Days 82 and 83: Out With the Old…

Day 82: Instead of giving semester finals, our school has a 2-week portfolio process. Teachers spend all day with their advisees, working on reflective essays on a variety of topics like what they felt successful about, what they felt they struggled with, etc. The process is often described as intense and at the end of it, I’d agree. I’m just beginning to wrap my head around what it all meant.

Elvis' essays on what he struggles with in school

In their essays, quite a few students said they struggled with math. Thursday’s picture is from Elvis, one of my students who was absent for most of the portfolio process, but worked on essays from home. His essays (sentences written first in Spanish, then translated to English) talk about how he felt math was difficult and how he sometimes felt angry because he didn’t always understand what was happening in math class and because his classmates didn’t always help him (we rely pretty heavily on groupwork given that students enter with a wide variety of math backgrounds). There are a million excuses and variables that play into why Elvis thinks math is difficult. His English is still developing and classes are taught entirely in English (though there is lots of native language support. Perhaps too much). He is sometimes absent (though not truant). His class is at the end of the day and struggles with staying focused. Many of the other students are also struggling with the math and often resort to distractions rather than asking for help, which affects the entire class.

Elvis is a good kid. He was one of the few kids who said goodbye to one of our students whose last day of school was Friday and he won a round of musical chairs for our advisory. Next semester, I’ll continue to think about how to help Elvis and other students like him gain more access to material in class. This means thinking about how to break problems down to the most basic level while still building in challenges for students who have been doing this math for years. It means really figuring out what my students know (we’re going into simplifying and solving expressions and I’m sure that some of my students aren’t quite comfortable with division and that most of them aren’t comfortable with exponents). It means pulling in Elvis at lunch and after school – I’ve gotten him to come in a couple times, but never really consistently and probably not focused on the things he needs to learn. We’ll see.

Day 83: After a few last portfolio presentations and a gradewide assembly, the last day of school ends at 1:05. Teachers finish last minute grading until the grading system closes at 3 and then everyone frantically cleans their rooms so that they can both be ready for the next semester and get home at a decent hour (the custodian kicked me out. You can guess which end of that scale I ended up on). In addition to getting rid of a mountain of paper and resetting my room after portfolios, I also re-taped manager roles on my tables (because I finally learned how to use the laminator, which is a whole other post in itself).

Roles

Each group has 4 roles: the resource manager, the group manager, the communications manager and the task manager. Theoretically, each manager is in charge of a specific part of the task that the group is working on so that everyone has something to do and some way to participate. In reality, I often use them more as a way to call on a member from each table, though I’m hoping to use them in a more authentic way next semester.

Day 60: Patty Paper versus Rubber Bands

2013-11-13 13.38.11Our transformation unit continues. Students spent most of today’s class practicing transformations. At this point, students seem to be stronger at translating than they are with dilating. I’m not sure if it’s because of the tools (patty paper versus rubber bands) or because dilation seems like a bigger change to wrap one’s head around. Flipping was a problematic word, but once I demonstrated (by flipping over a sheet of paper), students caught on pretty quick.

The blue paper is from an activity that Curriculum Partner designed last night on a whim. It gave students a chance to practice more transformations and to talk about naming shapes. I tried it with various amounts of structure and direct instruction. One group imploded when two group members started arguing. I think it sidetracked me more than I would have liked, though I figured out (I think) that one group member felt the other wasn’t pulling their weight while the other group member felt left behind. We’ll see how it goes tomorrow.

Mission #2: The Twitter Mission

Justin Lanier’s Math Twitter Blog-o-Sphere Challenge (#2 of 8):

Your mission—should you choose to accept it—is to try your hand at Twitter. Maybe for the first time, maybe for the first time in a while, maybe in new ways, maybe with new people.

 

This mission, combined with our blogwork in Mission #1, will provide you a sure foundation for all future Explore MTBoS enterprises. You’ll be platformed up and ready to mingle by the week’s end.

Continuing my theme of “evading work like my students”, I tried some aspects of this challenge and repurposed some of what I already do into something that sort of fits the challenge. And I took a lot of photos that I meant to tweet and then didn’t.

