Geometry Through Art

Norman Shapiro

Making Portfolios

What Children Can Learn About Art and Geometry

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Students can and should make portfolios of artwork accompanied by written notes or personal logs. Whether displayed or maintained in notebooks, these colorful visualizations offer the class as a whole a valuable continuum.

Students sense the raison d'etre, the "why and wherefore" of this laboratory/art studio experience. Hardly ever does anyone ask, "Why do I have to do this?" It's more likely that students will want to know more about the art and mathematics they have learned.

Artwork becomes a diagnostic tool for evaluating the effectiveness of learning and teaching. The teacher, and in many cases the student, can see at a glance the issue at hand. Effectively used, artwork can be a teaching 'manipulative': it is personalized, student-made, and utterly nonthreatening.


A holistic insight into angle properties and their relation to
measurement is gained by using the circle. Given that the sum
of the central angles in the circle is 360 degrees, the secret of
all angle measurement becomes plain. Grids reveal the direct
bearing of lengths of arcs and chords on the central angle.

Finally, as to attention span and whether the student will stay the course, this varies from grade level to grade level. I recommend that teachers explore only as long as their students show interest and enthusiasm. Learners need time, not only to make lovely art, but to interact with the process and with their peers. By all means allow the artwork to be finished - children like to see their work on display. With the crowded schedule of the school year the approach described here may seem expensive, but in the long run it is time well spent.

Heuristic learning, done well, leads to stronger and deeper understandings, to more creative involvement. Such creativity and insight are vital, whether in the arts, in mathematics, or in the sciences.

From the portfolio of Craig Borsetti, Grade 3


Copyright 1995 Norman Shapiro

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4 November 1995