Atelier Fibonacci
Art and Math Integration
Leman Middle School 7th and 8th Graders.
Teaching artist, Buddy Plumlee. Teacher, Jacob Hernandez.
HOW DID OUR TEAM CONCEIVE OUR PROJECT?
Prior to the summer program beginning, we (Jacob and Buddy) knew we had to develop some projects that focused on integrating visual art with math. In our naivete, we expected this would prove to be a peacefully undemanding task. The simplicity of it seemed beguilingly easy at first. But from the outset of our first casual conversation we concluded this was in fact a taller order than originally supposed. It became immediately apparent that a coffee-centered brainstorming session was inescapable. So we made haste to schedule an engagement three days hence at Kindred Coffee Roasters where we would convene a ponderous deliberation and formulate our plans.
After an inaugural cup of cappuccino derived from arabica beans grown on the lush slopes of the Sierra Madre de Chiapas in Guatemala, we drank another, or at least one of us did, followed by yet another about thirty minutes later. The boost from this elixir mobilized our creative faculties, and with the agility and enthusiasm of mesolithic inventors who had just discovered the wheel we contrived the framework of our plans.
Aided by the search engine Google, our virtual unpaid intern, we researched "art lessons that integrate math". The path led us to many and varied possibilities. We settled on the mathematically beautiful order represented by the Golden Ratio (a + b is to a as a is to b), which can be illustrated by designs created through employing the Fibonacci Sequence, and readily observed through numerous examples in nature (ie: the spiral arrangement of leaves, the spiral formation of sea shells, tidal waves, and the clockwise flow of water down a toilet that has been flushed). The Golden Ratio also has an intimate relationship with geometry where it is a prominent feature. For instance the Golden Angle, which is visibly evident when a three-dimensional cube (hexahedron) is represented two-dimensionally, with three faces of equal size and shape.
With this research having yielded fruits beyond expectations we decided on a course of action and adjourned our meeting. The geometric cube and the Fibonacci sequence would be our starting point.
Fibonacci Sequence and the Golden Ratio
Hexahedron and the Golden Angle
HOW DID OUR TEAM INTEGRATE MATH INTO OUR PROJECTS?
The hexahedron cube and the Fibonacci sequence seemed the way to go. With these two mathematically associated visual archetypes occupying our imaginations the most, we decided to develop our art lessons around them. The first project centered on the cube. We taught the students the anatomy of the cube, its vertices, edges, and faces, and how to design a two-dimensional cube that accurately represents the golden angle. First the students fabricated identically sized templates in the shape of a hexagon. They used these to trace their cube shapes. Over 100 individual pieces were created. Each one contained three faces formed by the "Y" shape of golden angles. Each face was decorated with "zentangle" designs, summery scenes, colorful patterns, and imagery of both a whimsical nature and a contemplative, emotional nature. The project culminated in a group mural containing all 100 or so individual cubes.
The second project focused on using the Fibonacci sequence as a compositional tool in the creation of a work of art. The students were taught the numerical sequence (0,1,1,2,3,5,8,13,21,34,... etc.) and how to translate that into a spiral of square shapes on graph paper. Once they established their spiral shape the students freehand drew a curved line that followed the path of the sequence. After this they decorated their spirals with various colored patterns.
After going through these projects we then pivoted to other related projects that incorporated similar mathematical concepts. One of these was the square within a square within a square, and so on lesson. This sequence also results in the shape of a spiral, very much like a spiral staircase. After the students had created their design they decorated the triangular shaped segments of each square with varied patterns and colors. By varying the colors and patterns from one outer square to the next inner square the shapes became more visibly unique.
Other projects concerning ordered chaos followed. These took the form of abstract designs and collages where order and balance was created through repetition of patterns. We also did some comical portraiture that centered on the canon of the human form, and in particular that of facial proportions that also follow a golden ratio.
See the photo gallery of student work below for more examples.
Hexahedron Cube Mural
Hexahedron Cube Mural
WHAT DID WE LEARN ABOUT OUR STUDENTS AND HOW THEY LEARN?
Here's a discovery: Summer break and math are not always a good mix. This was evident once we announced the theme for our art projects. We actually should have anticipated this. But we were so smitten by Fibonacci that it affected our judgement. Having already been accustomed to a life-experience of surprises and the unforgiving nature of Murphy's Law, we adjusted our outlook as needed and started acting more like artists rather than mathematicians. We talked about how art can imitate nature, and how nature holds many mysteries, and how those mysteries can be explained by mathematical concepts and equations, and how mathematics can be seen as a beautiful representation of nature, and ......but sometimes you just have to grab a pencil and start drawing.
What we learned about our students and the way they learn basically aligns with what we already knew about how we learn ourselves. One of the best ways to learn a new concept is to use materials and make something. The students responded well, for the most part, to this and ended up being able to explain in their own words the concepts we had been discussing. The process of "making" connected action to concept. Light bulbs went on. Understanding happened. And the making process reinforced this understanding. The more we made, the more we understood.
WHAT DID WE LEARN ABOUT THE WAY WE TEACH?
Being a lifelong learner should be the goal of any sentient being. A good teacher is always also a good student. Teachers teach the students, and the students teach the teachers. The exchange is mutually beneficial. Students are not just mere deposit boxes for information, like a piggy bank of facts, dates, and places. They are agile processors, curious explorers, brave risk-takers, and persistent engagers, and also reflective thinkers. Or they should at least be encouraged to be so. The experience of teaching art to students, and probably all other subject areas, offers a mirror to the teacher. Their classroom behavior is most of the time, mostly a reflection of the teacher's behavior. If the teacher is engaging and enthusiastic then most likely the students will be too, or at least more motivated by that. If the teacher is grumpy or acts unmotivated then the students' behavior may also reflect that in a negative way. The experience we had teaching art to these middle school students reaffirmed those convictions in us. To be a good teacher the teacher must also be a good student and always be willing to learn how to be more receptive to our students, more reflective in our self-evaluation, and more positive in our responsiveness. That is central to good classroom management. The generally good natured behavior of our students and their overall willingness to learn and make art was a reminder to us that we should as much as possible maintain the same attitude.
HOW DID OUR PROJECT CHANGE?
How did our projects change? When student choice is part of the teaching strategy, the act of making art becomes evolutionary in its nature. Change will happen. The original trajectory is likely to take a joyful detour along a more scenic route. Even when art making is highly structured many unexpected things can occur. There will be accidents and mishaps. But an "oops" moment can easily turn into an "aha" moment with fruitful results. This was especially true with our portraiture project and the abstract design project. The former started off with the fundamental structure of the canon of the human form and ended up morphing into something unexpected as a result of the students responding more to emotions than to rational problem solving. The latter started out as a chaotic, nebulous mess of no-direction and ended up maturing into something resembling a well-ordered but still organic artwork. That just about sums up for us what makes great art great.
GALLERY OF OUR STUDENTS' WORK
CLASSROOM GALLERY
This is our classroom mascot and muse. His name is Steve and he owns a hamburger food truck.
