My first Eastern I blog features the Upcoming New York State Affiliate Conferences, as well as our guest editor, Irina Lyublinskaya, from New York. I was fortunate enough to meet Irina when I attended her workshop sessions at the New Cubed Conference. If you ever have the opportunity to hear Irina speak, take advantage of it. You will not be disappointed.

Irina Lyublinskaya is a Professor of Mathematics and Education at Teachers College, Columbia University.  She received her Ph.D. in Theoretical and Mathematical Physics from Leningrad State University and has over 30 years of teaching and research experience at high school, college, and graduate school levels. Among her research interests are topics of integrating technology into mathematics and science education, pre-service and in-service professional development of STEM teachers, curriculum development, and international STEM education. She is a recipient of various awards for teaching excellence, including Radio Shack/Tandy Prize for Teaching Excellence in Mathematics, Science, and Computer Science, NSTA Distinguished Science Teaching Award and citation, Education’s Unsung Heroes Award for innovation in the classroom, and NSTA Vernier Technology Award. In 2011, she was inducted to the NYS Mathematics Educators Hall of Fame. She is a recipient of several outstanding paper awards from AACE and SITE, an author of 16 books and has published substantially in internationally recognized academic journals.

Creating An Active Virtual Learning Environment

By: Irina Lyublin

When in March 2020 all of us had to switch overnight to fully online teaching, it was clear that teaching has to become fundamentally different from what we were used to in the classroom. The challenges were enormous, from student lack of basic access to internet and curriculum materials, to teacher’s lack of experience and training of teaching online. Transforming the traditional in-person classroom to a virtual environment while maintaining student-centered and culturally responsive teaching became one of most difficult challenges for all educators during COVID-19 pandemic. This blog is a personal reflection on successes and challenges of teaching mathematics in a fully online course for preservice mathematics teachers. 

The most challenging aspects of online environment for me were: 1) truly engaging students in learning mathematics in and out of class, 2) providing space and time for collaborative/cooperative work, and 3) rethinking assessment. 

The virtual environment does not naturally support student interaction and collaboration. In order to create a highly active learning environment where my students and I could share ideas, information, and opinions, I wanted to incorporate high impact teaching strategies and select appropriate technology platforms that could effectively support these strategies and were accessible to my students at no cost. In his book Visible Learning for Mathematics, John Hattie identifies high influencers on student learning based on synthesis of more than 1,600 meta-analyses comprising more than 95,000 studies about factors affecting student learning. Among teaching strategies with largest impact were cognitive task analysis, classroom discussion, and providing feedback. I knew I could support these strategies in an online environment by using Nearpod ( Nearpod is a multimedia student engagement platform that allows integration of various multimedia content as well as different forms of formative assessment with immediate feedback. The content tasks include slideshows, access to web content, PhET simulations, interactive videos, VR field trips, Nearpod 3D, Desmos graphing calculator, PDF viewer, and Microsoft Sway. Assessment could be integrated through ten types of activities such as collaborative board, drawings, multiple-choice quiz, fill-in-blank, open-ended, memory, matching questions, and FlipGrid video responses. Live Nearpod could be used in synchronous mode of teaching enabling the teacher to control student screens. In asynchronous mode students can access self-paced Nearpod presentations to experience the same interactive features. It was very important for me to have an asynchronous option for students who might have internet access difficulties. I also wanted to be able to integrate various resources in my lessons and Nearpod allowed me to do that within one platform, so students would only need to join the lesson to have access to these resources. 

Research shows that students learn best when their teachers maintain a high-level of cognitive demand throughout lessons. In order to provide an active learning environment with high cognitive demand tasks, I decided to use a problem-based learning approach. In this approach each unit starts with a problematic situation that serves as the organizing center and context for learning. The problematic situation is usually ill-structured and messy, that students perceive as important and relevant. The PBL process steers students through the complex tasks of brainstorming ideas, identifying useful knowledge, asking appropriate questions, and crafting a strategy for finding answers. 

In order to illustrate this approach in an online environment, let’s consider an example of a series of lessons on proportionality and similarity in scale drawings for middle school. The unit would take 10 days with the plan shown below:

  • Day 1:  Introduction to the Crime Scene Unit. CSI Scenario using PBL grid. Joint development of learning issues and desired outcomes.
  • Day 2: Review of ratios and proportions. Introduction of similar figures. 
  • Day 3: Practice solving similarity problems, including problems with proportions in the human body.
  • Day 4:  Learn to use GeoGebra software. Practice constructing similar figures and exploring their properties in GeoGebra. 
  • Day 5: Practice solving similarity word problems dealing with indirect measurements. Group work with digital evidence – qualitative analysis.
  • Day 6: Introduction to scale drawings. Scale factor. Practice drawing objects to scale using ratios and proportions.
  • Day 7:  Practice finding scale factor and using scale factor on a map. Group work with digital evidence – quantitative analysis using GeoGebra.
  • Day 8:  Practice finding distances on the map or scale drawings given scale factor.
  • Day 9:  Group work on written report and presentation
  • Day 10: Group presentations of evidence, results, and conclusions

