“What is mathematics to you?” When I ask this question, my middle school students give answers that include four operations, numbers, algebra, or geometry. High schoolers add statistics, functions, and graphs to this list.
For me, defining mathematics is a bit difficult. It is a discipline that helps us, humans, to understand the dynamics of the universe. However, such a definition is also problematic. Indeed, it is just a getaway. Therefore we can try thinking of different attributes of mathematics.
These can be:
-beauty, elegance, and creativity (yes, this is the first one that comes to my mind)
-connection
-patterns (perhaps this is the most overarching concept in this list)
-problems solving (critical thinking)
-representation
-generalization
-logical reasoning
-abstract thinking
-counting, combination, and computing
Perhaps, mathematics is the study of all these above. Merriam-Webster dictionary gives a cold definition:
"The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations"
Galileo Galilei defines mathematics as:
"The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word." (Opere Il Saggiatore)
After his time, scientists and mathematicians used this language in various ways. Humanity saw many new ideas explained in that language and scientific principles developed. In my opinion, to be able to use that language, one needs many other skills. If Newton were not a critical thinker, he would not think of a theory for the fallen apples. Maxwell generalized many equations and prepared the mathematical background for electromagnetism. He was a mathematician; so he could make the connection.
Over time, mathematics developed in two major branches, applied and theoretical. Today's math careers follow one of the directions. Applying mathematical principles to complex financial or business problems, assessing risks and predicting future demands, analyzing the spread of diseases and populations, developing models, and interpreting data are a few examples of applied mathematics. Mathematicians on the theoretical side continue to explore the elegance of mathematics by studying in their field of work besides teaching and mentoring younger mathematicians.
Unfortunately and ironically, such examples and discussions are hardly on the agenda in schools. Of course, a student in the K12 process hears, learns, and discusses what math is, how beautiful and elegant it is, and how significant mathematics is as a discipline in humans' lives. However, this idea always stays in the shadows, neglected or forgotten while dealing with the stress of exam scores, drills, and homework assignments. After a decade, most people remember high school mathematics with a certain level of anxiety, never more than recalling a few theorems and problems.
In recent years, the idea of concept-based education has been on the rise. Everywhere around the world, math educators are trying to bring the essence of mathematics to the math class by using new approaches like project-based education, growth mindset, differentiation, student agency, and accessibility.
I believe that there are many things we can do in mathematics class to show the true nature of discipline to our students. After all, don’t we remember those teachers who inspired us or made a change in our lives when we were in school?
Perhaps the purpose of mathematics education shifted from what it needed to be. Students find themselves in a system where they need to pass tests and get degrees. All around the world, with exceptions, of course, teachers are given little chance to change or shape the current education systems. Everyone knows that it is the governing bodies' essential duty to provide ecosystems where students understand and experience the true nature of mathematics. However, our enthusiasm in class, dedication, and role modeling can be a great inspiration for many students to understand the essence and purpose of mathematics.