Mathematics Education

“Education is not preparation for life: Education is life itself.” – John Dewey (1859-1952). In light of this quotation, education begins at the informal stage of one’s life. Education begins at home. Education is being nurtured by children where the seeing and the doing are intertwined which mold and form their character into being.
Some roles that the family play in the educational aspect of their children’s lives are: setting expectations and goals for their children, nurturing the curiosity of their children through meaningful questioning and answering, cultivating discipline and finally creating a print rich environment in the home in promoting early enrichment.
Education can also be viewed as the formal training in any given institution which prepares the minds for future purposes for the wider society. There are many theorists who support the formal training of a child to be of most importance. Jean Piaget, Lev Vygotsky and Howard Gardner are such pioneers who believed in a formal trainer to train and mold their minds.
Be it formal or informal education, the theories that underline the concepts or approaches of mathematics have played an integral part in the teaching learning environment. The concepts of mathematics are considered quite relevant to today’s society in that; how do we know mathematics? How do we apply it? Where does it start? How does the sixth sense come into play?-Are pointed to the concepts and theories of mathematics. For one to think of the application, mental conceptions and the different ways in exploring mathematics are all intertwined in the three approaches: utilitarian, aesthetics and cultural.

Utilitarian Approach
Jeremy Bentham and John Stuart Mill posit: “Utilitarianism, at its most basic, states that something is moral or good when it produces the greatest amount of good for the greatest number of people. It's a theory of normative ethics that asks whether a specific action is good or bad, moral or immoral.” (1863).
The way in which one applies a mathematical concept in solving a problem can be considered to be good or bad. The utilitarian approach is the end product to be good –being good –meaning utilizing or applying the taught skill in our daily lives. For one to consider the different types of mathematical topics taught from pre-school to tertiary institutions, many persons will argue- “ how much will we be able to apply this to our daily lives?” if these topics are considered applicable it is considered to be good-morally good. If not it is deemed to be a “waste of time” and “unprofitable”. Measurements, basic additions, subtractions, multiplications, divisions and sets just to name a few are all a given functional operation on a day to day basis.
In considering certain topics as: algebra, functions, trigonometry- these are some few abstract mathematical topics which many students struggle in making the connections in seeing “how functional” they are in their lives. The basic application to life many will move towards. However; when one considers the scientific fields of life, one will see how applicable these topics are: in the geographical aspects - trigonometry, in the medical fields-functions and relations as well as algebra.
The pros and the cons may differ to an individual based on the interest of the individual, the culture of the individual and the career path of the individual. In surmising the utilitarian approach could be deemed a good moral based on the interests, cultures and career paths that are seeing from each person’s perspective.


Aesthetic Approach

This approach can be seen as the awe and the beauty that can be viewed in an interactive way. The beauty about having a constructivist mathematics classroom, students or pupils are able to: explore, manipulate and discover new concepts in a holistic manner. Hands-on materials in the classroom sets the stage or setting in the classroom. “Music is a universal language”, it plays an integral part in learning. Many students or pupil gravitate towards a vibrant, beaming, arousing class activity. In having such mathematical setting: songs, poems, games and story-puppetry for younger pupils, enhance the lesson and concretize concepts.
“It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.” Carl Friedrich Gauss.
Through this theory it is evident that students or pupils learn through engagements. Actions are more meaningful than mere theories. Students or pupils will gain knowledge through this medium and will find mathematics more meaningful, interesting and will appreciate it well.


Culture
Culture is a way of life. Everyone lives out culture throughout their thoughts whether it is through: speech, dressing, or the way how we interact with each other. Culture can be a positive motivating factor or a negative de-motivating factor. Culture in Mathematics has influenced the informal and formal training in education. For many persons the innate ability has been influenced in an individual due to its environs.
As the theorist who speaks about “Nature vs. Nurture”-culture is seen as such. The culture of an institution will influence the potential progress of a student in mathematics. The culture at home and the community will influence how an individual manipulate certain mathematical concepts. The culture of a nation will also influence how an individual view mathematics.
In a school-culture there are principles and guidelines that are needed in solving mathematical concepts. This level of formal training is needed in order for pupils and students to meet national and international standards. This is a form of training is nurtured.
The innate ability of an individual is their nature. Many children may not be able to get the formal training due to economical deprivation. However; they learn the basic life coping skills through: for example - working on a farm- in doing this they are able to do all the non standard units of measurements and have considerably considered to be accurate. They are able to make sets by multiplying and grouping by dividing. The actual level of practical experience has allowed them to be experienced in the work field than just to have attained a formal training with little application. Through this form of culture, these children are better able to see and view the connection of mathematics in real life situation.




Reference

Mill, John Stuart (1863). Utilitarianism (1 ed.). London: Parker, Son & Bourn, West Strand. Retrieved 6 June 2015. via Google Books

Carl Friedrich Gauss:
Adopted from http://www.brainyquote.com/quotes/quotes/c/carlfriedr319895.html