Monday / June 17

Moving Toward a Virtual Math Classroom? Matching Modes of Instruction to Learning Goals

We have spent the last weeks watching many schools close their doors–some for the rest of this semester—to  control the number of COVID-19 infections. I am excited to see our society’s strong commitment to public health. As many of us teachers face the daunting task of serving our students by transitioning to online instruction, most for us the first time ever, we find ourselves needing to learn how to provide strongequitable, and appropriate instruction for each and every student.  

Whether you are attempting to carry out teaching the rest of the year’s math curriculum or you are having students simply practice what they’ve previously learned, the choice of materials and instruction you provide during this time will drive students’ learning progression. When is it best to choose technology that values collaboration and social construction of knowledge and when can you use technology that students can work on independently to practice fluency? What risks does not matching the right technology to the right goal pose? Not all technologies are created equal. 

For example, I sit here working with my son whose school has moved to online instruction for at least the next three weeks. His teacher has assigned him problems and activities related to area and perimeter via an individualized learning platform. As he sits and thinks through problems, entering solutions into the computer to be evaluated for correctness, I informally note his solution pathways and find he has a typical confusion of the definitions of area and perimeter. He completes the assignment, but without really coming to a clear understanding of the differences. Yet still he earns a certificate of achievement and badge for his accomplishment.  

One risk in using some online software programs is that many evaluate and reward correctness and completion rather than true understanding. Further, if as teachers we are moving toward a flipped classroom model in which we provide videos and then related assignments we must be mindful of what we may be reinforcing. The flipped classroom model often places emphasis on procedural fluency by having students watch videos to understand a process then completing assignments to practice and reinforce these ideas.  

One of the most vital things we can do to ensure students’ success is to ensure we are choosing technology that fits the learning goal. With that aim, let’s look at three considerations: 

Consider the difference between synchronous and asynchronous learning  

One of the largest differences between synchronous (live online instruction) and asynchronous (not happening at the same time) learning is instant and immediate feedback while learning. With synchronous learning through a virtual environment, learners can receive immediate feedback from their fellow students or teacher. This allows for more efficient learning, because it doesn’t require students to come back and try to recapture a thought or idea hours or days later. Thus, we should first strive to provide synchronous instruction as much as possible. Granted, requiring synchronous learning may not be possible or equitable given individual contexts and during crisis. Therefore, using platforms that also allow for recording is important to increase equitable instruction.  A number of useful platforms for this include Zoom, Microsoft Teams, and Google Hangouts. Given the potential inequity of participation in synchronous instruction, teachers should devise plans to include asynchronous alternatives. In my own online classes, I have purposefully selected what I would like to focus on synchronously and asynchronously—choosing topics and tasks best suited to each mode. It has been great to see my son’s teacher just taking a few minutes of to meet with students virtually to continue to develop relationships and provide students an opportunity to socialize during times of social distancing. 

Prioritize conceptual understanding first 

Solid educational research over the years has shown that we should strive to move students toward conceptual understanding before moving on to procedural fluency.  Conceptual understanding establishes the foundation that is necessary for developing procedural fluency (NCTM, 2014).  Thus, teachers making shifts over the coming days should be as careful as they can to reinforce solid pedagogical practice by opting to use virtual manipulatives and virtual face-to-face meetings that strengthen students’ conceptual knowledge, then move towards the development of students’ procedural fluency. NCTM (2014) makes the following suggestions to ensure students are building a conceptual understanding before moving toward procedural fluency while I offer parallel technology driven recommendations: 

Developing Conceptual Understanding 
NCTM (2014, pg. 47-48) Recommendations  Virtual Recommendations 
  • Providing students with opportunities to use their own reasoning strategies and methods for solving problems.  
  • Asking students to discuss and explain why the procedures that they are using work to solve particular problems.  
  • Connecting student-generated strategies and methods to more efficient procedures as appropriate. 
  • Using visual models to support students’ understanding of general methods.  
  • Providing students with opportunities for distributed practice of procedures. 
  • Set up virtual discussion boards around tasks for students to share solution pathways and allow for task completion over a week period. 
  • Use virtual manipulatives and tasks for students to complete rather than just procedural problems. Provide instruction on how to screen capture and share their thoughts with others to make this interactive. 
  • Use instructional videos that require interaction and use conceptual understanding to build procedural fluency. Consider tasks with pause points in the video to facilitate discussion in online forums. 
  • Use synchronous instruction when available and record the video for students who may not be able to participate for various reasons. 
  • Use a virtual synchronous platform that allows for a class to be split up and broken into smaller groups to increase collaboration and discussion of learning tasks. 


Assign asynchronous instruction to promote active learning 

Teaching online provides challenges for most traditionally trained teaching professionals, but it also provides unique opportunities to engage learners. As teachers begin to create asynchronous course projects, assignments, and modules, they should consider some of the frameworks that have been created to ensure quality and equitable online instruction like Quality MattersQuality Matters provides secondary and post-secondary standards and rubrics for educators to ensure online instruction adheres to best practices. Using these standards, I urge teachers to consider some of these best practices: 

  • Provide purposeful opportunity for your students to become acquainted with new course procedures, routines, and expectations. Be flexible and provide delayed accountability as students learn these new routines. 
  • Make learning objectives and competencies for modules clear. Students shouldn’t be left on their own to realize they are working to understand somethingConsider using self-assessment rubrics or proficiency scales for students to complete that highlight intended competency and progression of learning in a module.  
  • Use multiple methods of assessment that target both conceptual and procedural knowledge and relate back to the learning objectives, standards, and course expectations. Remember the diversity in learners and contexts as you make assignments to ensure equitable, valid, and reliable assessment. 
  • Consider using discussion forums, online games, and family activities to encourage active learning. Require learning-content interaction, learner-instructor interaction, and learner-learner interaction. Consider rubrics that require students to read and reply to videos, the instructor, or others in online discussions using rubrics. The online software goreact allows for students to be engaged with videos in numerous ways to promote active learning.  
  • Consider each and every student when making adjustments towards an online class. Ensure videos are learner and objective appropriate. Consider using closed captions in videos to support diverse student needs.    

Written by

Basil M. Conway IV is an associate professor of mathematics education at Columbus State University and author. He teaches online graduate courses in mathematics education and is the program director for the online Master of Education and Educational Specialist Degrees in Mathematics Education 

National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. 

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  • I aim to implement some of the strategies suggested by you in your article in my Maths classroom in Term 2.

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