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.
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.”