In this post, you'll have an opportunity to learn more about synchronous learning and how it can:
 relate to classroom practice; and
 work with hybrid and online learning models.
You'll also have the chance to begin:
 learning about Thinking Classrooms through the vignette, below;

sharing your own and/or asking other educators about their experiences with different models of learning and modes of delivery; and
 expanding your professional learning network around assessment practices, various models of learning, and modes of delivery in mathematics teaching and learning.
So much of the educational landscape has been changingevidenced by the current, global paradigm; shifting priorities; and efforts to hybridize learning models and make online learning successfulfor example, synchronous online learning.
Synchronous learning occurs in realtimei.e., in realtime, it allows educators the opportunity to connect with their students such that the immediacy of feedback is greater.
When this mode of delivery is done remotely and online, with the support of videoteleconferencing platforms and a host of webbased applications, we need to remind ourselves that synchronous learning is but one aspect of authentic and engaging online learning.
Just like effective teaching requires opportunities for students to engage in self and groupdirected learning activities, educators working in an online environment can help support their students' learning preferences by intentionally incorporating asynchronous learning activities into their teaching.

 While a small group of students is working on a task, observations and conversation indicates that direct instruction (in the form of hints and answering keepthinking questions) is necessary (influence); on other occasions, direct instruction with several groups and/or the whole class points to using questions that are focusing in nature, followed by encouraging students to continue working on the task in small groups (inform).
The remainder of this post focuses on the following:
 examining and reflecting upon a conceptual model for synchronous online teaching and learning in mathematics in Secondary grades;
 sharing our own and connecting to the experiences of others with synchronous online teaching and learning across all divisionsprimary, junior, intermediate, and senior ...
... and all of this to help our professional community of practice support one another by providing the best answers we have, at this time, to the following question:
in synchronous online learning?
Mr. Stewart recognizes the value in providing space for his students to think, communicate, and make visible their mathematical ideas and struggles, and to ask questions of one another. It’s within these spaces where he’s better able to listen to conversations and observe and document his students’ thinking—all of this to provide timely, descriptive feedback to his students on how they’re working towards mathematical learning goals and monitoring their responses to feedback—feedback, generally, coming in the form of hints and questions that spur students to continue thinking.
In order that he is able to provide timely and relevant feedback to students, his students’ curiosity needs to be piqued and students need to be challenged cognitively—i.e., within the scope of something they are almost ready to do. With tasks that are lowfloor/highceiling, Mr. Stewart is able to elicit varying degrees of student thinking—thinking that is the driver of everything that happens throughout the lessons.
From the outset of the first synchronous lesson (in a series), Mr. Stewart recognizes that students will need to develop an understanding of the context in which the problem sits before the problem is fully defined. This early part of the lesson tends to be short and is narrative in fashion—generally, a series of questions are asked to activate students’ prior knowledge, clarify the information provided, and to come to a consensus on what problem needs to be solved.
Mr. Stewart often displays visuals associated with the problem through sharing his screen and invites students to add their ideas to a Jamboard. Students are also able to raise questions and add suggestions in the chat window.
With the introduction complete, students are randomly and visibly assigned to groups of three. Using Zoom, students are aware that Mr. Stewart uses the random breakout room assignment feature.
How Students Share Thinking:
As students move into their breakout rooms, each group is assigned a page in the recentlyshared Jamboard. Typically, Mr. Stewart asks groups to relay their thoughts to one student who can add their group’s thinking to their board. In some instances, students find it just as easy to work on the problem in a parallel manner on paper, having discussion along the way. 
At key points in the lessons, Mr. Stewart intentionally interrupts studentled, collaborative group work—i.e., returning to the main meeting by closing breakout rooms—to draw the class’ attention to some key moves students have been making. The placement of direct instruction at key points in the lesson offers Mr. Stewart a chance to help students cocreate a narrative from how they moved from understanding the problem, through various stages, and ending with checking the reasonableness of their answer. This narrative, really is composed of success criteria—some of these anticipated; while others occurring incidentally during the course of learning.
As he prompts groups to share their thinking, Mr. Stewart is listening and looking for conjectures, estimations, sketches, use of terminology and symbolic notation, strategies uncovered in building up towards the task, and explanations—early on, many of these being expressed in a lessthanformal way.
