Mathematics is actually an aesthetic subject almost entirely.
---John Conway, in Spencer, 2001, p. 165
Summary:
First of all, Henderson and Taimina point out the truth that intuitive understanding plays a major role in geometry. They agree with the tendency toward intuitive understanding fosters a more immediate grasp of the objects on studies, which stresses the concrete meaning of their relationships. In the field of geometry, concrete intuition is of great significance for anyone who wishes to study and appreciate the result of geometry. Amazingly, the artist and scientist both are contributors to constructing human mental and physical landscapes and are eager to show intuitions in their works. Henderson and Taimina's stories of their experience of meanings in geometry and art claim that aesthetics has always been a driving force in their experience of mathematics.
My stops:
1. Without understanding, we will never be satisfied; with understanding, we want to expand the meanings and to communicate them to others.
I totally agree with this quote. I believe that the construction of a knowledge system is based on understanding. Every now and then, I think back to my undergraduate PDE (Partial Differential Equation) and real analysis courses, I can still see our teacher energetically writing symbols at the front of the room. The teacher would spend almost the whole three hours at the board working with equations or formulas. We copied down everything he wrote, being afraid of losing one point on the quiz. We learned math by copying instead of understanding. I think I encountered with mathematics learning block when I was in junior year, I no longer learned mathematics with understanding and lost interest in learning mathematics. I wished I understood more about what all the symbols represented and which I was meant to put where in my homework or examinations.
Before I was in junior year, I had a different experience of learning mathematics. Whether or not I understand mathematics is responsible for the different experiences. When we understand, we can remember, transfer knowledge to new contexts, apply concepts to novel situations, look at problems from varied perspectives, and explain in ways that make sense to others.
2. Is creative thinking really different in its very essence?
Taimina shared her story with her students in her mathematics classes. Her students told me that the reason they took her class was to fulfill a distribution requirement. The students asserted that they were no good at mathematics, because they were artists, poets, musicians, actors, painters but not mathematicians, and their thinking was different. This made Taimina wonder: is creative thinking really different in its very essence? I also had the same assertion when I took two art courses last semester. The main reason for taking two art courses was to fulfill the credit requirement. I thought I was a math teacher and I would not be a qualified student in art courses. But I would be a good listener in those courses and now and then gave my peers nods and applause. Thanks to these two art courses, I realize that arts present a way to tap into these ways of understanding and learning knowledge.
When I look back to my math class, I found I have tried to integrate art into my Grade 2 mathematics class. “Making a Hat” was an activity to design a hat for the ping-pong ball with the shapes that students had learned such as rectangles, triangles, columns, or cones. Each student received a ping-pong ball and the first step for them to consider was how to keep the balls balanced. Some students stuck the balls on the desk with adhesive tape, and some students poked a hold on the top of the ball and put some plasticine inside. They cut the coloured paper into different shapes to design a unique hat for the ping-pong ball.
With art integration in mathematics class, it can make my own teaching more engaging and relevant to the lives of the children, and the students have more opportunities to practice and express ideas through language and their senses. There is also the pleasure of learning mathematical concepts through play and getting creative with and through maths.
Question:
Do you have the experience of making sense of mathematical concepts/context/knowledge through art or art activities?
I personally haven’t had too many experiences of using art to make sense of mathematical experiences which probably leads me to organize fewer of this type of experience for my students. When I lead guided drawing lessons, I often use fractions to describe where on the page I am drawing, and I use fractions for origami paper folding with the class. I think the opportunities I provide aren’t purposely for a specific math concept but use math concepts to explain the art or activity. I am very interested in integrating more purposeful art-based activities into my math class.
回复删除One project I remember from high school was called “parabola art.” We had to draw and colour a scene that included parabolas. We then had to label specific parabolas and find their formulas. I remember drawing a beach scene and had seagulls in the sky, beach ball and someone swimming as a few of my parabola examples. I remember really enjoying that project as a student as a different way to share my understanding of the concept.
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回复删除Hello Jianying,
回复删除I do not generally use art activities in secondary-level math classes. I can share one of my experiences when I used arts activities. I was doing my internship for my B.Ed. degree where I took math classes at the primary level for a couple of weeks. I used some pictures with different geometric shapes in them and asked students to identify those shapes.
I am not sure if that counts as making sense of mathematical concepts through arts. I will think more about how I can integrate arts to make sense of mathematical concepts. From the reading I had this week, I have learned that making sense of mathematical concepts through students' everyday life (using metaphors) has a very positive impact on learning. Maybe along with metaphors, different art activities can also provide this mathematics sense-making process.