A Coloring Book of Mathematical Equations – strange idea, right? When I first thought of this, I chuckled to myself thinking, how ridiculous that would be to color and draw on the letters and symbols of an equation, but as I thought more and more about it I began to think instead, ‘what a great idea’. Here’s why.
If you teach a subject that requires math you know it’s hard to convey that mathematics is a creative and fascinating area of study; in fact, most students, (indeed the general public), see math as just the opposite – unimaginative and boring. In attempt to make the subject more ‘exciting’ publishers often add cute illustrations or pictures designed to visually attract the student to the page thinking this will make the math more interesting. In fact, research has shown, often these added pictures tend to simply distract the student. As I see it, the problem is, that when students look at an equation, (if they look at an equation), they only see the symbols as letters, and this is 99% of the problem. Please read on…
Take for example Einstein’s famous equation, E=mc2. Nearly everyone knows this equation, but only a tiny number of people really know what it implies about our world. Some people could tell you that the ‘E’ is not a letter, but a symbol for an idea, a concept called ‘Energy’; take that a bit further and ask someone to describe or draw ‘Energy’ and you get a blank stare; a look of confusion from most people.
On the other hand, if I say, ‘red wagon’, everyone can picture an image in their mind of a red wagon and could sketch a picture of it as well. Why, because, by a fairly young age, we’ve shown you many examples of both red and wagon. How often are we shown ‘E’ associated with a picture of ‘energy’ ? And if you can’t form a picture in your mind what ‘E’ is, then I think a story about ‘E’ will be pretty boring.
Perhaps students need to be given more time to contemplate the meaning symbols in math equations essentially through drawing. To that end, I have created a series of drawings of equations with large, outlined letters that can be colored in and next to each letter is an image of what the term relates to. So for example, if you look at the preview you will see Einstein’s equation E=mc2, next to each letter is a deliberately simply image of what each term is. So in my class when I introduce this equation I hand out an 'eyeNOTE' worksheet and give the students time to actually color in the terms and images before I launch into calculations using it. While they color I talk about what each symbol means. I might tell them a ‘story’ about how they will learn that this equation unlocks the secrets of stars and stretches of perceptions of reality itself!
If you’re a not a high school or college teacher you’re probably not still reading this, but if you are, I would say why not do this even in elementary school? Why couldn’t you have students coloring math equations with pictures before they really are able to understand their meaning? Think about how we teach language, we all learn how to speak and read in a very organic way. The words a young infant hears initially have no meaning at all but eventually, somehow magically, we all learn how to converse. If we continue to teach math to young children before they have had exposure to the meaning of numbers and symbols, it will continue to be an uninteresting and laborious subject for the vast majority of students. (However, this booklet is not intended for elementary students – I’m working on that!)
If you’re a high school or college chemistry teacher and you’re still reading this, you might think, ‘I don’t have the time to ‘waste’ letting my students color’, or ‘my high school/college student will think this is childish’. Having taught AP Chemistry for more years than I can remember, I had those same concerns. Yet the truth is, my student success rate markedly improved and most students really enjoy and find this approach very helpful. (I am not advocating that you stop everything and have your students simply coloring in pictures during precious class time. But I do feel like there are many ways to meaningfully use this teaching technique to augment and strengthen your science/math curriculum. I look forward to your feedback!)
Please let me know what you think.
I hope very much that this is useful.
This Activity Booklet includes 23 color eyeNOTES templates and 23 duplicate black and white eyeNOTE worksheets each featuring math equations commonly used in high school and college chemistry and physics courses.
What are eyeNOTES? Simply put, it’s about teaching and learning through drawing and using pictures. It’s about visual learning. eyeNOTES are often deliberately simplistic, or incomplete drawings that serve as a template for developing fundamental concepts in science and math.
Let me give you 2 common examples how they might be used in the classroom:
1). If you look through the preview examples you will see an eyeNOTE on Albert Einstein’s equation, E=mc2, one of the most famous equations of all time. But do your students know what it means? Perhaps you could have them discuss the equation and ask them to suggest what each term represents. They can compare their theories to the correct one after you have completed the lesson. (It is perhaps a good idea to have students use pencil to make rough sketches on the worksheets first and later let them go to town using colored pencils/pens. If you’re very lucky and have tablets, such as iPads, you can import these and draw on them using a drawing app like SketchBook Pro or similar.)
2). Many teachers like to use these eyeNOTE images as a template for PowerPoint or Keynote presentations. I’ve done much of the work for you, and you can have fun personalizing the drawings to suit yourself and the needs of your students. All of the images are done using large font sizes and are generally black and white. This is because after thirty years of teaching I’ve finally realized that students have difficulty reading strange fonts and they are often distracted by too many images, bells, and whistles. Each drawing gets right to the point.
I hand out paper worksheets of the same eyeNOTES that are in the PowerPoint or Keynote to the students. They use these to write notes on and to complete the diagrams. (Suggestion, print them single-sided so students can write notes on the backside of the page.) I know teachers who work at schools that have 1-to-1 iPads, in which case students can again take notes on the iPad using the eyeNOTES as a template- this makes it way easier to write on the tablet; I would suggest using a stylus in this case.)
A Coloring Book of Math Equations, (Physical Science/Chemistry)
→ What you get…
23-Color eyeNOTES covering the following topics:
2-Half life equation
3-Speed of electromagnetic waves
5-de Broglie’s equation
6-Energy of a photon
8-Ideal gas law
9-Combined gas law
10-Dalton’s law of partial pressures
11-Dalton’s law of partial pressures #2
13-Root-mean square speed
15-Graham’s law #2
17-Reaction rates graphical
18-Average reaction rate
19-Reaction rates, graphical #2
21-1st Order rate law
22-1st Order rate law, graphical
23-2nd Order rate law, graphical
Also, 23-Duplicate Black and White printables for photocopies, (one of each of the above)
This activity meets and exceeds 21st Century and STEM learning expectations, and Common Core learning outcomes. Also, all the eyeLEARN units align with the 2014 AP Chemistry Revised Curriculum. (I think STEM, which stands for science, technology, engineering and math, should be changed to STEAM, where 'A' stands for Art. What do you think?)