Des-blog

This week the Desmos Fellows shared ways in which they “go over” or review a Desmos Activity to help students summarize and reflect on learning. We shared a variety of strategies, some of which take place during the activity and others that take place at the end or even the next day.

Leveraging Partial Understanding to Reflect on Learning

• Tony Riehl monitors student work on an iPad as he circulates the classroom. This allows him to check in with individuals or groups and help them as needed.
  
• Paul Jorgens is flexible in how he helps students reflect on their learning. He shares that reviewing an activity starts with the learning target and continues with the formative assessment. “Sometimes it makes sense that the formative assessment is within the activity and sometimes it might be outside or both. Perhaps there is a screen at some point that gets at the heart of that target. In that case, I will use teacher pacing and we will look at that screen together considering misconceptions and variety of approaches to close the lesson.”
  
• Allison Krasnow, Dave Sabol, and Shelley Carranza all shared next day strategies for helping students to reflect.
• Allison builds a new 1-2 slide activity that incorporates some of her favorite mistakes and asks students to collaboratively improve or correct the work. This strategy was inspired by My Favorite No from the Teaching Channel.
• Dave has reviewed homework using partially correct responses from a Desmos homework assignment. He had students discuss the slide below in groups and share out with the class.

• Shelley linked to an NCTM article by Martin Joyce in which he shares his strategy for extending a Desmos lesson. Martin printed out anonymized responses to a Marbleslides screen and had students provide peer feedback on the responses.
• Jenn Vadnais acknowledges that theses strategies help develop a culture of inquiry, conversation and sense-making, and she is hoping to share such strategies in workshops in her district.
  

Accessing Prior Knowledge and Connecting to New Learning

• Bob Lochel recently used a Desmos activity to unlock previous student understanding. He paused the class a few screens in to lead a guided discussion that would help students access material in a new unit.
  
• Lisa Bejarano uses Desmos activities as a visual starting point to introduce a topic, providing a graphical representation of a concept. After the activity students add notes to a composition book to determine what the concept looks like analytically, and then relate back to the graphical representation.
  
• Scott Miller helps students reflect by selecting and sequencing responses from less sophisticated to more sophisticated. He strategically displays the responses in that order so the class can discuss and build on each other’s reasoning.
  
• Anna Scholl has helped students build connections and summarize learning by exploring special quadratics using Desmos and a worksheet. Some students commented that completing the Desmos Activity first helped them understand the problems on the worksheet better because they understood the connections between representations.
  

Exit Tickets to Reflect on Learning and Plan Next Steps

Ayanna Ramsey, Heather Bolur, and Nerissa Gerodias have all used exit tickets at the end of a Desmos activity to help students reflect on their learning.

• Ayanna uses the results to help her go over misconceptions in small groups or with individuals.
  
• Heather Bolur uses pause during the activity to go over common errors, highlight student responses, or show the overlay. She then uses exit slips on paper that align with concepts in the activity.
  
• Nerissa projects her dashboard and switches between Responses and Graph Overlay to see if anyone needs help. She ends with a class discussion followed by a reflection screen where students write what they learned from the exploration.

What are some other ways in which we can review a Desmos activity? Let us know on Twitter @desmos.

This video is a math teacher’s dream.

So many possible questions, including How long will it take to mow the whole lawn? But before you can answer that sort of question, you’d better make sure you’ve got the set-up right.

That’s where Lawnmower Math comes in. We set the virtual stake nice and deep in the calculator’s ground. You decide how big that stake should be. What math do you need to know in order to mow both completely and efficiently?

Students estimate.

Then they calculate, and then generalize. Building algebraic understanding on top of numerical relationships is what this summertime, lemonade-sipping, lawn mowing version of Central Park is all about.

It’s challenging and beautiful—you and your Algebra, Precalculus, and Calculus students should give it a whirl.

One way that teachers support student learning during a Desmos activity is by facilitating classroom conversations. This week the Desmos Fellows considered ways to plan for those conversations by looking at a teacher dashboard with sample student work. We looked at Linear Systems: Gym Membership, which asks students to analyze several gym membership plans in order to make a recommendation to a friend.

We focused on the questions below to help us discuss the role of the teacher during the activity:

• Where would you pause for classroom conversation? How might this conversation support the goals of the activity?
  
• How would you prioritize which conversations to have with the class?
  
• Which single screen has the potential for the most powerful conversation to support activity goals and student learning?
  

Here’s our analysis:

Screens 1-3

These screens provide access to the context, and involve the students in developing the problem. There was also a general consensus that Screen 3 offers the greatest potential for class conversation.

• Jade White shares with us that “Screen 2 would be a great first place to pause; most students should have familiarity with gym memberships but checking in on this screen to ensure that they understand the context of the problem will help them understand the context of the math when they get there.” Jade appreciates that Screen 3 offers students a chance to ask their own questions, which can help students feel more comfortable asking questions in general.
  
• Serge Ballif points out that students need to understand the considerations from Screens 1-3 if they are to appreciate the rest of the activity. Pausing for clarification sets students up for success in the latter half of the activity.
  
• Stephanie Blair and a colleague planned to extend the work on Screen 3 by having students look at all of the questions from the class, perhaps using Anonymous Mode. From there students would choose the question they thought was best, justify their choice, and explain how they would use the information they got from the question to help Mateo choose a gym membership plan.
• Anna Scholl likes this screen coming early in the activity because students can discuss and “know” their answer, and then dive into how to show their answer visually, possibly with multiple representations.

Screen 4

The prompt for Screen 4 is to “Use Desmos to create a visual tool to help Mateo decide which gym membership to choose.” Here students will represent their mathematical thinking using either a graph, table, or equations. Student work for this screen leaves room for interpretation of what students understand and are still developing ideas around, and for that reason Screen 4 is our second place winner for classroom conversation potential.

• Jenn Vadnais would use this screen to highlight multiple representations by connecting a table and equation with the graph. Using points in addition to lines will help our concrete thinkers clearly see the monthly markers.
  
• Linda Saeta wants to make sure students understand what their models tell them about the world. Questions such as “After 3 months, what does your model say will be the cost of the three plans?” help us gauge whether or not students understand the connection between the model and the scenario.
  
• Scott Miller suggests pausing on Screen 4 to have students discuss and explain the change in scale that they made. This allows students that found an answer without using the graph to see another way of thinking that wasn’t accessible to them before changing the axes. Jade White points out that students may also make different decisions about what x and y represent, so discussing the graph on this screen can be especially illuminating.
• Paul Jorgens offers ideas around how to proceed when students need additional support. His strategy is to get two groups with different responses together and have them reason it out. “It might be a time to huddle with some groups as they work. In closure, I think I would mock up a misconception (or 2) on a preview of screen 4 and reason together with the class and then end sharing thoughts about best plan on Screen 5.”
  

Screen 5

• Nick Corley would give his students a chance to debate their answers, and to discuss if there is a right or wrong answer. Using the dashboard to select and sequence student responses can be powerful in facilitating this discussion.
  

Screen 7

• Jade White shares that her priority conversations would be on slides 5 and 7 around a deeper understanding of systems of equations and the significance of the intersection point. Screen 7 ties everything together by having students identify the slope and y-intercept and their significance as well as graphing two lines that have a specific intersection point.
  

These are just some of the ways that a teacher can play an active role in shaping student learning during a digital activity. What are some other teacher moves we might consider in this activity and in others? Let us know on Twitter @desmos.