# Learning math with robots

## Activity

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

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.

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).

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.

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):

## Assessment

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.