This week in the fellows’ lounge we looked at Desmos activities that didn’t work, and considered ways to improve those activities.

Whether it’s an activity that you made or that someone else made, reasons why a Desmos activity may fall flat will vary. Many elements of planning to teach a digital lesson will be the same as a paper lesson, while others will be different. Suzanne von Oy had a recent experience in which she reflected that having an appropriate activity to introduce students to Desmos would have been helpful before diving into a content based lesson. Bob Lochel offers additional planning advice: “My general comment is that I find Activity Builders require rehearsal - you need to move away from what your ideal lesson would look like as an educator and think like a student. Do the instructions make sense? Does the next task make logical sense given previous screens? Is there sufficient opportunity to reflect upon how screens connect together?”

Jenn Vadnais observed in a recent activity that the tool that she had developed to help students explore percent was challenging to use. Sometimes additional modeling of how to use the tool can help students be successful, and in other cases it is better to consider redesigning the tool.

The design of individual screens and interactions is important to reflect on, as well as the flow of the entire activity. Activity design can play a big role in whether or not an activity will help students learn. Allison Krasnow supports coaches in her district as they work to implement a new curriculum. They recently converted a paper card sort from the curriculum into a Desmos card sort. The result: students engaged in more mathematical conversation than if they had worked in workbooks, but the nature of the card sort was such that there was a right and a wrong answer. In this way students that didn’t know how to do the math when they started the activity didn’t get as much out of the experience as hoped. Allison is reflecting on how to use some of the mathematics of the new curriculum along with Activity Builder to help shift pedagogy and help students learn math at a deeper level. For example, adding a screen to a card sort asking students to settle a dispute over how a hypothetical classmate sorted cards can make for rich discussion and opportunity to correct introductory conceptions of the math topic.

In the past Paul Jorgens has had his students recreate simple designs using a graphing calculator. He found when he converted the challenge to Activity Builder that the activity didn’t capture their interest. His prognosis: the ease with which students can explore graphs with sliders made the Desmos version too easy. His students rescued the activity in the end by imposing rules for themselves about graphing the designs with as few equations as possible, therefore introducing a need for strategy. The Desmos Activity Building Code supports integrating this type of strategy into practice.

Anna Scholl’s students struggled with an activity that didn’t offer enough scaffolding and jumped quickly into abstract thinking. Heather Kohn experienced a similar struggle with a screen that asked students to generalize their thinking around exploration on a series of screens. From the design perspective it may be helpful to add a card sort before a generalization screen which helps students compare and contrast samples of screens that they have explored. Another option is to combine the visuals either on the whiteboard or on a slide and structure a class conversation around these visuals so that students can build on their previous thinking as they work towards generalizing a formula.

Ayanna Ramsey has noticed at times that her students will skip screens, which could interfere with their ability to complete tasks later in the activity. She wishes for required screens such as what we see with Google Forms. While that feature isn’t currently available, we can plan for key screens where teacher pause or pacing can be used to ensure that students get feedback that sets them up for success for the rest of the activity.

What are some other things to consider as we work to improve our activities? Let us know on Twitter @desmos.

This week we invited the fellows to share ways that they are using Desmos for assessment purposes. While many had never used Desmos for assessment, those who had did so in unique and interesting ways. Some examples include:

• Gerald Smith and Paul Jorgens have considered Desmos for part II of a test, where the topics aren’t as easily assessed on paper. Such is the case for problems that involve analyzing a set of graphs or creating graphs as part of a more open ended problem.
  
• Serge Ballif teaches a course that uses Desmos for all exams. Students in his class spend very little time on the mechanics of solving equations, because Desmos will solve for them. Instead the class focus is on setting up equations and models and interpreting solutions.
  
• Projects! Sarah Blick Vandivort has her students using Desmos to produce a graph as part of a project on linear systems. Linda Saeta, Anna Scholl, and Jade White have used Des-Art to assess student understanding of equations of lines and other function transformations.
  
• Tony Riehl’s students completed their first semester final exam review on Desmos. Access to data helped Tony determine areas where students needed additional review.
  
• Nick Corley has considered designing activities to help students practice for the PARCC exam.
  

Nolan Doyle pushed us mid-discussion to consider why we are using Desmos as an assessment tool, and to be purposeful in choosing ways to incorporate it. He wants his students to view Desmos first and foremost as a tool to help them explore math and make discoveries on their own, and wonders if students may view Desmos differently if used on assessments.

Some of the fellows are using Desmos on both formative and summative assessments in order to collect and learn from the data. Paul Jorgen’s PLC routinely uses data from activity builder dashboards to assess student understanding of topics and decide on activity revisions and next steps. Scott Miller noticed through looking at data that analyzing the graph responses helps clarify what misconceptions students have around more open ended tasks.

Even with the ease of collecting data, many of us wondered about logistics. Julie Reulbach shared her midterm with us, which included a mix of responses submitted on paper and on Desmos. Another idea for logistics and test security was to keep test problems on paper and have students submit answers only in a Desmos Activity.

What ideas have you tried? Let us know on Twitter @desmos.

In this week’s prompt we asked the fellows give this activity a makeover, increasing its depth, demand, or delight, by adding just one screen.

Though the makeover screens varied widely depending on lesson objective and course level, there were commonalities in how the fellows used Desmos to add value.

• They connected representations.
  
• They gave students opportunities to be right and wrong in different, interesting ways.
  
• They created activities that are easy to start and difficult to finish.
  
• They created objects that promote mathematical conversations between teachers and students.
  

(These are all elements in our activity building code.)

Connect representations.

Dan Anderson, Stephanie Blair, Sarah Blick Vandivort, Meg Craig, Nolan Doyle, Adam Poetzel, Julie Reulbach, Linda Saeta, and Suzanne von Oy all used a graph to help students connect the algebraic representation of functions to the graphical representations of functions. Directions on these screens asked students to represent various values of a given function. The way in which students would respond ranged from less formal representations such as dragging or sketching points to the more formal representation of plotting a point by typing its coordinates. Several of the fellows also made use of color and styling to help students interpret a graph or display understanding.

Give students opportunities to be right and wrong in different, interesting ways.

Dave Sabol and Jenn Vadnais included a table of values to help students reason about function operations and composition. In Jade White’s screen students can take a numerical or algebraic approach allowing them to get to the answer in a number of ways, creating an opportunity for rich class discussions.

Create activities that are easy to start and difficult to finish.

Mark Alvaro and Dave Sabol added challenge screens to our original activity, making it easy to start and difficult to finish.

Try your hand at Dave’s Marbleslides challenge here.

Create objects that promote mathematical conversations between teachers and students.

Serge Ballif, Nick Corley, Dan Henrikson, Paul Jorgens, Scott Miller, and Anna Scholl created screens that promote mathematical conversations between teachers and students by including problems designed to expose and confront naive conceptions that students may have. An example of this is Serge’s card sort, which gives students a chance to see both correct and incorrect uses of function notation.

Check out all of our activity additions here.