Thursday, May 30, 2013

Why Exploratory Learning Makes a Difference

We were randomly reviewing word problems on the last day before the end-of-year exam, and I wrote up a word problem on the board: "The height of a certain triangle is five more than its base. The area of this triangle is 42. Find the base and height of this triangle." Nothing fancy, standard quadratic problem (not based in real-world context, I know), except we haven't worked much with triangles this year.

I walked around and noticed that all the kids had drawn and labeled a diagram, then proceeded to write down x(x + 5) =  42. I asked the class how we would find the area of a triangle, and they said, "Base times height!" And I said, "No, that's for a rectangle, not for a triangle." Within seconds, all the kids who were in my class the previous year shouted out excitedly, "--Divide by 2!!!" Meanwhile, the other kids who didn't learn the triangle area formula via its connection to the rectangle had puzzled looks on their faces; my hint that "base times height" is the procedure for a rectangular area held no apparent meaning to them with regards to generating a triangle's area formula. Rote memorization of "the simple things" is really a problem, because if you start memorizing intuitive things like this, you'll never be able to memorize everything.

The issue here for teachers (not a new discovery, obviously) is that once a teacher just gives the students the formula, the students are no longer motivated to really understand why it works. Once a kid has a teacher who has taught them a certain skill by rote, their motivation to learn the intuition behind that particular skill completely disappears as the kids simply file it lazily into the "already learned, already can do" drawer in their mind. Please don't do this, as it's really hard to un-do down the road. For every concept that you rush through in order get to the "procedural" practice, those topics will never be properly understood, explored, and developed by the child. This not only robs them of the richness of mathematics, but also creates retention issues.

I know, it's not a new discovery by any means. But, I was reminded by this small incident, of the significance of exploratory learning.

Joy of Mathematics

Despite the kids going wild with the impending summer and grading and report-writing taking up a vast chunk of my life outside of school, I love this time of the year. I feel very gratified and humbled by the journey that my students have taken with me this year. Mathematics, for some reason, is such a defining subject for many students in terms of its impact on the way that they perceive themselves and their general capabilities. More than anything, I wish each year to change some kids' self-perception for the better by changing their relationship with math.

One student of mine was afraid to come to school in the beginning of the year. She missed dozens of days in the beginning of the year, because she was terrified of math based on her experience from other schools. Once the counselors and support people got her to come to school, I coaxed her into just trying the things that we were doing in class. Over time, it has been amazing to see her develop into a person who enjoys doing math. I know this to be true, because she sometimes would pull me aside after we go over a problem as a class, and then show me an alternative way to do the problem to ask if that's valid as well. She also does not like to ask for help easily, and prefers poring over/analyzing the problems on her own first. Her confidence has also developed tremendously. She is now rarely absent, and in general, she is just a different person than she was at the beginning of the year, always seeming eager and curious in class.

I know because of kids like her that I had chosen the right career for myself. For me, there's no success that is greater than the payoff I get from seeing kids like this blossom over the course of a full year. In the end, the patience that teaching requires is not on a day-to-day basis, but in being patient enough to wait a full year to observe the visible changes in the students. It has taken a village to reach this kid, and I hope that in the future, when she is in a different math class, she'll remember all the things she has been able to do this year and to still have faith in who she is and what she can do.

Tuesday, May 28, 2013

Lessons Learned

This school year was very challenging, ramping up to my role and responsibilities as a Department Chair. In the end, I feel that it has really helped me grow professionally; I now think constantly of all students in the school as mine. I have a responsibility for the learning of each child, not just of those in my own classes. When I make an instructional decision in my class, I immediately consider how that impacts my colleagues and our collective pacing, in addition to how it impacts the individual child. I have learned to talk to student parents more effectively -- when to listen, when to acknowledge them, and when to explain our procedures in a gentle way that helps the parents realize that 1. we're working in the best interest of their child, and 2. the school makes the ultimate academic decisions regarding the child. I have had to deal with some unhappy colleagues. Being the middle-person between management and teachers, sometimes you have to communicate unhappy decisions and still find ways to hold everyone together. Some days, it was hard to respond to my students and my colleagues all at once, so I had to choose whom needed my immediate attention. I have had to become more organized. In addition to reminding myself of deadlines, I had to look ahead in order to plan for all of us and to communicate deadlines, expectations in advance. I had to also mediate conflicts, and sometimes to create them if it meant to stand by a fair decision.

Sometimes, some things may seem like a lot of detailed work. It's not easy getting 4 teachers to give an identical end-of-year exam, when they each customize pacing and content instruction slightly to fit their classes. It's not easy to all agree on project deadlines months in advance, and to sit down amid very busy times to moderate grading and to create class lists for next year. It's not easy to get teachers to grade consistently across different grade levels. But, the better you can coordinate these things which may seem like minor issues when taken independently, the better they will pay off in the long run, resulting in less confusion for students and fewer complaints from parents, and thereby less bureaucratic overhead for everyone.