Each sample discussed has something of value to establishing success criteria, and as students share, he asks questions of the group about the approaches they’ve taken, as well as asking the class to discuss how they might connect the representations between different groups’ approaches.
As students share, he begins adding these highlights to some of the examples of students’ work in the pages of the Jamboard—essentially, codifying what’s been done; validating students’ contributions; and demonstrating that students can leverage what they’ve done to move into a more formal means of analyzing and solving the problem with calculations, graphs, and algebraic representations. During this part of the lesson, Mr. Stewart uses the recording (video) feature in Zoom both a means of further documentation and a resource that students can access through their LMS.
Knowing that formative assessment, up to this point, has been purely teacherdriven, he also recognizes the value of students providing feedback to one another. Having drawn the class together for direct instruction, students are encouraged to go back to working on the problem—this time, looking at the problem solving process through a formal lens.
Given that hints were given, keepthinking questions answered, and the class had been brought together for discussion about their approaches, students now have a few criteria that they can use to assess their next steps in the problem solving process. Through the use of breakout rooms, students are manually reassigned to their groups such that they can continue working together. Again, Mr. Stewart cycles through the various breakout rooms to observe and support students, accordingly.
Once Mr. Stewart recognizes a place where each student has been able to successfully engage in the task and has made some progress (which could take place over several days), he brings the class together again to have students discuss their thinking and strategies they used to solve the problem. Again, this part of the session is recorded for documentation and as a resource for students.
As he listens, he continues to annotate students’ Jamboard solutions and asks the class to review the list of success criteria the class has been developing for any refinements that can be made. As students were working, Mr. Stewart conveniently added an additional page to the Jamboard where both developing success criteria and learning goal have been posted. As the lesson wraps up, he reviews each of the criteria and how students have used them to work towards the learning goal.
At the end of each lesson, students are reminded that they have the Jamboard to reflect on during periods of asynchronous study. It’s often during these times, where students are encouraged to create notes that are meaningful to themselves—i.e., if you had to explain what happened in today’s lesson to yourself or to someone else, what would you say?
In order that he better understands what students know and are able to do at this time (as well as each day spent working towards the learning goal), he provides them with an exit ticket. On the ticket students will notice a problem that relates to the one they’ve been working on and/or some selfassessment questions—questions asking them to articulate what is going well, what they need to work on, and if there are any particular supports they need to keep going.
Mr. Stewart tries to provide students with options he knows will both engage and encourage continuous and shared reflection. For students who enjoy writing and diagramming their thinking, students can add to the digital notebook of the class’ LMS. For students who prefer to explain their thinking orally, Mr. Stewart uses Flipgrid.

Much of what students have shown and have shared in their work and comments will help Mr. Stewart decide if further consolidation is required, guided groups need to be formed, student thinking needs to be challenged, and/or extensions are appropriate for students to pursue. Occasionally, these exit assignments become much like a threaded discussion with students posting and commenting on each other’s posts in Flipgrid or through the discussion board in their LMS. Altogether, Mr. Stewart finds that this ‘twist’ on the use of these tools, allows students to connect and continue conversations during times of asynchronous learning.
Based on his ongoing observations and conversations with students, Mr. Stewart now provides his students with a set of questions (4 to 6 questions) they can use to check their understanding. These questions (posted on the LMS) are only released to students when he notes that students are in a position to practice correctly. These questions are for students’ selfassessment purposes only. Answers (only) are posted to the LMS so that students can quickly determine if they’ve made a mistake, and model solutions are only shared out once students have attempted solving each problem.
Based on all aspects of the formative assessments that both Mr. Stewart and his students have been doing, as well as his students’ interests, further consolidation sometimes involves reviewing and discussing model solutions to the questions students have completed to check their understanding. Sometimes these solutions and their explanations are recorded using screencasting applications and shared through the class’ LMS, where students can reflect on them during times of asynchronous work. On other occasions, these solutions are shared and discuss with students in a synchronous manner during Zoom meetings.
All too often we don't have an opportunity to see ourselves reflected through the examples being shared. We might also not have an opportunity to share our perspectives. This is much like what our students experience when there are many windows onto the world and others' learning and not enough mirrors to reflect their own needs and identity.

