Whether we are conscious of it or not, the way we teach mathematics is very much influenced by what we conceive mathematics is and what is important knowing about it. As part of our Lesson Study project with a group mathematics teachers, I was tasked to share my thoughts about the nature of mathematics and its implications to its teaching and assessment.
I have always believed that mathematics should be experienced by the k-12 learners as both practical and theoretical, as a language, as a process of thinking and, as an art. Of these five, I have always felt the least confidence in speaking of mathematics as an art. Most of the times, my “mathematics is an art” becomes “there is art in mathematics”. The latter is much easier to discuss because teachers know this so there’s not much need for me to explain. What I do and I don’t know if I get away with it, is give beautiful examples. Here are two of them. Click image to get to the source.
Math Art | Love and Tensor Algebra via kwout
Where there is art, there is beauty. And what is the beauty of mathematics? In most cases, it’s in patterns. I would regale teachers with patterns in nature that mathematics could perfectly represent and capped my lecture with Galileo’s pronouncement that Mathematics is the language used by God to write the universe. With this, I could get away from mathematics as art to mathematics as language.
Then I came across this post titled What is an art? which defined art as a habit of thinking, doing, or making that demonstrate systematic discipline based on principles. The post described arts as about connections and that understanding the connections between things allows designers to accomplish their goals. It described art as based on principles and not just a series or procedures or methods; that there can be many methods inside an art … Finally, and I love this part, it said that art must be acquired as a habit, so that its practitioners become “unconsciously competent.” I thought the post could very well be speaking of teaching and learning of mathematics especially in its giving importance to making connection, open-ended problem solving, and the acquisition habits of mind which are favorite topics of mine when I’m invited to share my thoughts about mathematics teaching.
You may want to view this beautifully crafted video about mathematic in nature. Click link.
Mathematics is an Art
Dear Erlina, I wholeheartedly agree with your view on what math really is and what we should bring to the classroom. It is general practice to ask students to make an art journal to show the development of an idea in a blank notebook. We can encourage students to make a math journal jotting down every thought, question, diagram, illustration, formula, graph or the like. This can bring math to life and also be a basis to engage in student-student and student-teacher math centered conversations.
Open ended questions and individual thinking go hand in hand with differentiation!
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Thanks 4 d write up,it really meant my nid at d right time.more grace 2 ur elbow
I am so interested in this topic. My work is integrating dance, rhythm, and elementary math topics in the program Math in Your Feet. I think you’re right on about patterns being the connecting point between math and art — it’s the starting point and focus on my program. Also, what you said at the end of your post: “I thought the post could very well be speaking of teaching and learning of mathematics especially in its giving importance to making connection, open-ended problem solving and the acquisition habits of mind…” describes my work to a ‘T’. Here are a couple links to posts in my blog that I hope might contribute to your thoughts and understanding of the nature of mathematics as it relates to art:
http://mathinyourfeet.blogspot.com/2010/11/power-of-limits-4-jazz-metaphor-in.html
http://mathinyourfeet.blogspot.com/2010/11/more-than-sum-of-its-parts.html
And, by the way, in reference to your Mathematics is… diagram, I think we could use almost the exact diagram to describe art of all kinds, but we’d have to leave out the category of ‘theoretical.’ Art is very firmly rooted in the present moment.
Thanks for your thoughts!
I want to add three defining characteristics (to me they are the defining characteristics) to the definition of art that you are constructing. I think all three help illuminate why math can be an art. I’m basing the choice of these characteristics on my own experience as a musician. Other artists might have other definitions, but actually I speculate that these are pretty commonly held as important characteristics of art.
1) Art is creative and expressive.
All the arts are about making things. Songs, paintings, plays, performances, etc. Crafts and industry are also about making things, but what distinguishes art is that the act of creation is an act of expression for the person doing the creating. Creating the painting, playing the sonata, singing the song, etc. are all ways of taking a part of yourself and giving it to others.
(Why math is creative and expressive: every time you figure out how to solve a problem you’ve never solved before, or how to prove a conjecture you have, you’ve made something new that expresses how your mind works to others.)
2) Art engages the imagination.
All the arts stimulate you to see, hear, feel things that aren’t part of the material world. You read a novel or see a movie and you imagine the world it creates. You hear a symphony and you may visualize all kinds of things, or you may just feel them. Either way, your mind and spirit are sent off in totally new directions.
(Why math engages the imagination: if not for math, would I ever have tried to visualize a 4-dimensional torus? The Riemann surface of the sine function? The real projective plane? The strange images in my head that I use to visualize concepts like exact sequences or field automorphisms?)
3) Art is driven by aesthetics.
Artists try to make their creations aesthetically captivating: beautiful, haunting, winsome, grotesque, tragic, delightful, etc.
(Why this applies to math: it’s different for every math person but we all have a sense of aesthetics – what makes math beautiful. For me and for many, a simple argument that proves a powerful result is elegant, for example Euclid’s proof of the infinitude of the primes. Even more beautiful is a theorem that describes a deep connection between apparently very different mathematical realms. For example the Pythagorean theorem as it connects “right anglyness” with “sum of sqaresiness,” the Fundamental theorem of Calculus as it connects “speed” with “area,” or Galois theory as it connects “groups” and “field extensions.”)
Two semi-classic pieces of writing on math as an art that you might find add to this conversation –
Paul Lockhart’s A Mathematician’s Lament.
G. H. Hardy’s A Mathematician’s Apology.
Both Lockhart and especially Hardy aggravate me (Lockhart with his blanket disdain for math educators and Hardy with his attitude that mathematical talent is an intrinsic attribute that declines with age), but both write eloquently and passionately about how math is a creative art.
Beautiful!. Thank you so much for sharing your thoughts.
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