Learning math with robots


In the last 2 years, students of IC21 lower secondary school in Bologna (age 13) attended their classes with several restrictions due to pandemic; cooperative learning helped to engage them after a longtime isolation experience.

In order to help students learning math curriculum contents, collaborative activities were designed with Lego WeDo2.0 © educational robots.

The contents selected from the math curriculum of the lower secondary school are:

  • measuring circumference
  • value of π (PI) with appropriate rounding
  • measuring the circle area
  • measuring speed in linear and circular motion

The activities were designed and implemented in collaboration with Drs Lorenza Prencipe, who has presented her dissertation in Mathematics Education at Bologna University on March 25, 2022. IC 21 school is accredited as a training venue for Bologna University students.


Resources used for the activities are: 

  • educational robots Lego WeDo2.0 ©
  • chromebooks with the Lego Education © app to program the robots
  • worksheets with driving questions to report observations, data and conclusions 
  • millimeter paper and other measurement tools (ruler, chronometer, goniometer)
  • instruction slides shared in Google Classroom
  • assessment rubrics regarding the learning outcomes and the collaboration skills

Students worked in groups of 3, distributing roles as building the robot, programming the robot motion and measuring data.

Students used two different models of robots for the linear motion (rover) and for the circular motion (satellite). The instruction provided in the Lego website was used to help students in building and programming the robot; the lesson plan was replaced by our own contents.

Students’ work

For the circumference measurement, students prepared the rover model with a pen and a reference mark on a wheel, and programmed its motion to draw a line as long as a wheel circumference. They measured both the line length C and the wheel diameter d in order to compare the rounded value of π with the ratio C : d.

diameter measurement
line drawing

For the circle area measurement, students prepared the satellite model with a pen and programmed it in order to draw a circle on the millimeter paper. They counted the cm2 included in the circle and compared this approximation to the area calculated by measuring the radius (distance from the center to the pen).

circle drawing
area calculation
circle area

For the linear motion activity, students prepared a unit line on paper sheets and programmed the rover model to run on the line with a chosen engine power (according to the programming app).  They measured time and distance in order to calculate the speed and made a distance-time plot.

reference line
time measurement

For the circular motion activity, students prepared an angle plot on a paper sheet and programmed the robot to move around its center. They measured the time needed to make a 360° angle and found different angular speeds depending on the programmed engine power.

For each activity, students used intructions and worksheets shared in Google Classroom. Here are some examples (in italian):


For each student, we prepared rubrics for formative assessment, written and oral tests and peer assessment tools.

In the students worksheets the answers were analyzed, dividing items into comprehension, mathematical skills, and critical thinking about mistakes and approximations.

As a peer assessment tool, a rubric with 3 levels of performance was provided to groups: students of each group had to report their observations on the third one based on the role taken in the group (building, programming or measuring).

In further problem solving tests, students had to apply math contents connected to the activities, in order to evaluate their comprehension of the properties involved.

In oral tests, students had to explain the activities using their own description of the working phases, measured data and conclusions, in order to assess communication and reflection skills. Presentations prepared in this phase were also a useful trial for the finale exam.

This activity has given students the opportunity to explore math in active and collaborative situations, and to develop further skills besides mathematical reasoning: problem solving in a real-world context, critical thinking, and cooperation in team working.

students questionnaire 1
students questionnaire 2

Cultural heritage in sustainable development – AR Quest

Do you know why Coca Cola has the Coca in the name? Are 24 “holes” in Petit Beurre biscuits accidentally there or they have deeper meaning? Do you know who invented ketchup? What types of cocoa beans are used for chocolate? Have you ever visited sanatorium where cornflakes are invented?

Cultural heritage and STEAM

At the mention of sustainable development and sustainability, the first thing that comes to mind is usually the thought of ecology, environmental science, recycling and similar. What is still very important, and lesser known, is that one of the crucial roles of sustainable development (SDG 11: Make cities and human settlements inclusive, safe, resilient and sustainable) plays preservation of cultural heritage. Target 11.4 calls for strengthening efforts to protect and safeguard the world’s cultural and natural heritage. UNESCO’s work has addressed this goal even before its formal introduction in 2015.

Each country has a rich cultural heritage that can be successfully integrated into the teaching process of each subject, especially in STEAM, in order to achieve curricular outcomes. Moreover, there are such elements of cultural heritage that are known on a global scale. How to fit them into the teaching process, achieve a high level of engagement, develop crucial 21st skills, and at the same time make the whole learning process fun? By using gamification and augmented reality technology in order to create an AR Quest.

Augmented Reality and gamification

Using AssemblrEDU app for augmented reality and Europeana resources students are taken on a global quest around the Earth. As they visit various places, they are discovering fun facts about various soft drinks like Coca Cola, well known food products (ketchup) and food plants (cocoa and corn) throughout the history. They are learning about rich cultural heritage while achieving curriculum outcomes. To finish their quest, they need to solve a problem attached to each location. By completing all the stations and by solving all the math problems, they unlock the words used in the word search puzzle created in Genially tool. When the student solving the puzzle finds all the words, the hidden message will be revealed.

