As I am enrolled in my Capstone class, I am currently working on my capstone project meant to reflect my learning on at least one area of mathematics.

During the semester, we talked a bit about tessellations.  We got the opportunity to make and color our own during and outside of class.  Although this was very time consuming, I thoroughly enjoyed the chance to explore the different ways symmetry can be applied through mathematical pictures.

Tessellations are symmetric designs featuring animals, people, shapes, etc. which can fit together like a puzzle.  Escher, known as the father of tessellations, is my inspiration for my project.

Because of my interest in these types of tessellations, and the fact that I am going to school to become an elementary school teacher, I have decided that I would like to make my very own coloring book for ages 6+.  In these tessellations, there will be a key that will start off matching colors with numbers then work its way up to matching colors with shapes .

To go about doing this, I will make a set of tessellations and from there order them in what I think is simplest to most difficult, so the readers level of thinking will go up the further in the book they get.

An example of the finished look that I will expect to see is attached below, made by me:

After looking over this tessellation I think that this would be one of the last tessellations in the book.  This was not only very time consuming to make, but would also be difficult for the reader to understand and color in.

While making this tessellation, I had to think about how I wanted it to look in the end and what forms of symmetry I wanted to display.  I had never made a tessellation prior to this one so I started my thinking with a blank slate.  I really just started with drawing out one of the K’s.  From there I decided that I wanted to move horizontally reflecting over a line each time.  However, when I moved vertically, it was simply just a translation.  Therefore, moving diagonally gave me a glide reflection.  After positioning all of the K’s where I wanted them, I saw an opportunity to make the tessellation more complex and full of lots of colors.  My thinking was that every time there was a closed up shape, there was a new color.  When that closed up shape was repeated, it was the same color.  I closed up as many shapes as I thought looked good and from there colored everything in giving me my final look.

What will a student get out of coloring?  I believe this is a great idea for young learners because it gives them the chance to see what symmetry, translations, reflections, rotations, and more are.  When they go about coloring each page, my hopes are that they get tougher for them and they begin to see a pattern of what a tessellation is.  Since my book will begin with them filling in shapes with numbers, they will just get a visual of what a tessellation is.  From there, the next section is filling in shapes with matching shape colors.  This will allow the student to see what tessellations are made of, different geometric shapes in my case.  And the next section is DIY, allowing them to explore what they have learned with the help of my and their imagination.

Summary:

My coloring book will be for those from the ages of 6+.  Towards the end of the book, it may be too difficult for 6 year olds.  In the start of the book, it will be too trivial for, let’s say, 7th graders.  Although learning about translations and geometry comes around middle school, this book will give younger learners the chance to explore and spark their interest at an early age.  The book contains three sections, 1. Matching numbers with colors 2. Matching shapes with colors 3. DIY.  This allows the student to grow their thinking as the book progresses.

If I had more time to expand this book even further, there are a couple things that I would do.  First, I would make the book lengthier, adding multiple pages to each section.  From there I would give the reader/student an answer key in the back.  I would try to do this by making a copy of each page, coloring it fully in by myself, scanning the outcome of each to the computer, shrinking them, and put more than one answer on each page in the back.  This reminds me of a  crossword puzzle book, where there is a place to fall back on when stuck or checking your outcome.