From formula to motion: robotics for understanding, verifying and correcting. PariPasso webinar with Michele Fiore
With robotics, a formula ceases to be merely a note in a exercise book: it becomes a distance to be covered, a trajectory to be constructed, an angle to be verified, an error to be explained. This is the principle at the heart of Mathematics in Motion. Solving Problems with Robotics, the new webinar from PariPasso, the Rizzoli Education project dedicated to educational inclusion, organised by the Fondazione Mondo Digitale.
Leading yesterday’s session was Michele Fiore, an engineer and teacher of computer science, mathematics and physics, who demonstrated how educational robotics can make mathematical concepts covered in lower secondary school tangible and experiential.
‘What if maths could move?’, was the thought-provoking question with which Fiore began. A circumference, a proportion or the formula for speed can, in fact, become the instructions needed to make a robot move. But the crucial step remains the one taken by the pupil: understanding the problem, formulating a prediction, programming a solution, verifying the result, correcting and improving.
A metre is not always a metre
The first challenge set during the webinar seems very simple: to programme a robot to travel 100 centimetres. Before moving it, however, some thinking is required. What is the circumference of the wheel? How many revolutions are needed to cover one metre? What is the relationship between diameter, revolutions and distance? With a wheel 6 centimetres in diameter, for example, one complete revolution ideally corresponds to approximately 18.85 centimetres. To travel one metre, therefore, just over five revolutions are needed. Then comes the simulation. And the robot might stop at 97 centimetres. It is precisely at this point that the activity becomes interesting: why are three centimetres missing? Is the formula wrong? The programming? The measurement? In a real-world situation, friction, slippage and the robot’s precision might also come into play. ‘Errors are essential for helping the pupil better understand where to take action,’ explained Fiore. The proposed method follows three easily replicable steps: predict, experiment, discuss. First, a calculation is made and a hypothesis formulated; then the robot is programmed and the simulation observed; finally, the data is compared, discrepancies explained and corrections proposed.
Drawing a square with a robot
The second task takes geometry off the page. The robot must draw a square with sides measuring 50 centimetres. To achieve this, it needs to know the perimeter, set a sequence of four identical movements and correctly programme the 90-degree rotations. With just a few modifications, the same programme can be adapted to draw an equilateral triangle: three sides and an outward rotation of 120 degrees. From here, we arrive at the general rule for regular polygons: the angle of rotation is equal to 360 degrees divided by the number of sides. And once again, it is the error that leads to learning. If the path does not close and the robot does not return to the starting point, ‘the error becomes a mathematical problem to be interpreted’. We must ask ourselves whether the distance travelled is correct, whether the right angle has been set, or whether the observed behaviour deviates from the theoretical model.
Distance, time, speed
The third challenge introduces new variables. The robot always travels the same distance, but the speed changes. What happens to the time taken? Students can work in groups, set different speeds, record the results in a table and compare them.
Distance, time and average speed thus become observable data, to be related to the formulas studied. The simulation also paves the way for inverse problems: given speed and distance, how long will the robot take? And does the time really halve if we double the speed? Simple questions that force us to compare the theoretical model with the observed behaviour, transforming the calculation into a problem-solving experience.
Reasoning first, the robot second
During the webinar, Michele Fiore used Open Roberta Lab, a platform that allows users to programme using graphical blocks and virtually simulate the behaviour of various robots. It is therefore not necessary to have a fully equipped laboratory or physical robots to carry out the activities. The activities can even begin with a ‘human robot’: a grid on the floor and students giving movement instructions. You can then move on to the digital simulator and, where available, to physical devices. ‘The end result is not that of the robot,’ Fiore emphasised. ‘The robot simply carries out the pupil’s reasoning.’ And this is also why assessment cannot stop at the robot correctly completing the course. One must observe understanding of the problem, calculation, strategy, verification and reasoning. A correct result, on its own, does not reveal the process that led to the solution.
Mathematics for everyone
The approach also lends itself to inclusive teaching. Activities can be differentiated by level of difficulty and roles distributed within the group: some calculate, some programme, some observe, some document and some narrate. In Year 7, work can focus on measurements, equivalences and paths; in Year 7 on polygons, angles, ratios and proportions; in Year 8 on average speed, graphs, the Pythagorean theorem and error analysis. The programme can also take on an interdisciplinary nature: maths for calculations and measurements, science for the study of motion, technology for programming, English for documentation and reasoning, right through to foreign languages for technical vocabulary.
Anyone who was unable to watch the live stream can catch up by watching the full recording and try out the suggested activities.
Watch the recording of ‘Maths in Motion: Solving Problems with Robotics’Materials and further resources for teachers are also available on the Fondazione Mondo Digitale’s FMD Academy.The webinar’s closing message is concise and effective: mathematics guides movement, predictions are tested against data, and mistakes become opportunities for learning. This is truly how mathematics comes to life.
