Third MTA Conference (online) 2021 — Workshop

Workshop on digital technology and online resources (for school teachers)


Learning with virtual manipulatives by Phillipp Lengner, CEO, Mathigon (for school mathematics teachers)

Date: 4th September 2021

Coordinators: Jonaki Ghosh

For decades, manipulative materials have been used to engage learners in mathematics classrooms. Such materials provide concrete representations and embody the underlying structures of mathematical concepts. They enable students to visualize, explore and discover using a hands-on approach. However, like all resources, the use of manipulatives by themselves cannot lead to mathematical understanding and insight. For learning to be effective, it is imperative that students understand the relationship between the concrete materials and the concepts they represent.

Manipulatives such as Dienes’ blocks, place value tiles, abacus, counters, fraction bars, number grids, tangrams, etc. provide students an opportunity to work in the enactive mode. The online mode of learning however makes it difficult to integrate such concrete manipulatives in the teaching and learning of mathematics. The virtual counterparts of these manipulatives, present a great potential for learning and exploration and have special relevance in the present times where classroom interaction is mostly in the online mode.

Virtual manipulatives are also great for inspiring creativity and teaching problem-solving skills. In this workshop, we will explore many different examples: from tessellations and algebra tiles to tangrams, pentominoes, prime factor circles, multiplication grids, Penrose tiles, number lines, dice, 3D polyhedra, balance scales, and much more. The workshop will be presented by Philipp Legner, the creator of Polypad, which has been used by millions of students all around the world.

The schedule of the workshop is as follows

3:15 – 3:20 pm   Brief Introduction to the theme of the session (Jonaki Ghosh)
3:20 – 4:25 pm   Learning with virtual manipulatives (Philipp Legner, CEO, Mathigon)
4:25 – 4:45 pm   Q&A and interaction with the audience

Biosketch of resource person

Philipp Legner is the founder and CEO of, an award-winning platform for learning mathematics that is used by millions of students every year, all around the world. His goal is to build the “Textbook of the Future” and to make learning more interactive and engaging than ever before. Philipp previously studied mathematics at Cambridge University and mathematics education at the UCL Institute of Education, and he worked as a software engineer at Bloomberg and Google.


To attend the workshop, you need to register for the conference.

Registration link here.