Reinventing Teaching and Learning in Mathematics Education — Part 2: Synchronous, Online Learning & Formative Assessment Practices

Christopher Stewart
5 min readDec 22, 2020


Welcome back to Flipping the Focus.

This is the 2nd post in a 5-part series devoted to re-imagining how assessment practices in mathematics education can be improved, in part, with pedagogically-driven uses of technology.

Part 1 of the series provided an example of pedagogical principles that can be used when making decisions about how a variety of tools and representations — including interactive, digital technologies — can be leveraged to improve student learning.

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.


Reinventing, now more than ever, how technology supports math teachers and students is so important. Educators need high-quality teaching resources, pedagogical supports, and professional learning that engender and communicate respect for equity and inclusion.

So much of the educational landscape has been changing — evidenced by the current, global paradigm; shifting priorities; and efforts to hybridize learning models and make online learning successful — for example, synchronous online learning.

What is Synchronous Learning?

Synchronous learning occurs in real-time — i.e., in real-time, 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 video-teleconferencing platforms and a host of web-based applications, note 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 group-directed learning activities, educators working in an online environment can help support their students’ learning preferences by intentionally incorporating asynchronous learning activities into their teaching.

For example, by incorporating asynchronous learning opportunities, educators can delay some of their feedback so that students can continue thinking and re-focus their attention on reflection and metacognition (Desmos, 2016).

There are also many high-impact instructional practices in mathematics that we often associate directly with formative assessment practice — establishing learning goals, co-constructing success criteria, and interacting with descriptive feedback. On some occasions, other practices might be thought of as influencing formative assessment practices like the use of problem-solving tasks, documenting and reflecting on how students use tools and representations, and actively listening to students during math conversations; while at other times, the use of other practices inform instruction and come about as a result of ongoing, formative assessment — e.g., teaching about problem solving, intentional and well-positioned use of direct instruction, small group instruction, deliberate and purposeful practice, and flexible groupings. Of course, these distinctions are but one way to think about the complex relationship between instruction and assessment: in many situations, practices that inform instruction become those that influence assessment, and vice-versa. For example:

  • We might decide to facilitate a math conversation to better uncover students’ thinking (inform); on other occasions, our assessment points to students being ready for a conversation that helps to consolidate their learning (influence).
  • 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 keep-thinking 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).

What might seem to be a dichotomy — practices that inform and/or influence — is much-needed to ensure that educators and their students are better able to interact with descriptive feedback that is based on the development and refinement of success criteria.

When it comes to formative assessment, the decision to use practices in ways that make us think versus uncovering and re-purposing our thinking moves us closer to attaining learning goals.

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 divisions — primary, 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:

How can teachers best implement these instructional practices with fidelity
​in synchronous online learning?

Vignette: Bringing Thinking Classrooms to Life Online

Secondary School Example: Problem-based Learning in Mr. Stewart’s Mathematics Classes

Introduction :
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.


Originally published at



Christopher Stewart

Chris Stewart, eduConsultant, Flipping the Focus | He/Him | OCT | Edublogger | Specialist — Teaching & Learning | Views are my own