Arithmetic is the laws of counting, numbers and symbols, which are basis of mathematical language.
“Number Theory”: is the study of proven patterns (called “theorems” or “proofs”) and immutable laws of arithmetic.
Law: An invariable phenomenon of nature, eg. A volcano will erupt exactly the same way every time. Eg. gravity
Theorem: The cause of the phenomenon has been tested mathematically and not ever disproven. Eg. Volcanic eruptions are caused by a pressure build-up under the earth’s crust or combined chemical elements resulting in explosions. Eg. Pressure x in gravity is required for a weight of xy to fall to the ground.
Kinesthetically speaking, Application and Practice:
Observe a natural phenomenon such as a leaf, flower, cell, or body.
Observe the patterns in what you see.
That is the universal harmony of mathematics. Our numbers are language used in the science of perceiving and learning about these patterns.
About me: I am Tara, the writer of these blogs about education and specifically mathematics. I am a (primary-middle school) teacher. I am interested in having accurate materials and teaching methods.  By composing this series of mathematics lessons, I am preparing for my classes.  I am also a dancer. It is hard for me to sit in one place. It is easier for me to learn with movement, color, examples and ideas. According to research  60% of children learn kinesthetically, like I do.  I hope to be an Educator who has developed a way to provide this service of kinesthetic learning for others as well as myself. I also hope to find the philosophic answer to this question: “WHY I am doing mathematics in the first place?  Because I am not going to use the information.” Discovering the answer to this question has sent me on an adventure to learn the fundamentals of nature and our universe as expressed in mathematical language. “God is universal harmony perceived through numbers.”  – Pythagoras.  xo Tara Pelton