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3 Practices for Teaching Math at a Distance and Face-to-Face Simultaneously 

In this post from September 2020, education leaders Doug Fisher and Nancy Frey describe “simultaneous learning” as the situation in which all students in a class are learning the same content, together, but some are not physically present while others are.Those not in the classroom are generally at home on a computer, watching and participating in the class in real time.  This situation may also be called hybrid, hyflex, or concurrent learning, and is a scenario many schools are implementing today. It is a daunting task, to be sure, but Fisher and Frey suggest three guidelines for success when teaching synchronously in a simultaneous learning situation:  

  1. Limit the amount of time on a single task to 10 minutes or less  
  2. Ensure that the task is specific and understood 
  3. Ensure accountability   

Let’s take a look at how these three guidelines can manifest when implemented in a mathematics classroom. 

Example 1 

Third grade teacher Mrs. Jansen teaches four students in-person and 21 students virtually Tuesdays and Wednesdays. She teaches six different students in-person and 19 students virtually on Thursdays and Fridays. The in-person students do not have access to laptops, so she uses a variety of personal whiteboards and paper/pencil materials to ensure that these students can interact in a meaningful way.  Here is what a math block looks like for one day: 

Time  Purpose  Activity 
5 min  Community building  Welcome & celebrations 
5 min  Math Routine  Would you rather? 
5 min  Lesson Hook  What other ways could you cut brownies? 
10 min  Group Activity 1  Sharing Brownies 
5 min  Whole class summarization  Gallery Walk with Discussion 
10 min  Group Activity 2  Fraction Compare Game 
5 min  Whole class summarization  Whole Class Exit Ticket 

As you can see, she begins with a community building routine where every student can share a personal celebration. Her in-person students write their celebration on their whiteboard, and the virtual students type theirs on a shared Google slide. Mrs. Jansen calls on 3 students to share out loud. Her classroom microphone picks up the in-person student responses, but when they are too quiet, she rephrases so that her virtual students can hear as well.  Her in-person students can hear what the virtual student is saying through her speaker. 

Next, Mrs. Jansen introduces the Would You Rather? math routine (wouldyourathermath.com), and displays the following prompt on a shared Google slide.   

Figure 1. Prompt from wouldyourathermath.com 

Her in-person students write out their responses on a personal whiteboard and the virtual students type directly on the slide.  Within a minute, Mrs. Jansen is able to see 25 student responses and selects a few students purposefully to share their reasoning based on the mathematical topic of the day—comparing and simplifying fractions.   

Figure 2. Virtual students work all on one slide. The predictable text boxes ensure that students know where to type in order to be successful in this task. 

Figure 3. A virtual student explains how A is larger than B.  Mrs. Jansen models the slide difference so that all students can see, but then the conversation leads into how A needs to be cut because it is shared with another person. 

Figure 4: An in-person student shows a line cutting the brownies in the first image horizontally.  Mrs. Jansen models that and discussion continues about how it is too hard to tell which is larger. 

Figure 5. A virtual student explained how he held up a sheet of graph paper to his monitor and traced the images, but that it was still too tricky to tell which is larger.  Some students used fractional terms like 1/2 and 1/3. 

Then, Mrs. Jansen asks students to draw the best way to divide a pan of brownies. She leaves the question vague so that she has a variety of responses. All students are drawing either physical or virtual lines on an image of a pan of brownies. She has verified that students know how to divide brownies in both modalities (paper and computer) They are hooked and ready for the small group activity. 

Mrs. Jansen creates eight small groups of two to four students. She puts her in-person students into pairs who maintain a distance of six feet from each other, but can still see each other’s paper-and-pencil work with relative ease. She places her virtual students into breakout rooms where they can view and edit their groups’ Google slide. All students are exploring multiple ways of dividing up pans of brownies for various scenarios. Mrs. Jansen also snaps a picture of the in-person groups’ work and adds it to the interactive slides. 

Next, Mrs. Jansen holds a gallery walk. Her virtual students move freely between slides and comment by adding smiley face emojis to the slides to show personal connections (like ah-ha!). The in-person students use hand signals to show  personal connections to other student work as Mrs. Jansen scrolls through the slides. Mrs. Jansen calls on two students to explain their reasoning to the class. 

Figure 6. Mrs. Jansen shows a visual model of 2 ÷ 4 = 1/2 and the discussion about how you cut a brownie continues as students explain that it doesn’t matter how you cut it as long as it is one half. 

Then, the students play a game called Fraction Compare.  In-person students play a modified game that doesn’t require sharing cards while the virtual students use a collaborative game site (playingcards.io) to reveal cards and compare them together in real time.Mrs. Jansen visits groups to question students and further their thinking. 

Figure 7. Students play fraction compare (similar to the game WAR) in a collaborative space where they can view each other’s cards and shuffle the deck live. 