The problem placed students in an active role of forensic specialists to investigate the theft of Picasso’s masterpiece The Tragedy from the National Gallery of Art in Washington, DC. Taking into account the fact that we worked in an online environment, instead of a real crime scene I used digital images taken at the crime scene that were “sent” to the forensic lab, thus creating an opportunity for students to do investigation using online resources only. You can read the full problem statement by accessing self-paced Nearpod lesson for day 1 at with the code JHM5V or by clicking here. The lesson first reminded students of the rules of working with the problem-solving grid, a graphic organizer for logical brainstorming, as a whole class. The process involves assigning one of students to be a scribe, a person who types information provided by other students into the grid. The whole class starts working with the first column until the scribe decides to move to the next column. Students can still add information to the previous column, but they cannot move forward until the scribe decides to do so. One of the very important aspects of this whole class activity is recording all student ideas without judgment or evaluation.  My next slide in Nearpod took students to Microsoft Sway that included a full problem statement, digital images from the crime scene, link to an editable Google document with a blank problem-solving grid, as well as some additional information about the actual painting. At this point students were given quite time to read the problem and then each of them had an opportunity to “raise hand” in order to add information to the grid. This process took about 30 minutes with adult learners, but I would have allocated one full class period for working with the grid if I was working with middle school students. My class had 18 students and I noticed that every single student participated in this process. Students were truly interested in the plot and wanted to add their ideas about solving the problem. The Google document that everyone could see replaced the white board we would have used in the classroom. At the same time, it saved all student ideas in a document that was easily accessible to all my students. This is just one example of how Google Apps could be used as tools for collaborative problem solving, inquiry-based learning, and student discourse in online courses.

As I wrote earlier, a problematic situation is used as a context for learning the topic. Thus, it is really important that as students complete their work with the problem-solving grid they identify their own learning needs that match my teaching objectives. In the past whenever I used a problem-solving approach, the first time around students would come up with about half of my objectives, and with each subsequent time the match is getting better and better. I consider it a successful problematic situation and student experience if their learning needs and my teaching objectives match at 80% or higher. In my previous experience teaching high school it took about 1-2 months to get to this matching level. 

The problem becomes a student group project for the length of the unit as we are exploring mathematics that they know they need. When a problem is engaging, they want to learn mathematics as they immediately see how they can use that to resolve a given problematic situation, and I think that is the major advantage of problem-based learning. I continued using the Nearpod platform to embed inquiry activities, problem-solving, technology tasks throughout the unit to maintain level of engagement and to provide students with collaborative activities and feedback. Nearpod has over 8,000 premade lessons available online, so I was able to find lessons that met my teaching needs for most of the unit. You can review the Nearpod lesson for day 6 that was modified from available premade lessons to introduce students to a new topic of scale drawings by accessing self-paced the Nearpod presentation with the code  WGBV4. Interactive features such as slideshow, video, and VR presented material to students in an engaging way. The collaborative board served as a place for sharing ideas, and student drawings and answers to open-ended questions provided me and my students with ongoing feedback. At the end of the lesson students were asked to reflect on their learning and how what they learned could help them in their crime scene investigation. All student work was automatically saved in Nearpod reports providing me with another opportunity to review student learning and make necessary adjustments to the next lesson.

By no means I found a solution to all problems of teaching online. I cannot resolve any internet issues for some of my students, and that makes it difficult to get them engaged. Some students cannot turn on their webcams because they have a very weak connection, and it is hard to teach without seeing student faces. I have some students who prefer not to participate in class discussions unless they are called upon. Small breakout rooms help in these cases, but then I cannot be in all breakout rooms at the same time, so I am missing listening to their discussions. Nevertheless, I believe that I found a way to create a virtual learning environment that became engaging and challenging (in a good way) for most of my students. I see their excitement when they get a new problem and I am hearing from them stories of how they could not stop working because they wanted to “find a thief”. I know that the pandemic will be over some day and I can’t wait to get back to my classroom, to see my students in person and not on computer screens. But with all that, I also know that I learned a lot during this time and I will be a better teacher when I am back in my classroom.

The Association of Teachers of Mathematics of New York City

Come join us and become a member. Our annual conference will be held virtually on Saturday, January 9, 2020. Sponsored by Texas Instruments. For further information: Or contact Ronni David:


Save the date: Friday March 12, 2021 

Celebrate Limaçon’s 35th year providing professional development for math teachers and administrators. 

A Taste of Limaçon Transforming the Learning and Teaching of Mathematics 

Join hundreds of educators at the first ever Limaçon virtual conference. Share the excitement as we bring the math community together and provide engaging content for  all math professionals. Sponsored entirely by Texas Instruments.

Complimentary Registration for all Participants 


  • 11:00 AM – 12:00 PM Session A 
  • 12:15 PM – 1:15 PM Session B 
  • 1:15 PM – 2:00 PM Lunch/Coffee Break 
  • 2:00 PM – 3:00 PM Session C 
  • 3:15 PM – 4:15 PM Session D 

For Registration Information and Updates visit Limaçon 2021.