Like all schools, my school has committees. And, like all schools, my school has a student government. But, unlike other schools, our student government is a single body: the Student Senate, comprised of one representative from each advisory. This year, the Student Senate split into subcommittees to align themselves with the faculty standing committees. I’m on the Academics Committee – the group charged with looking at curriculum & standards and how they are aligned. On Monday, we met with the Senate subcommittee during lunch to discuss different ways that students can demonstrate what they’ve learned. We talked about the possibility of students creating portfolios and presenting their portfolios to teachers in a particular learning area to have them assess which standards the student has met, and to what level. So, while the teachers keep working on tightening up our standards & curriculum (we’re halfway through year three), our students are developing a portfolio review process.
It would appear that I can’t resist a challenge from the #MTBoS. And so, this January, I’ve been challenged to update my “About Me” page. Feel free to check it out. I’ve updated it with a bit about the school where I teach and what happens when I talk about teaching at a public charter high school.
By the way, we will be graduating our first class this year, and that’s pretty exciting. Even more exciting is the fact that they’re actually getting accepted to college! (Of course they are. But as the first group, this is still pretty exciting for us.)
I’m hoping to blog a bit more this year. A bit more than once a month (or less). But I’m not promising anything. I’m still building brand new classes – which takes a ton of time. I have a couple of drafts still in the pipeline that need some attention. Maybe I’ll get to them soon.
In the meantime. Thanks for the push #MTBoS (and Tina C). And Happy New Year!
This week I begin Exploring the MathTwitterBlogosphere. I’m looking forward to these missions and challenges because I need someone pushing me to find the time to write in this blog. It’s good for me. Like spinach.
This week’s mission: What is one of your favorite open-ended/rich problems? How do you use it in your classroom?
One of my favorite open-ended/rich problems comes at the end of a unit on trigonometric functions. After exploring, transforming, and applying trig functions to Ferris wheels, tides, pendulums, sound waves, … I assess my students’ understanding by giving them some almanac data of sunrise and sunset times for a specific location on Earth. Their job is to analyze the data and create a trig function to model either sunrise times, sunset times, or hours of daylight – their choice.
The data looks like this
and that makes it somewhat challenging for students to even begin. They are reminded that they should have “enough” data to know if the model they develop fits well. I point out that the times are given to them in hours and minutes, but that they probably want a single unit (hours or minutes after midnight). From there, they are on their own to solve the problem. Usually, they work with a partner.
In the classes that I’ve used this task with, we’ve modified the amplitude, period, and midline of the sine and cosine functions. We haven’t introduced phase shift, yet. So, there is also a reminder about selecting a convenient “Day 0” for the function they choose to model with.
What I love about this task:
- Students are talking math, asking each other about the number of data points they should use: “Should we just pick the same day every month? Are 12 data points enough?” or “Do we just go every 20th day?” or “What should we use for the first day?”
- Students are problem solving. They have to convert the times into a single unit. They have to make decisions about which variable to model, when to start, which type of model to use. Then, they can collect the relevant information to modify their chosen function.
- Students are using technology. Although they don’t have to, it’s really easiest to have the kids making scatterplots on calculators or computers and then graphing their model on top of that. Then they have a built in way to check their work – they don’t have to ask me (the teacher) if they are correct. It shows up in the picture that they create.
- Students think that working with trig models is really hard, so they feel very proud when they are able to complete this task without any help from the teacher.
- It’s really easy to grade. Either the model fits or it doesn’t. Kids turn in their data tables and work showing how they calculated the necessary values for their model. This precludes anyone from using the old SinReg command.
- Even though I’ve used this task for about ten years, it’s a perfect fit with the Common Core math standards (trigonometric functions) and practices. And since I live in a SBG world, this is a very good thing.
My favorite kind of assessment is one where students have to apply what they’ve learned to a different situation. Even though we create lots of different trig models in class, sunrise, sunset, and daylight hours represent a new application. And a new challenge.