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Selecting and Sequencing Mathematical Discourse with Desmos

Listen and learn

Listen and learn : Snapshot

Wednesday, June 26, 10:30–11:30 am
Location: 107AB

Presentation 2 of 2
Other presentations:
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Bob Janes   Robert Lochel  
Desmos Classroom Activities empower mathematics teachers by making student thinking visible. Based on the work of Smith and Stein, the new Snapshot feature creates a framework for linking digital responses with in-person discourse. Teachers can now digitally select, sequence, and build questions around student work to promote rich discussion.

Audience: Coaches, Curriculum/district specialists, Teachers
Skill level: Intermediate
Attendee devices: Devices required
Attendee device specification: Laptop: Chromebook, Mac, PC
Tablet: Android, iOS, Windows
Participant accounts, software and other materials:
Focus: Digital age teaching & learning
Topic: Instructional design and delivery
Grade level: 6-12
Subject area: Math
ISTE Standards: For Students:
Knowledge Constructor
  • Students curate information from digital resources using a variety of tools and methods to create collections of artifacts that demonstrate meaningful connections or conclusions.
For Educators:
  • Design authentic learning activities that align with content area standards and use digital tools and resources to maximize active, deep learning.
  • Model and nurture creativity and creative expression to communicate ideas, knowledge or connections.

Proposal summary

Purpose & objective

The Desmos Activity Builder is a free online tool for math educators and students to experience custom-built digital activities. Through these digital activities, students respond to prompts and create their own mathematical ideas through text, drawings, graphs, equations, card-sorts, and more. Teachers can see these responses presented in real time, but until now there has been no way to facilitate a meaningful discourse by connecting these digital ideas to organized in-person discussion.

In this session, participants will learn about Smith and Stein’s 5 practices for orchestrating productive mathematics discussions, and how this framework has been applied to new features in Desmos Activity Builder. This framework includes (1) anticipating students’ solutions, (2) monitoring students’ work, (3) selecting approaches purposefully, (4) sequencing students’ approaches in a logical progression, and (5) connecting students’ approaches via discussion questions.

Next, participants will take part in a brief Desmos Activity and watch as the presenter uses the new Snapshot feature to select work samples, digitally curate them, and develop questions for discussion. Participants will learn and discuss ways that the Snapshot feature empowers teachers to facilitators of ideas, rather than purveyors of information. Finally, participants will have a chance to reflect on how they would implement the snapshot feature through a turn and talk and finally an exit survey.

Participants will demonstrate evidence of success if they leave fully understanding how the 5 practices has been integrated into the Desmos Snapshot feature, how to use the Snapshot feature and if they are able to produce actionable next steps on the exit survey.


1. Participants will gain a conceptual framework by listening to an overview of Smith & Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions. (5 min)

2. Participants will use technology (laptops, tablets, phones) to participate in a Desmos activity containing one open-ended mathematical prompt. (7 min)

3. The presenter will demonstrate how to use the snapshot feature to select specific responses, sequence them onto slides, and add discussion questions. If time allows, participants will be invited to turn and talk to a neighbor about the discussion questions. (7 min)

4. Participants will reflect on how they would implement this feature via a peer-to-peer turn-and-talk. More specifically, participants will be asked to discuss what type of activity would fit in their classroom, what potential ideas students might generate, how they would curate the ideas, and what questions they would choose to promote discussion. (5 min)

5. Participants will record their reflections on a digital exit survey. (5 min)

Supporting research

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

Book found here:,-2nd-Edition/

Hill, Z. (2016). Mathematical discourse, part 2: Planning for the task (anticipating, selecting, and sequencing). Except from: teaching children mathematics.

Article found here:,-Part-2_-Planning-for-the-Task-(Anticipating,-Selecting,-and-Sequencing)/

Fenton, M. (2014). Technology and the curious mind. Recorded at CMC-North. Asilomar, CA.

Blog post found here:
Video found here:

Meyer, D. (2015). Functionary: Learning to communicate mathematically in online environments (Doctoral dissertation). Graduate School of Education, Stanford University.

Dissertation found here:

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Bob Janes, East Hartford Public Schools

Bob Janes is the 6-12 Math Supervisor for East Hartford Public Schools in Connecticut where he supports teachers through curriculum, coaching, and workshops. Bob strongly believes in using technology to augment, not replace, teaching and learning. He has previously coached teachers in the use of digital formative assessments, reflection, and discussion techniques. Bob also understands the importance of collaboration. He has previously participated in PCMI; attended ICME13; received a MET Future Leader grant; and been granted a Desmos Fellowship. In addition, Bob is an active member of the online education community and often blogs, tweets, and attends meetups.

Robert Lochel, Hatboro-Horsham High School

Bob Lochel is a 22-year veteran high school mathematics teacher, and has also served as an instructional coach in his home district, Hatboro-Horsham, outside of Philadelphia. Bob's educational passions lie in meaningful technology integrations within math classrooms, and working with teachers to design experiences which cause excitement in their classes. Bob is a Desmos fellow and certified trainer who has facilitated sessions at the local, state and national levels. In addition, Bob is an AP Statistics teacher and exam reader, and the president of his local NCTM affiliate,

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