Visible Maths

Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualization, and flexibility, the mathematics comes alive.


The starting point of the Visible Maths series of workshops was the fact that students have difficulties understanding mathematical concepts. So, I thought that creating real objects that show mathematical concepts might support students’ understanding.  


The students involved in this project were 9th graders (14-15 years old) and I worked with Miruna Batin, a professional designer from Scientifica, for designing and implementing the workshops.


The workshops started at the begging of February, and we organised and implemented two workshops each month.

Workshop 1 (3 February 2022)– Launching the task

We started by launching the task.

Choose a mathematical concept (e.g. radian, cone sections, trigonometric circle, function, number, Pascal’s triangle, etc.) and design and make an object to illustrate the concept.

After that, the designer made a presentation about what is the design of an object & how to go from design to object.

Then, the students organized themselves in groups. After that, in the Zoom breakout rooms, they started to brainstorm for choosing the mathematical concepts.

Workshop 2 (17 February 2022) – Defining the idea  

The students’ teams continued their work in the Zoom breakout rooms for deciding on the mathematical concept chosen by the team. They had to vote for their favourite idea as a team. For this, they took time as much as they could to learn about the concept. They reflected on their learning by writing down on the team’s Jamboard:

  • information they already knew
  • 3 unanswered questions
  • 3 new information about the concept they found in their research
  • 1 thing other students should know about “their” math concept.

Workshop 3 (3 March 2022) – Function, form, and materials

Each team presented, in the plenary the maths concept and the object/ the mathematical experiment they intend to create, pointing out how people could interact with the object.

Then, the designer made a presentation on different types of materials and how object creators choose the materials for making stuff.

I never thought about the materials in such a detailed way.

Ana – student

After a Q&A session with the designer, they worked in teams (in the breakout rooms) for designing the objects and for deciding on the materials (type, quantity, providers) they need.

Workshops 4 & 5 (25 March & 13 April 2022) – Prototyping & testing

Each group created a mock-up of their object – from recycled material – as the students wanted to check if the maths experiments can be implemented.  

The Golden Ratio mock-up

Further, the students wrote on Jamboard questions about the prototype, dimensions of the objects, and materials. Both the designer and I gave feedback on the students’ work and tried to support students to find answers to their questions.

The Pascal’s Triangle – work in progress
The Pythagoras’ theorem – work in progress

Before the 5th workshop, the students “asked” for the materials they need by filling out a Google sheet. So, I bought the materials.

Radians & degrees – work in progress

So, the students started to work on the final version of their objects. Some of the groups have already finalised the work, and some are still working on them.

The inverse of a function

Workshop 6 (planned on the 28th of April 2022, postponed for mid-May) – Presenting the prototypes and the work process

As not all teams finished their work on the objects, we had to postpone the last workshop. Can’t wait to try all the maths experiments, together with the students’ teams.

Cone & Cylinder volumes

All the created objects will be donated to the maths teachers in our school – so, next school year we will use them and do the maths experiments with our students.

This series of workshops are local activities implemented in our school, Colegiul National Emil Racovita Cluj-Napoca, within the Smart Hands (Erasmus+ project).