Creativity is one of the most powerful learning tools that students all possess, yet it is rarely utilized in schools today. Students may be told to “be creative” on an assignment, however they are not given instruction on how to nor time to do so. With the focus on test scores and performance of content knowledge teachers and administrators may argue that there is no longer time to be creative. As more art programs are cut from schools it is crucial for educators to bring this focus into their classrooms. Creativity is not something that a person has or doesn’t have, it is something that can be developed and improved over time.
As a high school special education teacher in a Geometry classroom I have struggled with finding ways to tap into my students’ creativity. The curriculum moves quickly and notes can become routine and boring. Making changes to develop more engaging lessons is a challenge. Robert and Michele Root-Bernstein have outlined cognitive tools that may be used to spark creativity in people of all ages. These seven tools include perceiving, patterning, abstracting, embodied thinking, modeling, playing, and synthesizing. Educators may use these tools in their instruction allowing students to express themselves creatively and build a deeper understanding of the content. I have discovered a new side of my own creativity and developed lessons that I can implement in my classroom.
Perceiving requires a combination of both observing and imaging. Observing entails more than just visual perception. We must use all five senses to observe and then translate the sensory information into an image. Right triangles are a crucial part of Geometry and connect many different topics and ideas together. Learning about right triangles dates back to elementary school math class, however they still tend to be a tricky concept for students to grasp. There is so much to learn with their properties including their angles, names of sides, and how to apply various theorems and postulates to them. As I observed my topic I found it easy to list characteristics and examples, but hard to describe the triangle with “non-mathematical terms”. As I continued observing, I tried to use all of my senses and although this sounds crazy, imagine what it would be like to be a right triangle.
At first I really struggled with re-imagining a right triangle. It was difficult to “see” the image in another way other than what was in front of me. As a former college athlete and huge sports fan, I started to imagine myself becoming the right triangle in sport. I chose to write a basketball poem where I was the right triangle and detailed my multi-sensory experience. It describes the last few plays of an exciting basketball game where I end up completing a right triangle as the hypotenuse to win the game.
By presenting the material this way, I may reach more students and bridge some gaps in understanding. The most common question I am asked is, “when will I use this in real life?” By using re-imaged right triangles for problems in math students will discover that they use this content without even realizing it. I could have students go to the gym/field and act problems out, or create their own word problems. By perceiving and re-imagining we can make math real and bring it back to life for our students. Perceiving is a powerful cognitive tool that we need to bring into the classroom more often. By using all of our senses we can discover new meanings, experiences, and a deeper understanding beyond what is there on paper.
It is important that students see patterns in figures in order to solve problems and proofs in Geometry. When I thought of existing patterns with right triangles I immediately thought of special right triangles. We usually cover this idea after learning the Pythagorean Theorem with some direct instruction on the shortcuts: x – x – x root 2 for 45-45-90 triangles and x – x root 3 – 2x for 30-60-90 triangles.
In addition to the exploration of existing patterns, students should come up with their own patterns because “making patterns for oneself is a lot more fun than memorizing” (Root-Bernstein, 1999). I noticed that the some of the numbers and vocabulary terms with special right triangles rhymed so wrote a little chant or poem. It has patterns in the way I decided to write it as well as what it represents.
This process of patterning is can be difficult, but is important for any learner. Too many times students are just memorizing information to get by and pass the test. As teachers, we need to foster deeper learning and understanding through cognitive tools like patterning. It is natural to look for patterns all around us, let’s not lose that when teach our students.
Abstracting is not looking at something in its entirety, but focusing on one feature or viewpoint of it. An abstraction may represent specific properties that are not obvious when viewing a whole object. The goal of abstracting is to find “minimum visual stimulus that can be put on paper or canvas and still evoke recognition without spelling everything out” (Root-Bernstein, 1999).
Abstracting plays a very large role in the field of mathematics. Although we always say that math is “real”, much of the work we do is not obvious. We use abstract symbols, numbers, and equations to represent concepts. I created some graphic art expanding on the basic ideas that Pythagoras used from the tiles. By narrowing my focus to the hypotenuse of right triangles I could think of the Pythagorean Theorem in a new way. Abstracting allows students to deepen their understanding by viewing specific parts of something instead of the whole thing. They may see new relationships, create images, develop meaning, or relate to a content area in a way that is not possible otherwise.
