ICT for Language Learning

Edition 10

Accepted Abstracts

Circular Functions: Unravelling the Mystery of Music

Ninfa Radicella, ITI ‘Enrico Medi’ – San Giorgio a Cremano (NA) (Italy)

Abstract

This work is based on a CLIL Unit realized in a class at the third year of senior high school, an IT technical institute. The Unit lasts 10 hours and deals with the relation between trigonometric functions and sound waves, focusing on the mathematical representation of notes and chords. This approach has a two-fold advantage: on one side it sparks students’ interest, on the other side it allows to make clear at least one among all the practical implementation from the very beginning, in order to make more meaningful their learning. The plan has been developed by using realia, mainly from Khan Academy. For each lesson the students have been provided with a worksheet with instructions and activities for each phase of the one or two-hour lessons. Useful vocabulary for each lesson has been provided, as well.  Teacher’s notes for each lesson have been prepared.

The Unit has been developed in six lessons, including the final assessment with a two-hour written test. First lesson is devoted to a warm-up phase and some group activities on a video on sinusoids in music: periodic features, mathematical representation and manipulation. Then, by means of flipped class methodology, the students are asked to practice with trigonometric ratios and right triangles. After that, as a classroom activity, the trigonometric definitions of sine, cosine and tangent are generalized for all angles through the unit circle. The subsequent lesson is devoted to graphing trigonometric functions by deducing their values for remarkable angles. The last two lessons have been spent to analyze periodicity properties of sinusoids: period, midline, amplitude, phase shift. This topic is developed both by reading the graph and deducing the function and the reverse.

In the final part, the first video has been re-proposed to reanalyze notes and chords, sound in general, through their mathematical representation.

 

Keywords

Circular functions, waves, sinusoids, periodic properties

 

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