Mathematics is the abstract study of topics such as quantity (numbers), structure, space and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Teaching mathematics is essential for all students as they grow to understand their world and become productive citizens. Mathematical models explain, celebrate, and analyze the world around us; from economic models on the stock market to musical models of symphonies, our world is mathematics. All Colorado students must understand mathematics and its relevance in their lives.