Math Munch provides. More often than not, I find myself clicking on these links to find out more about the chosen topics which is great because many of the topics are new or are concepts that I don’t know much about.
  • Short and sweet. When reading Math Much, I don’t feel overwhelmed the way I did when slogging through 20+ page articles for graduate school. Similarly, I appreciate that Math Munch only covers 3 topics a week. In an ideal world, I’d find more time to do my own research on math. But in the reality of the teaching world, learning about 3 new topics seems like enough without being overwhelming (see prior point about being to extend research through links as needed).
  • Hands on and Theoretical Content. I’m liking that some themes are very practical while others are more theoretical. I find myself still thinking about the Coastline Paradox and feel that students (at least where I live, where we are relatively near the beach) could access this idea. At the same time, I like that many of these ideas are more theoretical, such as prime gaps and Fermat’s Last Theorem. While I have a harder time wrapping my head around theory, I know that it’s important to understand (and be able to explain to students) and that there’s some good background reading to get started here. I also like that most of the posts have a hands-on component (the nets for the rhombic dodecahedron) and that there are games (I’m especially eyeing this section for my class next year)
  • History of Math. I’m liking that Math Munch is connecting math to history and to people. I feel like none of my math classes talked about the history of math, which I’m learning is a big part of how math came to be. Incidentally, one of my students last year kept asking “who invented math?” and I never had an answer for him (until now?). Incidentally, I’m thinking there must be “modernized” drawings of mathematicians somewhere – sketches that depict them as real people rather than the fancy, wig-wearers we usually see (not that these pictures aren’t valid, but I feel like my students think of them as distant, historical figures)

What I’m Still Wrapping My Head Around

  • How exactly to use Math Munch in a classroom. I can see some great uses for this as an extension/differentiation technique or at lunch/during advisory (all teachers at the school I’m at next year meet with a small group of students 4 days a week). I’m still trying to wrap my head around how to integrate this directly into the classroom curriculum, both because our curriculum is arranged in specific units and because we’ll most likely be trying to milk every precious minute out of the classroom. Incidentally, I’m also trying to wrap my head around our curriculum for next year, so the timing on these 2 may work out. I do know that we have a unit on tesselation, which was one of the topics from Math Munch, so…)
  • How to connect to the larger Math Munch community. Or how to work with other people who are using Math Munch. This is more of a question of what I want to do about this. There are other math teachers in the same sMOOC who will likely be looking at and using Math Munch. I know a few math teachers in my area who might be open to using Math Munch or at least bouncing ideas off the drawing board, or however the saying goes. 

What do you think of Math Munch? Any ideas for how I should attempt to integrate it into next year’s classroom?