Des-blog

We asked the Desmos Fellows to give this classic transformations activity an upgrade by adding one screen. The Fellows blended student background knowledge, goals for learning, and design principles to create these screens to enhance the original activity.

Reverse the Direction

• The original activity gives students a graph and asks them to generate a function. After practicing this skill, Bob Lochel and Anna Scholl like to see if students can go in the reverse direction by asking them to generate a sketch given a function. Asking students to describe their process allows teachers to see if students can decompose a function transformation into stages.
  

Delay Feedback for Reflection

• Paul Jorgens noticed that a student could complete most of the screens by guessing and checking answers. He added a cart sort so that students would have a chance to do some reasoning after the initial exploration.
• Sarah Blick Vandivort suggests adding a screen where students can predict what a function will look like using words and a sketch, before having the chance to check their thinking. Similarly, Scott Miller asks students to explain their reasoning for the composition of transformations of f(x). Analysis of responses allows the teacher to see what level of understanding, vocabulary and connections students are making.
  

Opportunities to be Right and Wrong in Different, Interesting Ways

• Linda Saeta added a screen that asked students for a second way to match a transformed graph. This flexible thinking about transformations and the ability to recognize them in a graph helps students with some of the problems they’ll encounter in Calculus, so having students look for them in earlier classes is good practice.
  
• Nick Corley asked students to create their own function similar to the ones encountered in previous screens, and to predict what the graph would look like before having a chance to check their thinking. This type of screen also offers a way to provide closure on the activity. Teachers can select several student generated functions to compare in words, with the teacher revealing each graph after students have had the opportunity to discuss similarities and differences.
  
• Shelley Carranza asked students to transform f(x) so that it would go through a given point. Using the dashboard to share solutions and ask questions such as “Which of these graphs used the MOST transformation types to go through the blue point and how do you know?” can make for rich conversation and formative assessment.
  

Extensions

• Meg Craig added the screen below to provide an additional challenge for Precalculus or Algebra II students. This challenges students to make connections to other function types (absolute value) and also brings up function composition, offering students the chance to think about what happens if we reverse the composition order of the solution.
• Patty Stephens expanded on this idea and asked students to explore f(abs(x)).
  

What are some other ways we can upgrade this or other practice activities? Let us know on Twitter @desmos.

One of our most used activities is The (Awesome) Coordinate Plane Activity. We think its popularity speaks both to the ingenuity of its author, Nathan Kraft, and also to the math student’s great need for graphing practice. Math teachers know what students need and Nathan knew how to help.

Since Nathan created that activity last year, we’ve upgraded our internal toolbelt and also our internal style guide for making great activities.

One of those principles is that practice should also involve elements of strategy. Practice should propel students towards procedural fluency, but that fluency should propel students towards more than just more practice.

So in our current version of Nathan Kraft’s classic, students receive feedback on exercises like this.

But later they’re asked to work without the axes.

And then later they’re asked to throw the darts.

So use Nathan’s activity as you’re helping students review or practice coordinate graphing. But ask yourself also how you can inject strategy into your existing practice sets – whether they’re on computers or on paper.

We asked the Desmos Fellows to describe some challenges they face when planning workshops or presentations, and to share resources or practices that help them overcome these challenges. While not a complete list, here are some of our best practices for professional development.

Audience and Differentiation

Anticipating the needs and experience levels of participants can be challenging. Desmos fellows had several ideas for how to handle this.

• Harsh Upadhyay has seen that workshop participants often have a wide range of skills, and encourages participants to sit in skill alike groups to support differentiation in the workshop.
  
• Sara VanDerWerf spends the first 10-15 minutes of a session assessing the skill level of participants using a quick write and share out session along with a quick Desmos graph or activity that allows participants to show what they are comfortable with.
  
• Jed Butler is interested in using prompts to help learn more about participants and their hopes for the session. This can help with shaping goals for the session and differentiating to meet the needs of participants.
  
• Stephanie Blair addresses the challenge of different levels of learners by planning in 10 minute chunks. This allows her to spend more time on earlier parts of the presentation when needed and to skip chunks in order to make sure participants leave feeling empowered to apply the learning to their own classrooms.
  
• In addition to differences in skill level, Patty Stephens has found that participants often teach a range of math courses. The example graphs at learn.desmos.com have been a big help in differentiating workshop experiences for participants at all levels, and they also are a great resource for participants wanting to learn more after the workshop.
  
• Glenn Waddell has used Desmos Bingo to help differentiate the experience and to keep sessions learner focused.
  
• Tony Riehl has used a shared Google Doc with opportunities for feedback during the conference and multiple entry points and options for activities.
  

Focus and Framing

• Allison Krasnow shares her thoughts on the planning process and keeping the workshop focused: “I find that in a 1-2 hour workshop I can do one thing well. So I have to think a lot ahead of time about my goal. Is my goal to have teachers do a variety of different slide types and problem types to leave with an overall view of the power of AB? Is my goal to have teachers do a single activity, experiencing it as a student would with plenty of time to think about the pedagogy? Is my goal to have teachers learning to build their own activities and have one ready to use in class? Is my goal to have teachers bring student work from an activity they already ran and reflect on it to think about how they could improve the activity to gain deeper insights into student thinking?”
  
• Dave Sabol reminds us that good professional development models good teaching. “I know that a learner’s direct experience with the tool can be most memorable. I know that it’s my job to find tools, activities, and tasks that will frame everything and illuminate the objective of the day.”
  
• Scott Miller considers how he can model instructional strategies and teacher moves that teachers will use in their classrooms. He asks teachers to partner with each other during the session and share a device in order to increase discussion.
  
• Paul Jorgens acknowledges that not all workshop participants will share his enthusiasm of technology, and that the group can find common ground if the focus is on the students and their learning.
  
• Adam Poetzel helps participants focus on student learning by having them experience Desmos activities from the student perspective, followed by reflecting on how the experience can help students learn math.
  
• Jenn Vadnais helps participants reflect on principles that support student learning as well as teacher moves that support effective use of Desmos Activities.
  

Next Steps

Leaving time for participants to reflect and plan next steps helps ensure that new learning will be applied to the classroom. Nolan Doyle also provides follow up support to teachers in his district once they’ve left the session. Many of us offer follow up support via email or Twitter.

What are some other resources or practices that you keep in mind as you plan professional learning experiences? Let us know on Twitter @Desmos.