The "Balance Series"relaunching in 2021 with new webinars on assessment practicesworks with you and other educators from around the globe to examine the complexity of teaching and learning mathematics. This series is being offered for one, simple reason: educators, myself included, aspire to be and do more in the service of student learning. And much like our students, we, too, recognize that where there is a student learning need, we might need support in how we can best support them. You can learn more about the "Balance Series" from its Summer 2020 delivery here (information updates coming soon ...).
As the "Balance Series" prepares to launch for sessions geared around formative assessment, I would like to invite you to do two things: 1  Freely contribute to our Virtual Community Builder  Formative Assessment and as often as you like (see below) and 2  Join the "Balance Series" of webinars related to assessment as they become available.
Webinar notifications will be sent directly to the email you provide through the community builder form, below. Please rest assured that only I will use your email only to communicate with you about professional learning opportunities I'm preparing and offering. The price of admission? The only thing I ask is that you support other math educators, starting with a contribution to the community builder.
If you have any questions about this post, the "Balance Series", and/or participating with the community builder, please feel free to contact me here.
 Option 1: Note that this would not be much of a learning opportunity without having access to the examples and comments made by other math educators. Here's my commitment to you: If I receive Survey1 responses, they will be openly accessible to all respondents. Once you complete the survey, you'll notice a link to view a summary of all responses. These results will not have your name or contact email, as the form will not be collecting this information. With this option, you'll be able to read about other educators' experiences, but you won't have the option to interact with them. You'll also be able to contribute more of your experiences if and when you decide you'd like to.
 Option 2: Respond to Survey2 if you'd like to share your contact information with others who have responded to the same survey. I.e., You want to build your professional learning network about assessment in mathematics education. When you respond to the survey, I'll send you a link to view a "Results2" summary of all contributions. Like Survey1, you'll also be able to contribute more of your experiences if and when you decide you'd like to. As this form will be set up to collect names and emails, you'll then have a way of reaching out to any or all participants in this version of the survey to further your learning. By networking with other educators, you'll be able to raise questions, have conversations, and coordinate opportunities to communicate and collaborate.
Absolutely! We always want to know if what we share will be of benefit to others.
When you access and respond to the Virtual Community Builder  Formative Assessment, expect to answer questions about the following:
 Grades you commonly teach or have a hand in supporting (e.g., School Administrator)e.g., Primary (K to Year 3), Junior (Years 4 to 6), Intermediate (Years 7 and 8), Secondary (Years 9 to 12).
 If you're engaged in synchronous facetoface learning, synchronous online learning, a hybrid of both synchronous facetoface and online learning, or other modes of delivery, what does your assessment practice look like? Over longer periods of time (e.g., several lessons)? What does the asynchronous aspect look like? What's working? What wonderings do you have? What supports do/might you need to reach your goals (real/anticipated)?
In support of #2, you can describe how you provide opportunities for students to interact and construct their learning together, and how students are interacting with feedback. For example, you might choose to discuss one or more of the highimpact instructional practices listed above and/or how digital technology is being used to support your students' learning.
I am more than happy to collaborate with you and make our learning visible, here. If at any time, you have questions or comments, please feel free to comment to this blog and/or contact me.
Professionally Yours,
Chris Stewart, OCT
Educational Consultant, Flipping the Focus (c) 2020
Government of Ontario. (2010). Growing Success: Assessment, Evaluation, and Reporting in Ontario's Schools, Kindergarten to Grade 12. Retrieved from http://www.edu.gov.on.ca/eng/policyfunding/success.html
Government of Ontario. (2020). Instructional Approaches in Mathematics. Retrieved from https://www.dcp.edu.gov.on.ca/en/curriculum/elementarymathematics/context/someconsiderationsforprogramplanninginmathematics
Gutiérrez, R. (2018). The Need to Rehumanize Mathematics [Introduction]. In I. Goffney, R. Gutiérrez & M. Boston (Eds.), Rehumanizing Mathematics for Black, Indigenous, and Latinx Students (pp. 110). Reston, VA: National Council of Teachers of Mathematics.
Liljedahl, P. (2021). Building Thinking Classrooms in Mathematics  Grades K to 12: 14 Teaching Practices for Enhancing Learning. Thousand Oaks, California: Corwin Press.