The students only need a mobile device with AssemblrEDU app to activate AR Quest. This activity is made for a remote teaching environment but can be easily used in any teaching environment.

running augmented reality experience

Aim of the lesson and integration

The aim of this interdisciplinary lesson is to practice math modelling real life problems, learn about cultural impact of various famous food products, gain new vocabulary in English and gain skills in using augmented reality technology.

Students develop all language skills (reading, listening, speaking, writing).

In the national Math curriculum for the 1st grade (15-year-old students) there is an outcome “Applies proportionality, percentages, linear equations and systems”, by which students need to gain skills of mathematical modelling in math, from other fields and life. Also, to solve linear equations and systems of linear equations.

Learning scenario is easily integrated in any  English language lesson. As in national curriculum stands a unit for students to analyse a custom text in writing and also to listen with understanding all this is supported in scenario. One of the outcomes is to communicate in formal and non-formal situations, therefore, it fits in any of English lessons.

History curriculum contains a unit on industrial revolution, which covers the topic of key inventions and scientific discoveries as drivers of industrial revolutions and changes in daily life.

This lesson can be used for Biology covering a topic on various food plants, and nutrition facts.

ICT has a unit on using new technologies and apps, in which this scenario fits perfectly with using AssemblrEDU app as a tool for activating AR Quest and using augmented reality technology.

Augmented Reality EarthQuest

After intriguing the students with questions posted above, they were provided with a QR code for a quest around the Globe to answer these questions. Students get a math Worksheet which they individually need to fill visiting stations on an AR Quest. Using AssemblrEDU app they „visit“ different places, read and watch fun facts about food products, drinks and food plants. On each station, one math problem is given. They need to write it down and solve it.

A story about Pemberton as embedded YT video

In the last location of the tour, link to an interactive quiz for self evaluation is given. As students give the right solution, a word appears. If their solution doesn`t make sense or it is not given, students will know they need to reassess their errors. At the end the words should be crossed out in an online word search puzzle (students can also print it out if it is more convenient for them). After crossing out all the words, a hidden message appears as a final solution. (“Enjoy little things in life”).

the final task of the Quest

Last year during the lockdown I made and used this learning scenario with different tools and with different students (the original learning scenario can be found here). I have used Google Earth app in order to make a virtual tour. But this year I have used a different approach to achieve an even higher level of engagement. I wanted to give my students the opportunity to interact in a different way. So, I have modified the activities and combined immersive AR technology with gamification. The use of AR and AssemblerEDU app was a real game changer for achieving high levels of engagement, excitement and teaching for and with creativity. Students were thrilled with this AR Quest. The activity was implemented on students aged 17-18 of age as a retrieval practice for state exam. It was a great addition after learning about sustainable development goals for raising student awareness about cultural heritage as one of the SD goals.


The place and importance of Mathematics in STEM Education

STEM education has attracted the attention of educators all over the world in recent years. Since the 21st century is an age of information and technology, new career needs arise every day in the business world. These emerging career definitions also change the expectations of the business world from education and training institutions.

Today, individuals should equip themselves in the fields of science, technology, engineering, and mathematics. To meet this demand of the business world, many educational institutions, especially the Ministry of National Education of the countries, have focused on the STEM education-training approach. The basic philosophy of STEM education is to realize the disciplines of Science, Technology, Engineering, and Mathematics simultaneously and in an interrelated way within the context of education and training activity.

Since ancient civilizations, mathematics has been one of the most important components of education. Although the nature of mathematics knowledge has changed compared to the past, it easily continues this feature today. While theoretical mathematics knowledge was at the forefront in the past, applied mathematics knowledge has become an important need in the fields of engineering, design, finance, informatics, and similar fields today.

Mathematical modeling that can be applied to problems is very important for STEM. Students grow up as individuals who can produce solutions to real-life problems. They have the equipment required by them and the age of technology.

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Geometry and optical illusions

Author: Daniela Leone

Methodology and tools

This is a remote learning activity, developed in March 2020 with 1st-grade students of IC21 Bologna lower secondary school.

The tools used are GSuite for Education, GeoGebra and Go-Lab resources. The activity is based on Inquiry-based Learning methodology.

Students had a little experience with GSuite, Go-Lab and GeoGebra but no experience of learning from home. To be able to communicate we used GSuite tools (email, tutorials on Google Classroom, Google Meet calls).

The Go-Lab Inquiry Learning Space used for the activity is a translated version of the French ILS “Changer de perspective” created by Valentin Roussel.


Thanks to the author, the ILS was useful to guide students in discovering basic geometry in a playful way: it aroused their curiosity about the features that add special effects to images. The questions helped students to reflect and recognize the main properties of parallel and perpendicular lines, angles, areas, by manipulating dynamic figures. The images included in the ILS were inspiring for students.

At the end of the translated version made for the IC21 school, I added an extra task for my students: they were asked to make and share their own images containing optical illusions or special effects, using the GeoGebra Geometry App. 

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Symmetry in Mathematics and Art

On April 23, 2019, the topic “Symmetry in Mathematics and Art” was presented at Teodor Trayanov’s 10th School in Sofia. During the hour Neda, Koya and Toni introduced the students of the 5th grade with several types of symmetry in mathematics and art. With the help of dynamic resources created with Geogebra, the pupils made an author’s works.

Axial symmetry
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