Today, I was quite touched by my senior colleagues coming to me to say that they've really developed respect for me during the past year. Although I had never looked for it, it was a validation for the work this year had required of me. If I could go back, I would have waited until I was several years into the school to apply for the same position, because then my learning curve would have been a bit less steep. But, it was still a great (albeit challenging) experience, and one that will help me in the future to maintain a balanced perspective of all the considerations that go into a seemingly small decision at school. Most of all, I have appreciated the friendships that I have formed with these colleagues. In ways big and small, they have supported me as much personally as they have supported me professionally.

But, the departmental work is not over quite yet. As I'm counting down the weeks to summer, I'm also making a list of the endless things that still need to be done. Only about 3.5 weeks to go! That's hardly a blink away! This summer, I OWE MYSELF A VACATION!!*

*Obviously, this is not just because of the department chair work. I got married this year, found a job, did a bunch of prep work to move overseas, and had battled allergy for months. I think I have earned some time off this summer, just sayin'

Wednesday, May 22, 2013

If only all right triangles were this cute...

Hi, I'm teaching trig to my ("low" math group) 9th-graders, and loving it. We only had time for 1 day of trig lesson before we will have to concentrate on reviewing for the end-of-year test (after which we'll come back and do some outdoors trig/angles of elevation and depression type of stuff, leading into complicated trig word problems). The kids were awesome at basic trig! They learned how to apply sine, cosine, and tangent correctly and consistently in one 80-minute period. Rock stars, these kids. They use the tactile trick to figure out which side is opposite, adjacent, and hypotenuse, and then they use cross-multiplication to consistently and correctly solve for x. For now, since we're only learning the whole of right-triangle trig in one day, I am going to give them the acronym SOH-CAH-TOA on the exam and just require them to remember what the acronym stands for. Eventually, they'll have to memorize SOH-CAH-TOA, obviously.

Anyway, totally apropos, this totally cracked me up today.
Anyhow, this week is a killer. I keep trying to get ahead, but it seems impossible, as I am pulled in all directions as a teacher, a department chair, and a person soon to move across a big pond. I wonder when the next sigh of relief will come. Hopefully, there is one scheduled before July...

Sunday, May 12, 2013

My Shiny New School Next Year!

This year, job search had been particularly challenging for me, since I was juggling planning for my wedding and the long-distance interviews with schools that typically hire people only after having met them in person. But, in the end, I couldn't be happier to say that I will be moving in July to a great school in Seattle!

Most exciting for me is that I'll be part of a fabulous math department. They are highly collaborative, and they love hanging out with each other on a daily basis. These math teachers are also highly reflective/self-improving, and were especially commended for this during their school's recent accreditation cycle. The school as a whole has a very special culture of sustainability, which is seen through things like the staffers taking all the kids 3 times a week to scrub down the whole school, including cleaning bathrooms and compost bins. Their kids do this (surprisingly) gladly and learn to protect their school environment. They also, on Fridays, serve food in the cafeteria to recycle leftovers from the week, as part of their sustainability theme. They're in the process of building a new green building that is solar-powered, collects rain water, and has an energy counter. When I visited the school, I loved seeing the seamless integration of student art into every corner of the beautiful, historic building. Everyone I had met -- including the class of Grade 11 students that interviewed me -- had asked me tough questions, and I tried to answer them thoughtfully to the best of my ability. It seemed to work out OK, because in the end they had decided to offer me a job on the spot, at the end of the long interview day!! (They said that they don't typically do this, but they had already gone through most of their candidates and were pretty confident that I was the best fit for what they were looking for.) Considering that at that point, I had already fallen in love with the school, I am really glad this was the outcome, because otherwise I would have probably felt totally crushed over a rejection.

I would have been happy to commute for a long time to work at a school like this, but it turns out that this school is actually in a fabulous location, right downtown! I'll be able to walk to work easily, which is an amazing perk for both Geoff and me.

I am very happy with this job-search outcome, and I look forward to a fabulous year! Geoff and I plan to stick around Seattle for a while (probably until our babies grow up to an age where it's appropriate for us to take them abroad), so I'm extra glad that I've found a school that I think I would be happy to stay at, for the duration of that whole time.

PS. By the way, as part of my interview day I had done two demo lessons for them. Despite having run out of time, I really liked the trig lesson that I planned (, and I think that in the future, when I start teaching PreCalc again, it could be fleshed out into a multi-day technology project for the kids. During the demo, since we didn't have time for each kid to build their own ferris wheel animation, I simply pulled this up to show what is possible, given their understanding of circular modeling and parametric equations. In a multi-day project, we'd start with analyzing / building a ferris wheel together, and then from there on they would create their own story involving circular rotation and minimizing / maximizing distances, and model accordingly.

PPS. An example of why this school is a great fit for me is that they were actually amused and delighted that I had negotiated with them for a better demo lesson topic. For some other schools, that could have been a deal breaker, but for them, they liked that I had a preference and an opinion about the relative boringness of topics, and they also liked that I tried to choose a less-dense topic that allowed me to showcase different ways to engage students instead of requiring me to stand at the board for most of the period. My kind of people!