Embodied thinking is when we do not have to consciously think of the actions that are needed; our body just automatically knows how to do them. However, not all embodied thinking involves physical movement. Empathizing is understanding and sharing the feelings of someone. This emotional feeling and connection is another great means of embodied thinking. Empathizing may come into play when you are reading a book and you feel yourself becoming a character and sharing what they are experiencing. Embodied thinking and empathy are important to use in the classroom as many students learn kinesthetically. Making the content available in a variety of ways will offer more opportunities for students to succeed.
It may be difficult to incorporate embodied thinking in some courses that students are taking. Most mathematical concepts are abstract and students may have a hard time “becoming an equation” or “thinking like a square”. I had to take time reflecting on some geometric concepts before figuring out how I could use embodied thinking in my classroom. In Geometry, there are several new terms for students to know throughout the year. To grasp the vocabulary, I would have them make connections to the word through their bodies and physical movement. This could be done in a variety of ways: charades, gestures, Simon Says, or a dance. I would choose to use motions or gestures and have the high schoolers display the term with their bodies.
Although this type of thinking may seem elementary, there are huge benefits to using it. It would engage some of the students who are kinesthetic learners or “bored” in geometry class because they would be up and moving. It encourages math conversation, creative thinking, and could be a game changer for some of my special education students who learn differently.
Dimensional thinking “involves moving from 2-D to 3-D or vice versa” (Root-Bernstein, 1999). It also involves scaling which is altering proportions within one set of dimensions. Typically, we introduce the Pythagorean Theorem after proving triangles congruent. Triangle similarity and dimensional analysis of areas/volumes of similar figures is not covered until second semester. That is also when we go over different polygons and find the area/volume of them. Even though these topics are found in different chapters, they are all intertwined together.
In order to incorporate more dimensional thinking, I began to explore through modeling. Modeling involves the representation of an idea or concept to be better visualized or understood. Not only are these ways of thinking helpful in making the ideas stick, but they bring math to life!
Play involves no rules, no success, no failure, and freedom to do things just for fun. Play is for the enjoyment of doing or making with no responsibility or accountability tied to it (Root-Bernstein, 1999). Bringing play into the classroom is important and something that I am passionate about. Play engages students, reduces anxiety and stress, brings the class to life, and makes the curriculum fun! Just because teenage students are growing up, it doesn’t mean they can no longer play and have fun in school.
In my Geometry classes I incorporate games and activities to get students up and moving. To help me figure out a different type of playful introduction to right triangles, I thought back to my childhood and what I enjoyed. Besides sports and physical activities, I loved to draw and color. Coloring sparked an idea and I immediately ran with it. I chose to design an adult coloring page for my students. There is a huge boom in our culture with the “adult coloring book” market, as more people are recognizing the positive effects of coloring. It is utilized for reducing stress, anxiety, and for relaxation.
This activity would be fun for them and meaningful because it helps develop their visual skills, recognize patterns, shapes, and give them a chance to talk with their peers. I can see students who are quiet and more talented in the arts loving this activity and sharing it in front of the class. During the next chapter I could use this image again to talk about the different parts of a polygon and how we classify shapes: triangle, hexagon, square, quadrilateral, convex, concave, etc.
Synthesizing involves “synthetic understanding, in which sensory impressions, feelings, knowledge, and memories come together in a multimodal unified way” (Root-Bernstein, 1999). Synthesizing is not only experiencing, but understanding things at a much deeper level. Our future will depend on synthetic minds to be innovative across curriculums.
As Steve Jobs puts it simply, “Creativity is just connecting things” (Henriksen & Mishra, 2014). It is not something give, but something to be nurtured and developed. It is important for educators to develop lessons and activities that support the growth of creativity in young minds today. This does not require changing what they are teaching, only how they teach.
Henriksen, D., Mishra, P., & the Deep-Play research group (2014). Twisting knobs and connecting things: Rethinking Technology & Creativity in the 21st Century. Tech Trends, (58)1, P. 15-19
Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.