A motion sensor is a probe for collecting motion data, such as distance, velocity and acceleration, over time. Connected to a calculator, the motion sensor gives data that can be represented on real time on the screen of the calcolator, through a graph, or that can be collected in a table.

Many studies in literature report on the cognitive support that experiments with sensor and calculator can give to the construction of mathematical concepts, as for example the linear function, the parabolic function, and so on.

Some of them:

• Ferrara, F., Robutti, O. (2002). Approaching graphs with motion experiences. In: A.D. Cockbrun & E. Nardi. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (PME 26).
• Arzarello, F., Robutti, O. (2003). Approaching algebra through motion experiences. In: Perceptuo-motor Activity and Imagination in Mathematics Learning, Research Forum 1, Proceedings of PME 27. Honolulu, vol. 1, p. 111-115.
• Robutti, O. (2006). Motion, Technology, Gesture in Interpreting Graphs. The International Journal for Technology in Mathematics Education, vol. 13 n.3; p. 117-126.

A graphic calculator has the same functions as a normal calculator plus the capability of representing data on a graph, a table or through a formula. The different environments of the calculator are connected in a way that the same mathematical object (e.g., a function) may be represented in all of them and the user can pass from one to the other representations. Moreover, the calculator can be linked to a probe (of motion, or other quantities vs. time) and in that way, receive data from measurement on real time, representing those data on a graph. The motion sensor can acquire data relative to body movements and the student can explore the mathematical relations between distance, velocity, acceleration and time. The students of a class can see the building of the Cartesian graph on a big screen, while one of their school-mate is moving.

Since "vast tracts of the brain are engaged in perception and construction of imagery, [but] there are also huge areas of the cortex that are plastic and useable for a variety of activities including the many processes involved in thinking mathematically" (Tall, 2000) such representations "can provide a powerful environment for doing mathematics and, with suitable guidance, to gain conceptual insight into mathematical ideas". In fact mathematical symbols can be used as cognitive "pivots between concepts for thinking about mathematics" (Tall, ibid.).

Tall, D. (2000). Biological brain, mathematical mind & computational computers. Plenary presentation for ATCM conference, Chang Mai, Thailand, December 2000.