Summary
Gerdes begins with comments on the high illiteracy rate in Africa and the methods of teaching math based on rote memorization which downgraded children's informal practical math skills. Even worse, colonization that took place in the past in Africa had a huge impact on the Mozambicans there and wiped out their unique cultural and mathematical traditions. Later, a "cultural rebirth" recognized and incorporated the Mozambicans' indigeneous mathematics into the new curriculum, emphasizing geometrical forms and patterns of their weaving skills. A new generation of math teachers now investigates and rediscovers the math ideas and the geometrical thinking that their parents and ancestors unconsciously used when weaving various products. One example that the author presents is a square woven button consisting of 4 right triangles whose hypotenuse forms each side of the button and a tilted square in the centre of the button. He explains how to take the button apart in a manner that shows the use of the Pythagorean theorem. Other examples of woven products are funnels, fish traps and soccer balls whose geometric patterns and properties are associated with pyramids, similar figures, polygons, and the sum of all the interior angles of an n-gon.
Reflections
First, the author's statements, "The artisan, who imitates a ... technique, is ... not doing mathematics. But, the artisan(s) who discovered the technique, ... (was) were thinking mathematically. (p140-141)" really resonate with me when I think about the students I tutor. Some of my students tend to imitate how they learn from their math teachers without injecting any creativity into their own problem-solving strategies. The reason is that they fear they will lose marks for not "imitating" their teachers' ways of doing math. Imitating is not learning and telling is not teaching. To ensure "real" learning, I think as an activity, teachers can give their students an opportunity to prepare a lesson plan, deliver it to their peers and demonstrate their creative ways of doing math. Teachers need to be more open-minded about the ways their students do problem-solving.
Second, the weaving skills of the Mozambicans lead me to think of the excellent carving and drawing skills of the Aboriginal Canadians. The First Nations' history in Canada is rich and diverse. Their artworks and sculptures, especially the totem poles, involve a lot of geometric thinking and reasoning, a practical math skill that the indigenous people use unconsciously. Incorporating their artistic works into the math curricula is a way of recognize their contributions to Canada. This makes math more meaningful and interesting to students when they can learn math in the context of Canadian history.
This sounds like an interesting reading. I'm often interested in mathematical patterns in art, and the ways that they can be expanded upon and interpreted by artists. This can also be a good entry point for some reluctant students. One of my favorite assignments has been asking Grade 12 classes learning about transformations to use computer software to make some designs using the various functions (quadratic, linear, exponential, trigonometric). Some students have made some amazing works of art with these. I"m going to try to attach a sample to this comment.
ReplyDeleteOK. I can't figure out how to attach here, I'll bring some samples to class tomorrow.
DeleteThat's an interesting phrase, ``geometric thinking... unconsciously used.'' I wonder how much that unconscious geometrical thinking, in a broad sense, is found throughout the world, in many other cultures. I would guess it is nearly ubiquitous. Mathematical thinking is certainly not reserved for classroom use only, and I like Dave's description of patterns in art as `a good entry point.' I also wonder: could it be enough to do math unconsciously? Sometimes placing the label of `math' on an exercise seems enough to drive away the masses that would otherwise be completely competent, enthusiastic even.
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