Des-blog

Applications for Cohort 4 of the Desmos Fellowship are now open, and we think you should apply! Here’s what our current Desmos Fellows are saying about the Desmos Fellowship:

• Desmos Fellows weekend was the most amazing professional development I have ever experienced as a math educator. It is difficult to find PD that is a room packed with people so passionate about how we help students learn math and how the technology of Desmos has completely changed how we can do it.
• Desmos Fellows are the math department we all dream about. Supportive, collaborative, caring, and innovative. I strive to create experiences that parallel the experience I had over the Fellows weekend. I didn’t want it to stop and although the weekend did, the support didn’t.
• I was so grateful for all the Desmos knowledge I gained, but more than that I was inspired by the exceptional collection of math teachers. The fellowship felt more personal and impactful than any other PD I’ve attended. The weekend created long lasting connections, both mathematical and professional.

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Let’s say you want to draw a line segment that connects two movable points. You can write your line in point-slope form, use the changing coordinates of the movable points as parameters in the equation, restrict the domain, and you’re good to go.



But what about when the point on the right becomes the point on the left? Now your domain is bad so you need a workaround. Easy peasy—just make a second line segment with the domain restriction switched: less than becomes greater than and you’re back up and running.



Wait. What if the points are aligned vertically? Now you need a third, and maybe even a fourth expression. That’s a lot of work for a line segment, and it is why you will be delighted to learn about this week’s Friday Fave: parametrically defined curves.

Here’s the idea: You want your line segment to begin at one of the movable points, and end up at the other one. If you can make a POINT do that, like so…



…then you can use the parameter t to trace out ALL of those points.



Now it doesn’t matter which point is to the left or the right; and it doesn’t matter if they’re vertically aligned. In the latter case, the x-distance between the points is 0 so the x-coordinate will remain constant for all values of t.

With time and practice, this way of thinking will become natural—make a point move from one place to another, then use t to define the entire path. Pretty soon, you’ll be tracing all kinds of fun paths!
That’s why parametric curves in the graphing calculator are this week’s Friday Fave!

We learn through relationships and connections with each other. Teachers can build these relationships by valuing students’ ideas,making connections, and building on these ideas. As a result, students learn that they have ideas that are worthy of consideration, and they learn to consider the perspectives of their peers.

How do we get students to feel safe and share their ideas?

Desmos designs activities that are easy to start and difficult to finish so that all students can understand the task and contribute to the learning of the class. Tasks using this structure help ensure equity in the class since students are building mathematics that comes from their own understanding.

Anonymize is a Desmos tool that replaces students’ names with mathematicians’ names. When students work in a Desmos activity they can share their ideas and the teacher can use students’ responses to facilitate discussion while keeping each student’s identity hidden.



On some Desmos screens, after a student shares a response, they get to see the responses of three of their classmates, and revise their own thoughts if they choose.




With the snapshot tool, teachers can record student work—either different strategies for the same solution or entirely different solutions—present this student work in collections to the class, and use the thinking of the students in the room to facilitate class conversations around the content.



When students feel that their ideas are valued, they become more likely to share their ideas, leading to a increasing diversity of ideas shared in each lesson. Students’ ideas are this week’s Friday Fave.

Here are four activities for eliciting students’ ideas in your classroom:
Avi and Benita’s Repair Shop
Point Collector: Lines
Picture Perfect
Translations with Coordinates