Finally, Mrs. Jansen ends her class with a whole class exit ticket.  Her virtual students all respond on the same slide while her in-person students respond on their personal whiteboard.  Mrs. Jansen now has formative feedback on generalizations that her students made about today’s activity.  She logs this information on her running record.  

Figure 8. Students respond in a whole class exit ticket. 

Example 2 

Algebra I teacher, Mx. Baker, teaches 11 in-person and 14 virtual students in their first period class.  The in-person students have laptops with an earbud and microphone accessory to allow for verbal discussions without feedback noise. Because of internet bandwidth challenges, the in-person students cannot use their cameras, but they are able to use audio, chat box, and Google slides to communicate with virtual students. Here is Mx. Baker’s lesson plan for the day. 

Time  Purpose  Activity 
5 min  Community building  Welcome and celebrations 
10 min  Math Routine  Which One Doesn’t Belong 
5 min  Launch rich task  What other lines are possible? 
10 min  Group exploration  Using visual patterns to make graphs (growing growing activity) 
10 min  Whole class math discussion  What is different about the visual pattern?  How does that relate to differences in the graph? 
5 min  Whole class summarization  Whole Class Exit Ticket 

Class begins with a community building activity where students write their successes and celebrations on the opening shared Google slide. Mx. Baker calls on four students to share over the microphone. Armando, an in-person student, turns on his mic and shares the news that he won a race at a recent track meet (note that since all students and teachers in the classroom have their mics off, Armando can speak without feedback noise). When the other three virtual students share their celebration, every student is able to hear it. 

Next, Mx. Baker introduces the familiar routine, Which One Doesn’t Belong (wodb.ca). The class begins by moving the doesn’t belong symbols to various quadrants of the Google slide. Once the initial, anonymous slide is complete, Mx. Baker asks students to explain their reasoning on the second slide, then selects purposeful statements and asks the student authors to elaborate over the microphone. 

Mx. Baker: Trevor, what do you mean by origin and why don’t we see it in the second image? 

Trevor: Cause it doesn’t go through it.  The origin is (0,0). 

Figure 9. Students respond anonymously to the Which One Doesn’t Belong prompt. 

Figure 10. Students type rationale for the Which One Doesn’t Belong prompt. 

Then, Mx. Baker launches the task by asking students, “what other types of lines are possible on graphs?” and asks the students to respond using a chat waterfall.  A chat waterfall is a strategy where all students write a description in the chat box, but Mx. Baker gives a full minute of wait time before they tell the students to press enter.  All at once, Mx. Baker has 24 responses and confirms that students are thinking about a variety of linear possibilities. 

Next, Mx. Baker creates five breakout groups with five students in each. The heterogeneous groups are composed of in-person and virtual students, and all students turn on their microphones to say hello and begin the task. In this task, each group has a different visual growing pattern that they will represent as a graph, table, and equation. Mx. Baker can view all five group slides in the shared Google slide deck and joins various groups to listen to their thinking and pose purposeful questions. 

Mx. Baker brings all five groups to a close for a whole class discussion where they asked students to explain the meaning of the y-intercept and slope in relation to their visual model. 

Figure 11. Group 1’s work for the five representations of y = 2x – 1. 

Figure 12. Group 2’s work for the five representations of y = 2x – 1. 

Figure 13. Group 3’s work for the five representations of y = (3/2)x – 1/2. 

Finally, the class ends with a whole class exit ticket (Wills, 2021). Mx. Baker displays a new growing pattern alongside its table representation, and asks students, “How many squares would be on image #8, and how do you know?” Each student types their response in the shared slide, and Mx. Baker has a measurable formative assessment about their students’ understanding. 

Figure 14. Students’ responses for number of squares in image #8 using the table. 

In both of these math classrooms, the teachers expertly assign a variety of purposeful tasks that limit the amount of time to 10 minutes or less. They ensure the goals and instructions are clear to students, and they use accountability slides so that students know where to type, and how to be successful on the task. Both of these student-centered math classes not only gave students the opportunity to communicate and explore with their peers, but they also nurtured a community where in-person and virtual students felt a sense of togetherness. 


References 

Fisher, D. & Frey, N. (2020). Simultaneous Learning: Blending Physical and Remote Learning. Corwin Connect. 

Wills, T. (2021). Teaching Math at a Distance: A Practical Guide to Rich Remote Instruction. Corwin.

Written by

Theresa Wills, PhD, is the author of Teaching Math from a Distance, K-12: A Practical Guide to Rich Remote Instruction.  She is an assistant professor of mathematics education in the School of Education at George Mason University, where she works with inservice mathematics specialists and preservice elementary and secondary teachers.  Theresa has taught synchronous online classes and webinars since 2010 and researchers teaching practices that are adaptable to the online environment.  She is a former classroom teacher and math coach who still volunteers regularly in K-12 classrooms. 

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