CMC North 2018: Reflections Part 2

Part 1 reflections are here.

Session 2

The theme of CMC North this year was "Student Voice, Let's Hear It!" I don't think you'll find a math educator that can disagree with this statement, and it was great to be able to spend an hour with Paul Jorgens and Richard Hung exploring different strategies and activities to promote student voice. You can access resources from their session, titled Fire Up The Math Classroom With Conversation, here.

I am grateful for the opportunities I've had lately to deepen my understanding of why student voice is so important. For Paul Jorgens and Richard Hung, student voice is an essential part of how their school is working to close the achievement gap. For many schools, the path to closing the achievement gap lies in creating support classes, intervention classes, after school programs, summer opportunities, etc. These are all important. But what you do during the time you have students in your class is equally important, and that was the purpose of Paul and Richard's session. Their course team is intentional about planning opportunities for classroom conversation throughout each unit. During the session we worked through WODB problems, Open Middle problems, as well as strategies they use to launch data lessons. I don't feel like I can do justice to this experience in a blogpost. Fortunately Paul has written about how he uses WODB and Open Middle problems using Desmos as a tool to support student understanding. I also recommend checking out Paul's Desmos activity on categorical data where students explore the impact of the Voting Rights Act of 1965. When exploring this and other data, Paul doesn't immediately include the context. Instead, he invites students to notice and wonder and do some computations before revealing the contexts.

Perhaps my biggest takeaway was the importance of giving students a chance to use their own language to describe things before we give them the words we want them to use. For me, an added bonus of building in social experiences to practice vocabulary is that students learn that their ideas matter, and that there isn't just one right answer in a math class.

If you want 180 ideas from Paul for supporting students, check out his #teach180 resources from the 2017-2018 school year. And if you want 180 more ideas consider following Paul and Richard on Twitter for their 2018-2019 #teach180 ideas.

Session 3

Scott Davidson and Ethan Weker led a session on 3D printing. When I am learning about a new tech tool, I find it helpful to know some of the What, Why, and How of the tool. This session delivered in a really nice way on all three of these categories. Scott showed us how his students use a free program called Tinkercad to make name cards in his class. Ethan shared some of his student work from an assignment where he has them make their names in Desmos to 3D print. He has found that students made much more interesting designs for the name project vs before it was 3D printed because students knew they would have something to take home. Student ownership for the win!

In addition to student made products, we learned how teachers can 3D print their own manipulative. We played with 3D printed dice and learned that they were unfair, first by experimentation, and then by inspection. Ethan showed us a really interesting manipulative that helps explain why adjusting the b value in the standard form of a parabola moves the vertex in an parabolic path.

Teachers are creating and sharing designs for their own 3D printed manipulative at Thingiverse.

Session 4
Jenny Wales and I presented "Designing with Desmos" during this time. Always a blast presenting with Jenny! Thank you to everyone that came to our session!

Session 5

I went to a session on story tables led by Shira Helft and Taryn Pritchard. I didn't take any notes during this session because we spent nearly the whole time doing math! Really glad I had the chance to learn about this tool, which Shira and Taryn compared to a knife (practical and multi-use). You can use story tables to help students make sense of any function type, and they can be used to help students understand the relationship between the graph of a function and solving equations that involve that function type. Not only that, the story table helps students develop an intuitive understanding of how the order of operations plays out when solving equations.

Check out Shira's Global Math Department Webinar on story tables if you want to learn more.

Thanks to all of the presenters for helping us learn, and to all of the organizers for making CMC possible! Always a great time and top notch experience.

CMC North 2018: Reflections Part 1

I was fortunate enough this year to be able to attend (again!) my favorite math conference, which is CMC North at the Asilomar Conference Grounds. The view, the people, and the sessions are always great, and I always leave with a full head and a full heart.

This post is mostly a reflection and a record for me to look back at, but I hope it can be helpful to others as well. If you see something interesting in here and you'd like to know more, please reach out!

Session 1
I went to see Juan Gomez talk about tools he uses to promote student inquiry in his class. He talked about the importance of differentiation, and gave us ideas and examples for differentiating process, content, and product.

Differentiating the Process

We looked at Graspable Math as an example of how a teacher can differentiate the process by which students learn. One example we looked at consisted of graphing a polynomial function and using the scrubber tool to change an exponent. This allowed us to see the graph change, and we could compare to the original graph.

Differentiating the Content

We looked at a Desmos activity by Jon Orr called Pumpkin TimeBomb Prediction. In this activity students use scatterplots and relationships to predict the number of rubber bands wrapped around a pumpkin it will take to make the pumpkin explode. (Check out the results here.)

Next up we looked at CODAP, which is a free online data analysis software. Really interesting and powerful. Lots of ready to use data. One interaction that seemed really useful is that you could click on a point in the scatter plot of a large data set, and CODAP would auto-scroll to that data point in the table. Another feature that Juan showed us was that you can upload a csv file with your data, and then use the program to draw random samples from it.

Juan shared the Desmos Halloween Coloring Book project by Luke Walsh as an example of differentiating the product of learning. Luke had his students make halloween themed art using the function types they were learning about. Check out their work!

We ended by looking at Paul Jorgen's "My Wedding Dance Dilemna: Shout." In this activity, we use math modeling to make a dancer move to the different parts of the song Shout. This had us all giggling out loud. A powerful aspect of this activity is that you can revise your wedding dancer's movement and check your thinking. Students begin by sketching the height of the dancer over time before moving into more formal thinking of using equations to represent the height over time.

Juan helped us summarize our thinking at the end of the session and reiterated that his goal as a teacher is to be able to think flexibly in the moment and have tools that allow for that flexibility. 

As I was looking through my notes, I found this: 

"How can I do the pumpkin activity and still teach my content?" 

I believe this was a question asked by a participant in the session. Leaving this here as an open question to consider in the future. 

Desmos Animation 101: Part 2

Suzanne von Oy shared a graph titled The Tree of All Seasons awhile back as one of her #graphjam submissions. It's mesmerizing at the very least, and left quite a few of us wishing for a Desmos art course so Suzanne can teach us her magic.

I look forward to this course, but as I dove into the graph, I found myself quickly overwhelmed. So many variables and functions. I wasn't sure where to start with understanding the various parts. This left me wondering what the different parts are of the Desmos art course that will allow me to build this (and any) awesome graph.

So where would the course start? There are quite a few things going on just with the flowers in The Tree of All Seasons graph.

1. The flowers are all different sizes. Suzanne uses exactly one image to render all of the flowers, so I'm curious as to how she made them all different sizes.
2. The flowers start growing at different times. They start falling at different times. They start shrinking at different times. I imagine these are all related somehow.
3. Once the flowers shrink down to size zero, they stay at that size throughout the animation.

In my first post, I looked at the way in which we can control the size of the flowers using a function. In this post, I want to look at the way in which we can control the timing for which the flowers bloom and shrink.

I stared at this line of Suzanne's graph for a really long time.

After breaking it down and figuring out that the first expression (in parenthesis) assigns each flower its length and width depending on its y-value, I looked at the second expression and thought about what it does:

If I graph this I see the following:

This graph assigns a "size" to the flowers depending on time. It essentially says the flowers will grow from size 0 to full size (or size 1) in a certain amount of time. Then the flowers will stay full sized for a different amount of time, after which they will shrink down to size 0 and stay that size throughout the animation. Super useful!

Question: What are other uses of this function that people might explore before working on the The Tree of All Seasons problem?

Note: I am interested in exploring what a Desmos art/animation course would look like for personal reasons, but also I am interested in exploring what it would look like because I'd love to see a course like this offered at the high school or college level as a math elective.