In general, I use Twitter to find information. If I see a blog post or article that’s been reposted by a handful of people, I’ll check it out.

Missions

While I love blogging, I haven’t been able to find the time for it these days, which is why the brevity of Twitter (and Instagram) is nice. I’m experimenting with posting photos of my board and my classroom on Instagram. I’ve gotten some good reactions from friends on Instagram (who aren’t math teachers, but still have contributions all the same). It’s neat to see how people connect to math and what they learned about math. I’m not sure how much of a presence the Math Twitter Blog-o-Sphere community has on Twitter, but given how visual teaching math can be, I think it’s a neat space to explore. I try to cross-post these photos to Twitter in conjunction with #180blog posts, though I’m  behind on both.

I tried started some hashtags – #MusicWhileGrading, #MusicWhilePlanning, #TeacherPockets, #MyBoard. None really took off, but I wasn’t consistent about using them. They are also less related to math. I also acknowledge that many people don’t listen to music while working and that even fewer want to know that I basically only ever listen to the Old 97’s and Billy Joel. I am curious to see what #MTBoS hashtags start trending.

Most exciting twitter moment

Through a professor that I follow in Twitter, I connected with a math teacher in Pennsylvania who is working on complex instruction. Short twitter conversations were had, emails were sent, I’m excited to see how it goes. Even if nothing concrete comes of it (teachers are busy, planning is hard, implementing groupwork is really hard), I’m excited that we got in touch and am excited to follow the work that he does online.

The Future

Moving forward, I am trying to contribute more to the world of math online. Right now, I’m more of a passive consume and I’d like to be more of an active participant. For me, this means trying to be consistent about posting and trying to stay active on Twitter (short attention span, relatively little free time, etc). I am trying to take part in #AlgChat (Algebra Chat) on Sundays, if nothing else, just to see what other teachers are doing.

Related but Unrelated

Related but unrelated #1: I thought it would be cool to tweet my first tweet from the top of Mt. Cotopaxi. Unfortunately, my cheap Ecuadorian phone couldn’t quite connect to Twitter and we didn’t make it to the top anyway, so…

Related but Unrelated #2: A few of my students from last year used to randomly say “Follow me on Instagram, Mr. Chan!” If only they knew…

Related but unrelated #3: Possibly my biggest accomplishment of my last job was convincing my boss that he should be on Twitter. It hasn’t 100% happened yet, but he texted me a month ago to say he’d gotten an account. Baby steps, y’all…

Day 41: Elevators and Negative Numbers

Weird day today – the 10th graders all took the PSAT (whole ‘nother post) so I had my 9th graders, plus the 9th graders from the other team. And also took half a day off to go to professional development.

We wanted to use what time we had wisely (with a sub facilitating at least half the classes), so my curriculum partner and I cooked up a lesson on negative numbers based on this worksheet from Illuminations. I got to see the first two classes, which happen to be my tougher classes.

Lots of students struggled with “up” being positive and “down” being negative. At one point, I made tables point up and say “up is plus” and “down is negative”, which I now wish I had made everyone do.

This photo of Jaime’s* work is pretty representative of some of the errors I saw – kiddos were able to connect the different numbers, but not always in the way I wanted them (and to be fair, I don’t know how culturally relevant elevators are to most of them):

Elevator misconceptionsI’d rate today a 3, but I don’t know how fair it is to give such a weird day a rating.

Here’s a shot of the board and my pockets and other work:

2013-10-16 19.18.25

*not his real name.

Day 40: Triangle Area Equations

Triangle Area Equations

This photo is of two ways of finding a formula to calculate the area of a triangle and how I marked up the diagram to help students think through it. In retrospect, I wish I’d held the camera more steadily when taking this photo. I also wish I’d done more thinking on this beforehand (aside from the grading and other work I did this weekend. Uy.)

I’d rate today a 2 (in my ideal world, I rank every day on a 0-5 scale and then see how the ups and downs play out throughout the year). Today’s lesson was rough. Curriculum partner and I spent quite a bit of Friday afternoon planning, but I think the idea was still too abstract for our kiddos. First period was struggle bus (though they fought valiantly). I think they had trouble wrapping their heads around why we were multiplying (to get the area of the rectangles) and then dividing (because the area of the triangle is half the area of the rectangle). Possibly too abstract, possibly casualties of the 3-day weekend.

