Rose Curves, Tattoos, and Weekly Journals

Last year and the year before, I stared every Thursday’s class with a journal entry. The students wrote to me in response to the questions “how was your week?,” and “what did we do?,” as well as some third thing. This third thing was almost always a writing prompt about the math that we had done that week, or that we were about to do. Then I wrote back to them on little post-it notes. It created this nice sense of ownership of their learning, offered them a chance to reflect on and write about their week of mathematics, and provided a space to give me feedback about the class. I would always dread reading these on weeks I had deemed bad, but nobody ever wrote anything terribly negative.

Towards the end of last year I stopped doing this. I felt that it was taking too much time out of the day Thursday, which at our school is only scheduled to last 30 minutes (impossibly short!). I also felt that writing only one day out of the week wasn’t organic since the most prompt-worthy topics might have been covered on Monday. I told myself I would have them stop and write every week whenever it seemed like a good time to put math into sentences, but since the schedule wasn’t forcing me to do it, I hadn’t been since.

NEW SOLUTION: weekly journals will still be due each week, but there is no specific class time carved out to do them. They are expected by class on Monday, and students can do them after school, in the morning, over the weekend, and whenever they get done early in class. I will see if it works and let you know. I already got a “good luck with that” from one fellow teacher.

I polled the math 4 students about journals (yes or no about bringing them back) on an assignment from Monday involving plenty of purposeful writing. I will likely do a whole separate post about that because my polar unit got really excellent this year, but basically they had to discuss the visual and numeric patterns of the number of petals on rose curves with fractional coefficients. This is the best visual that I have found for that. I summarized the results on excel:

tats roses

In addition to the more mathematical questions, I asked them about the journal (the aye’s have it! good thing I was going to re-institute it anyway!) and which rose curve I should get as a tattoo. Yet another thing to stay tuned for – new math tattoo!

My major conclusion right now is that I should do more polls. When I was in high school we would do this thing we called “carpool car poll” where anyone could just declare a poll and we’d all have to say our opinions on a topic. I want a catchy phrase like that and more chances to give opinions.

Advertisements

Summer PD Part II

Flipping the calendar to August and seeing the words “retreat and teacher workdays” on the page was a little bit of a shock, I have to say. But I’m feeling more and more ready. I’ve been at work on my arts integration plan.

I found out about the the national core standards during a Kennedy Center workshop, and so I just read through them. This was extremely helpful to me because they bring up questions and concepts I would have never thought of. For example, the idea that students should be planning their project and choosing an appropriate medium makes a lot of sense, but it’s not something I’ve been having them do. If I introduce a math/art thing, I usually just tell them what to do and how to do it, then help them with the math if they need it.

The concept behind arts integration is that the students learn an art form and the math content in ways that are “mutually reinforcing.” The art standard that most closely mirrored a math standard was “Through experimentation, practice, and persistence, demonstrate acquisition of skills and knowledge in a chosen art form,” which could reinforce and be reinforced by “Make sense of problems and persevere in solving them.” I love the wording behind both of these because they don’t expect us to be talented or to find clarity instantly, they encourage us to keep working even if things aren’t coming naturally. That’s a huge issue in both math and art, the notion that it’s only for people with a natural aptitude.

The project that I’m most excited about trying next year is a rose curve/ op art/ colored pencil task. In the past I’ve just told students “a rose curve is in the form r = a sin (theta b)” and told them what a and b do. Then I’ve taught them the other types of polar graphs similarly, with notes. This year I want them to investigate using different coefficients to see what types of graphs are created, then generalize. Then I want them to choose two and color them either in black and white, or in colored pencils, and explain why they chose the graphs they chose. I made some examples and they look pretty neat.

rose color rose op

I just really want to make sure that when we’re doing this, they understand a) what polar graphs are, and the different categories they fall into b) what types of equations generate rose curves c) good colored-pencil techniques so that these actually look decent [my example could totally be better] d) what would create an appealing black-and-white “op-art” style piece [so why would I not have chosen the first curve to color in black and white]

Once we’ve got all that, then we can talk about fun things like converting between rectangular and polar. The company I’m tutoring with lets us write problem sets for $$$, and I just wrote a bunch of those problems. I hadn’t done that math in a while and it’s actually great.

In terms of other arts integration stuff, I still need a lot of help with my sine curves/ jazz unit, and I’m also developing a similar figures/ architectural drawing project, right now mainly by reading through all the architectural drawing books at the library. Stay tuned for whatever I end up with!

A quick love letter to Desmos

Desmos is so lovely. Unlike GeoGebra, which is great, too, it can graph polar things!

desmos polar

It is super user-friendly: to get theta you can click the button for it, or you can just type “theta” and it knows what you mean. It is very easy to edit and delete functions. Making a slider is as easy as typing a non-variable letter and just clicking on it. Idea that I’m having too late: type in r = 2 + bsin(theta) and drag the slider to show how cardioids and limaçons and the loopy ones are related!

I had the students do an investigation about polar graphs in pairs. Last year I gave them some work ahead of time about what polar coordinates were, but I decided to postpone that this time. I thought it might be better to let them discover more on their own.

I’m attaching my PDFs, but mainly I just gave them a good amount of each type of equations and asked them to sort and then to generalize.

I cut these functions out and put them in an envelope: polar task chart and functions
These are the instructions: polar task

Polar Graphing

I’m teaching a Math 4 class that is almost entirely collaborative tasks. Common Core has less guidance for an integrated fourth course, so I’m feeling free to teach whatever strikes my interest. Honestly, at times this is overwhelming – there’s a lot of math out there in the world! But I’m pleased with the way things are going. I’m using this as an opportunity to teach visually interesting, complex topics. This week they worked with polar coordinates. I had each group use a computer program to graph 20 functions, then sort them into 4 different groups based on their shapes.

This worked really well as an introduction to the different types of polar functions. They discovered not only their basic shapes, but the general equations that create them.

The next day I had them explain the different shapes and the equations that form them, and we determined what impact each component of the equation has on the shape. I love these things!

Cardioids:

Image

Spirals:

Image

Circles:

Image

Rose Curves:

Image