"This is a process that is echoed with every math problem a student encounters..."
"Mathematics is built on patterns and is a study of analyzing situations..."
"...through practice with mathematics, their brains learn to work with more abstract and less tangible realities."
"It is the attempt to do so that leads each individual to an appreciation for those who can, and do."
"Spectators don’t expect to see a football player lifting weights on the field, but they recognize that it is an important component of the athlete’s training."
"Eventually, students appreciate that everything can be modeled in some way with the use of mathematics."
"...the exercise that their brain gets from persevering through problems involving difficult concepts will help it to navigate complicated and potentially dangerous, or highly important and stressful situations in adulthood."
There are a multitude of reasons as to why mathematics education is so prevalent in schools and why it is deemed so vital, despite the common complaint and misconception that the student is never going to use what they learn. It is not the specific formulas that are crucial for each student to carry with them into life, but rather the skills that they gain through the struggle with those formulas and other mathematical concepts.
Among the reasons that people learn math are:
Consider the situation of a mother away from home on business, who is informed of an accident involving one of her two children and her husband. Clearly, this constitutes a problem for the mother who wants to be with her family so that she can care for them. Will things just automatically happen for her? Does she need to examine the facts and unknowns? Does she need to put together a plan? Should she call someone to help, or just head to the airport? Can she pay for a ticket? How will she pay for a ticket? ...I think quickly, one can imagine the process that might be going on in her thoughts and appreciate the turmoil that this poor woman will be juggling while trying to make important decisions. Perhaps, having been previously placed in stressful situations where she needed to make choices, will benefit her ability to operate under these circumstances.
A common and useful method for addressing any problem a person faces in life is to first, familiarize oneself with the intricacies of the information regarding the issue by identifying all of the constraints and each of the variables, and second, to develop a plan, taking into consideration many different possible pathways to resolution. Thirdly, one executes their plan, and fourthly, they evaluate the effectiveness of their plan to inform their future decision making. This is a process that is echoed with every math problem a student encounters, and through repeated practice, the learner establishes habits of mind to manage obstacles and achieve success determined by perseverance and analysis.
Such problem-solving is facilitated by the recognition of patterns and the processes that lead to the greatest success. Simply getting to school safely everyday relies on one’s ability to make a number of observations and look for recognizable patterns of behavior, so that they can decide when and where and how to move in order to arrive at school on time and in one piece. Mathematics is built on patterns and is a study of analyzing situations to look for patterns so that individuals can make calculated predictions using algorithms, which themselves are a repetitive processes.
The first pattern one focuses on in mathematics is that of counting. Starting with the “smallest” single digit, zero, and then increasing up through the largest single digit, nine, the mechanism continues by placing a one in front and repeating this process, only to then increase that first number to two (in the same fashion as the single digits) and repeat again. From this viewpoint, counting is just a simple, repeatable pattern. It is a gentle leap to see how addition is connected to counting and virtually everyone is familiar with the algorithm for addition that involves “carrying.” However, a deeper appreciation for the construct of a number allows one to alternatively add from left to right, and in fact, some find it more efficient on occasion. Thus, it is important to recognize that the routine one has previously established or learned is not always the most efficient and they should always be willing to consider other options.
CONCRETE TO ABSTRACT
Mankind's study of mathematics begins with young children exploring that which is concrete - simple, tangible, and unchanging. They learn about numbers and how to use them to count and quantify things. They also learn about the basic shapes that they recognize in the world around them. Their brains are inexperienced, so they can only accept that which is clearly defined and physical. In part, through practice with mathematics, their brains learn to work with more abstract and less tangible realities. Those simple shapes become much more complex, leading them to a truer understanding of the physical space in which they live. Additionally, as their comfort level with numbers grows, they learn that people can collect data on all sorts of subjects, and that they can then analyze and use that input to make predictions or develop protocols.
HUMILITY AND APPRECIATION
People also gain respect through mathematics. The course of a mathematician could be considered similar to that of a sculptor, who can start with a mound of clay and initially only create a simple bowl shape that could effectively hold something else (but may not be interesting to look at), and later fashion a beautiful vase with intricate design and subliminal context. A math student can start by counting teddy bears, and eventually predict the orbits of stars or explain the theory of multi-dimensional realities. Not every person is going to be able to design a suspension bridge, or analyze big data, but neither will each of them be able to produce beautiful works of art. It is the attempt to do so that leads each individual to an appreciation for those who can, and do. Therefore, because someone recognizes and understands how challenging an achievement can be, each person can come to honor all individuals, and should be grateful for those who can meet that challenge and improve the lives of everyone through their efforts. It allows individuals to be proud of their own accomplishments while also admiring the accomplishments of others.
Furthermore, learning mathematics is exercise for the brain. Spectators don’t expect to see a football player lifting weights on the field, but they recognize that it is an important component of the athlete’s training. So too, most adults don’t perform complex calculations on a daily basis, but their brains complete many other tasks. The minds that are best equipped to handle those challenges are the ones that were enhanced by the “stretching” they were influenced to do in school and in every other environment in which they had to learn something new. A person can only benefit from attempting to reach a greater understanding of their world. Such actions increase the capacity of a person’s intellect to perform at its peak.
Eventually, students appreciate that everything can be modeled in some way with the use of mathematics. They observe that it is possible to make very precise calculations to build and do amazing things. They recognize that it is possible to make sense out of highly abstract concepts. They discover that mathematics is a universal language; that no matter how one communicates with words, the principles behind numbers and how they operate is the same. Thus, people come to appreciate the importance that mathematics must have played in the development of the “world” in which they live and the significant role it played in different cultures learning to communicate and coexist.
In conclusion, mathematics teaches individuals to use logic, to look for patterns, to recognize possible outcomes, and to deduce the best course of action. Perhaps a student won’t work with complex formulas later in life, but the exercise that their brain gets from persevering through problems involving difficult concepts will help it to navigate complicated and potentially dangerous, or highly important and stressful situations in adulthood.