AN EXAMPLE OF EDUCATIONAL INNOVATION IN PHYSICS AND CHEMISTRY: THE TEACHING OF LARGE NUMBERS. MODELS AND ANALOGIES THAT FACILITATE THEIR COMPREHENSION

摘要

Teachers know from their own experience the difficulties the students face when working with large numbers in Physics and Chemistry. Also, they know their lack of understanding of the real significance of these large numbers in relation to other numbers they recognise and that are near to their daily experience. Normally these large numbers are usually expressed in terms of exponential notation makes them be more Abtract that if stated in a notation that might be called "school", ie without resorting to such exponential notation. Thus 1023 will write the drive of 23 zeros. Students and even university teachers are not fully aware that for each zero added to the right the previous amount is multiplied by 10 or that for each zero removed it is divided by 10, despite knowing it theoretically. Films such as "Powers of 10" have been made in a quite visual and didactic way with the aim of making students understand what means to increase or decreases by a factor of 10 (multiples and submultiples) the magnitude of the distance in meters between the observer (the audience through the camera) and an object (a young man lying in a park in New York). Thus, we move away from the boy to reach the limits of the universe in 30 steps, or we introduce a pore in the skin of his hand to reach the interior of the nucleus of atoms in 15 other steps. In spite of efforts as commendable as this, we repeatedly find that if we consider other values and even the same magnitude "length", students still have great difficulties to perceive the real meaning of such large numbers always expressed in the form of exponential notation. The fact that most books (and consequently most of teachers) continue to pose exercises -not real problems- with unrealistic results do not contribute to improve the situation. What we try to do in this work is to try to schedule a series of tasks that lead the students to be aware of this reality by the method of the comparison or analogy between the calculated or estimated amounts and other amounts that can be close to the people's reality or, at least, intuitively intelligible in comparative terms.