Des-blog

Feedback comes in many forms. We can give feedback by evaluating a response as correct or incorrect in order to report a score. Alternatively, we can reflect back what we hear from another person, support them in considering if that is what they really mean, and allow them to make revisions until what they are trying to communicate is consistent with how it is being received.

In Land the Plane, students see that their slope is incorrect if the plane doesn’t land on the runway. They can refine their thinking in an effort to be successful - and to learn how to compute the slope of a line.

In Match my Parabola, Students see the parabola that corresponds to an equation they submit. Students are empowered to use this feedback to modify their equation, and move on when they are satisfied, resulting in increased student learning and motivation.

In Laser Challenge, students see the angles they selected cause a laser and mirror to animate to get feedback on the accuracy of their predictions. Through revisions, students develop their intuition for angle measures and properties of reflections.

Being told an answer hinders motivation and discourages revision. It implies that someone else already knows the answer and that your thinking is insufficient.

Being shown what you’re saying without judgment supports thinking more deeply. It can make the goal feel attainable which encourages learning through revision. That’s why interpretive feedback is this week’s Friday Fave.

The Friday Fave is a big fan of tasks with more than one right answer. If the Fave asks Which One Doesn’t Belong? you’d better believe each of the options can be a right answer. If the Fave asks How do you know? well, it’s because the Fave really doesn’t know how you know, but really would like to, and there’s more than one right way of knowing.

So it is with the newest Desmos activity, Coin Capture. The challenge is write equations for lines that go through the coins, capturing them along the way.

In the introductory challenge, you can get them all with one line. But that’s just Desmos getting you started. As the screen numbers increase, so does the complexity of the challenge. Here are four solutions to the challenge on screen 3.

While we keep track of the number of lines you used, that’s not the only way to describe these. What kinds of thinking is behind each of the solutions above? Which is most interesting? Which one doesn’t belong? Posing the task is straightforward, but there are many right answers that vary in interesting ways. That’s the kind of thing that qualifies an activity for the Friday Fave.

Also there’s a challenge creator.

Now, while you’re thinking about coins and/or targets in the coordinate plane, here are three more delightful activities:

Penny Circle

Marbleslides: Lines

Mini Golf Marbleslides

The bell has rung, your classmates have settled into their seats, and the teacher stands at the front of the class next to a chalkboard and overhead projector, ready to deliver today’s lesson.

“All right, everyone,” she announces while gesturing towards the blank chalkboard, “please solve these equations using your handheld calculators– the ones with the broken displays.”

This assignment may sound outlandish, but students with visual impairments face similar challenges using technology in the math classroom every day. New technologies have the potential to empower students, but without care, they may instead present insurmountable barriers to access.

Our mission at Desmos is to help every student learn math and love learning math. Not some students. Every student. With that in mind, we introduced improvements to the calculator to ensure students who are blind or visually impaired have the same opportunities as their peers to discover the joy of learning math. Thanks to technologies like screen readers (which provide spoken or Braille feedback to mainstream computers, tablets, and phones), people who are blind or low vision have the opportunity to use the exact same programs as their peers. Naturally, it made sense to extend the utility of our existing calculator offerings to include screen reader support.

More recently, we extended this functionality to our activities, modifying them to meet the highest possible standard of accessibility our tools can offer. You can find all the screen-reader friendly activities here, or by visiting teacher.desmos.com and typing “screen reader” or “accessible” into the search bar.

So how did we make this happen? Many of the components of a Desmos activity have built in accessibility, meaning that you can interact with them via the keyboard and a screen reader. We added to this accessibility by adding narrations to graph screens to help students learn about a graph, interact with it, and receive feedback.

In this screen from Match My Line, when a student submits a correct equation, the screen reader tells them the number of lines that have been correctly graphed.

Students can also use the audio trace functionality from the graphing calculator to learn more about a graph within an activity.

Interested in learning more about Desmos accessibility? Get started at learn.desmos.com/accessibility, then dive deeper by watching our Introduction to the Desmos Graphing Calculator and Accessibility Tools webinar and heading to www.desmos.com/accessibility.

We’d love to hear your feedback! Let us know what you think at accessibility@desmos.com.