I did have a talk with a student after school, who I’m trying to get to reflect on his behavior and he mentioned that he can do basic area things (count the squares in a gridded rectangle and even multiply base and height when they are numbers) but variables are still a jump for him.

And a collage of today’s photos:

2013-10-15 18.31.29

(the behavior contract in the middle frame is from the same student)

Day 21: Structuring Growth Exercises

One period in, curricular partner (the teacher I plan with) and I realized that the lesson we planned for today (“growth by shrinking” with negative numbers and decimals) was too ambitious. Kiddos seemed OK with negative numbers, but struggled with place value. We decided to review/practice growth by adding and growth by multiplying (which is what we had just finished learning on Thursday). The idea is to start with a number, then grow four times, either by adding or multiplying the same number.

I wonder how much the structure of the activity/graphic organizers confuses our kiddos.  There were stairs that were supposed to help students organize the starting number, ending number, and steps in between. Most students understood the addition and multiplication bits, but I think they were confused about where to put which numbers and operations. Photo below is 2 student work samples. One shows a bit of confusion about how to use the steps, one shows some pretty good multiplication. I would have loved both kiddos to show more problems in general, but you take what you can get. 

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Also featured: Things in My Pocket at the End of the Day:

Things in My Pocket - Monday, September 16th

Left school at 6:30. Pretty bad considering I thought I could get out at 4:30.

#180End

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.”

CHOMP

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):

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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?

Automathography

Automathography for “Math Is Personal” (based on previous mathographies for graduate school and student teaching).

I attended middle school and high school in a small suburb or the San Francisco Bay Area with high-performing public schools where math was heavily tracked. As a blanket statement, I was not as good at math as most of my friends. Admittedly, some of my friends memorized the periodic table and programmed music in their free time, so they aren’t the most objective measure of “average” mathematical knowledge. Still, they often understood things about math that I did not. They were also passionate about math in a way that I was not – while I went to class, did the work, generally understood and did well enough, they were petitioning to skip courses (or just skipping them, to the chagrin of the administration), taking advanced online courses, and competing in math competitions.

I remember liking 8th grade Algebra (it was systematic and logical) and 11th grade Calculus (it was also systematic and felt higher-level) and not caring as much for 9th grade Geometry (it was too abstract and proofs were too much writing and confusion). Surprisingly, my geometry score on my teaching certification test had fewer red flags than my algebra score. I don’t know if this is due to the passage of time or a change in understanding.

I specifically remember learning how to calculate the derivative and second derivate of an equation (from a math teacher who, while good, was not considered particularly strong at our school). Not only did calculating derivatives make sense arithmetically, it made sense as a real world concept – I was calculating the rate that something was changing (or the rate of change of the rate of change), not just plugging numbers into an equation. On the other hand, I liked Algebra – while more systematic and abstract than Calculus, it was logical and (somewhat) easy to understand. It felt like doing a mind-teaser that was tricky, but not impossible. I think I would like statistics a lot as it tends to be very applicable to “the real world” – however, my knowledge of statistics (from college) is a bit shaky.

Back to high school – although I liked Calculus, I opted not to take math my senior year, instead taking a course at a local community college over the summer so that I could free up space in my schedule senior year.

Four years later, I graduated from college with a Bachelor’s in Product Design (an interdisciplinary major combining Mechanical Engineering and Studio Art), but the mixture of both majors meant I didn’t know either major very in-depth – including some of the math that I wish I had internalized a bit more now. I was also still burned out from high school and didn’t pay as much attention as I wish I had now.

Though I might not have been the strongest math student, I soon found that I was interested in education, especially in low-income communities. My junior year, I tutored local high schoolers from through Upward Bound. I remember loving working with and interacting with students (though I don’t remember doing much math tutoring).

