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PHILOSPHY OF MATHEMATICS EDUCATION
RICHARD EBU AWUAH
LECTURER: DR. ERNEST AMPADU
SUPPOSE YOU ARE A TEACHER WHO MUST CHOOSE ONE OF THE FIVE SCHOOLS TO TEACH. EACH SCHOOL REFLECTS ONE OF THE FIVE MAJOR PHILOSOPHIES DISCUSSED IN CLASS. WHICH SCHOOL WOULD YOU CHOOSE TO WORK AS A TEACHER? DISCUSS AT LEAST FIVE REASONS FOR YOUR CHOICE.
Philosophy is how a person perceives something. It is individual specific. Like the formalist, their philosophy about mathematics is that it's just about characters and symbols. So they believe that mathematics is only characters and symbols.
Philosophy can also be said to be an attitude that acts as a principle guide to behaviour. It's a certain kind of thinking as well as a certain kind of approach to a particular problem. Thus, philosophy of mathematics education is the approach used in teaching mathematics in the classroom so as to be effectively done to the required criteria.
There are a lot of philosophies of mathematics education. These philosophies can be classified into two groups. The theory of Behaviourism and that of the Constructivism. The behaviourism perspective is the teacher-centred type where the teacher dominates the affairs in the class. They believe that the factual knowledge should be given to the child and the child has no say in the classrooms of such teachers who practice this philosophy. They teach the core component of the syllabus, they are very strict, they believe that things have a set of characteristics which makes them what they are and they also consider the child as an empty vessel (tabula rasa). Students in such classes tend to memorize a lot and also are passive learners since they don't take active part in the teaching and learning process. Most importantly they are result oriented. They are just interested in teaching the students to pass. Just like killing a cat, whether it is shot, drowned or poisoned, the most important is that the cat is killed. Essentialism and perrenialism are examples of the teacher-centred philosophies or the behaviourist.
The other group has the belief that since knowledge is being transferred to the child from the teacher, the child must be the point of attention, therefore, such philosophies are teacher-centred, and that is, particular attention is given to the student. In such philosophies, students become active learners and hence take up important roles in the teaching and learning process. This group is the Constructivist and believe in conceptual knowledge that is to allow students explore things for themselves. Examples of such philosophies are Progressivism, Social Constructivism and Existentialism.
After carefully scrutinizing all the above philosophies, both for the behaviourist and constructivist, I also started philosophizing on what teaching is about and how should it be done effectively. I realized that teaching is done so that the child will gain knowledge from the teacher, so why must teaching be teacher-centred when the teacher already knows the concept he is about to impart? It should rather be more about the one at the receiving end, therefore, I go with the conceptual way of teaching that is the learner/student-centred school of thought. If you are fetching water from a river with a bucket into a basket, all the effort will go waste since the bucket can carry the water alright but the basket can't contain anything. Here, the river is the knowledge, the bucket is the teacher and the basket is the learner, virtually meaning that the basket which is the learner will not grasp anything taught by the teacher in the case of the behaviourist.
As a teacher, I believe that a child is the centre or the most important variable in the teaching and learning process, thus, I consider myself Sa constructivist. All the three philosophies of the constructivist, Progressivism, Social constructivism and Existentialism are all good but I will opt for Essentialism.
According to the internet encyclopaedia of philosophy, existentialism is a philosophical approach which emphasizes the existence of individuals as a free and responsible agent determining their own development through acts of the will. The existentialist believes that the student is not an empty vessel (tabula rasa) but has some characteristics in which if he is guided, may produce the desired results. They believe in making the classroom a conducive atmosphere for the student to be comfortable so as to really work together for their academic achievements. The following are some of the reasons why I will apply this philosophy in my mathematics classroom.
To make the classroom conducive for learning.
According to Thorndike, students tend to learn when they are ready. They have a maximum output when they feel safe in the learning environment. This is also known as the philosophy of classroom management. Acknowledging the fact that these students with very exciting and formulating minds need lessons that will arouse their curiosity and unearth critical thinking skills. The main aim is to create loving and caring individuals who will take risks, establish realistic goals and assume personal responsibility for the outcome of their input. Thus, a learner-centred classroom that produces critical thinkers, who are at the same time seriously involved in the work at hand and finding the learning process very enjoyable. The classroom will be a conducive place to participate, have fun and learn as well. In this type of classroom setting, students are engaged in stimulating lessons that demands most of their attention so they have no reason to misbehave.
Considering the individual differences among students.
Students learn in different ways. The visual learn by seeing, the sensory learn by hearing and the kinaesthetic learn by doing. Most of the work done in the classroom will be demonstrations and group works. Here all the learning types of students can engage themselves in the activity to also make an input. It it's the lecture type as in the case of the behaviourist, it may not cater for all the types of students with different learning skills in the classroom. Only a few may benefit.
When students are motivated, they work harder to gain more recognition and appreciation. If the teaching-learning process is learner-centred type, students also participate in the process to also gain such recognition and appreciation. They may even read ahead, understand and even have a different fashion to the solution of such problems. This serves as a form of intrinsic motivation to help and encourage students to learn more for their academic upliftment. Students will have more experience and interest in the subject through a lot of exercises as proposed by Thorndike in his law of exercise.
An assessment strategy
When students work in groups, they know the marks that the group gets go for all of them so they will work hard to produce good results. If the group is made up of a lot of members, some members will not contribute or make inputs but if the group has fewer numbers say three or four, it will keep all the members on their toes to work hard since they know their inputs will be much needed. Some schools have large class sizes, some 60 and even more, so if students work in groups, the number of works to be marked will reduce.
To encourage peer teaching.
Most students learn and understand concepts very well through diverse ways when they are being taught by their own peers. The brilliant students in class may even use certain jargons to teach the weaker ones so that they can also have an idea about the concept and grasp the idea. So this is a way of helping each other to escape from getting a bad grade. It also fastens the unity and togetherness among the members of the class in order to achieve a common goal.
Illeris, Knud (2004). The three dimensions of learning. Malabar, Fla: Krieger Pub.Co. ISBN 9781575242583.
Ormrod, Jeanne (2012). Human learning (6th edition). Boston: Pearson. ISBN 9780132595186.