My actual appreciation for math began at my last job, 6 years after graduating from college. The nonprofit where I worked recruited recent college graduates to work as teaching assistants in high-need high schools. During our first year, we focused exclusively on Integrated Algebra. My co-worker, the Site Director for Math, said that math was the easiest subject to pick up for college graduates (even those who weren’t math majors). He said this somewhat flippantly as he’s good at math (and teaching math and coaching math teachers) and tends to gloss over the details in conversation. Around the same time, my boss also mentioned that research showed that only 15% of youth from low-income communities would graduate from college in six years. Those 15% would be the ones with the most rigorous academic high school courses. He also said that success in algebra was one of the best indicators of academic success. While these numbers shocked me a bit at first, they made sense. I saw this, even in the high performing schools I attended: friends who did well in algebra generally did well in geometry and algebra II/trig (or at least took and passed them). Friends who struggled in algebra were turned off to math and, while they usually continued taking courses, they generally didn’t do well and opted out as soon as possible (taking algebra II instead of algebra II/trig).

On a more personal level, I was beginning to work more with Excel and statistics in my job as the Operations Manager. Being a “data-driven” organization meant that we tracked data, calculated it, and then made decisions based on it. Now, I had to know how to relate our numbers and our data to our organization – not just to each other, but to last week’s numbers and to future projections. I also had to explain to my boss and other stakeholders what the numbers meant and what actions we should (or shouldn’t) take, based on these numbers.

Jargon-heavy B-school talk? Perhaps, but all of a sudden math was very, very relevant to my life. And I loved it. While running weekly reports for recruitment and program, I could look at numbers, figure out what they meant, figure out why they were different from what we expected, and recommend a course of action to get to where we wanted to be. I struggled a bit with the finance side of things – while I could generally make the numbers fit in the right places, I didn’t have an accounting background and wasn’t sure how to work the software or run or interpret the reports. After inadvertently leaving out a $100,000 check (oops) in our monthly finance report, we got help from a bookkeeper who helped me navigate the software and enter things correctly so that we could keep track of our finances in real time (including how much we owed and how much we were owed). I struggled with finance to the end. While I know there’s a narrative/story that the numbers are trying to tell, I was still trying to figure out how to easily decipher and share that.

That was how I found myself applying to graduate school, 12 years after opting out of math during my senior year of high school. Although I thought about teaching high school English, I decided to apply to math programs, knowing that math was a gateway course (among many others) to college.

Through graduate school, I student taught in three Geometry classes at an urban comprehensive high school, which had a heavy focus on groupwork and actually tried pretty seriously to detrack its math classes (all incoming students were placed into geometry, regardless of whether or not they’d taken algebra; we tried to provide the necessary support in class with mixed results). It was interesting to see how students related to math; some looked at it (as I once had) in very procedural ways while others were almost scared to do it. Many of the students who claimed to be very bad at math said they’d “always been bad at math”. I also began to see that math was about more than just measurements and calculations – we tried to make concepts and reasoning a big part of the course as well.

Given these experiences, here’s what I value and believe about math (subject to change, as always):

  • Math describes the world around us (if you know how to interpret it).

  • Everyone can learn math.

  • Everyone can teach math.

  • Neither learning nor teaching math is easy – they require a lot of work, as do most of the worthwhile things in life.

  • The “smart kids” are often able to make math look easy, which can be discouraging to the rest of us. The smart kids do, in fact, struggle with math, but either make it look easy or just manage to hide it from the rest of us.

  • Many students are scared of math. Partially from watching the smart kids be really good at math, partially because they think they haven’t been as successful at math in the past. Possibly because math is not always taught in a way that is easy to interpret.

  • The more you can break math down into small steps, the better people tend to understand it. It helps people who are struggling with math make connections they wouldn’t see otherwise and it keeps people who are good at math from making sloppy mistakes.

  • I’ve noticed that my friends who were “good at math” tended to be fearless about math – they just went at problems (whereas other people would stop, get confused, and give up). I’m not sure if this was because they were more confident or because they had a better handle on what they were doing. But they never just gave up without trying several times.

Here’s what I’m curious about:

  • How do you “catch students up” when they’re behind? (either a couple units or a whole course)

  • How do you build up students’ confidence in math?

  • Do you need different kinds of math to be ready for college versus to be ready for a job?

  • How does building relationships tie into math education?

  • How does one effectively teach math to English Language Learners? To a math classes with many, many different ability levels?