A research done by Juniece Skinner, Mathematics Methodology student at IUC.
|It is important for teachers to let students know the importance of mathematics. In the classroom of mathematics, the teacher must create this atmosphere where everyone can learn something from the content taught and experienced. High expectation must be held for all students and students being monitored for progress. Mathematics is seen as problem solving; such is the claim of proponents like Dewy who believed that, “Problem solving is important in each area.”
This paper will look at mathematics as it relates to the kind of approach: utilitarianism, culture and aestheticism.
Utilitarianism can be discussed as morally right based on the culture and religion of issue deemed discussing. In every decision, there is a consequence. In making a decision one has to think about the consequences. In utilitarianism, consequentialism is strength, because it is only natural to weigh your consequences when it comes to making a decision. The theory is subjective and relative and so remains flexible and applicable to the greatest number of people.
In mathematics based on utilitarianism, this is doing what it takes for students to learn mathematics. The teacher will find all means to allow pupil the opportunity to grasp most, if not all the concepts being taught. There is no place for neglect of one student. No child should be left behind. According to Ediger M, (1994), “A mathematics teacher has to determine what the literature in the teaching of mathematics indicated to be trends in selecting objectives, learning opportunities and calculation process.” Ediger (1994) believes that by communicating relevant concepts, the mathematics teacher may benefit in upgrading the curriculum. Hopefully, pupil achievement will increase as a result of the teacher’s increased knowledge pertaining to the teaching of mathematics.” This is clear that on both sides of this experience there can be equity for all involved. In utilitarianism, the teacher must provide equal opportunities for all to learn, especially in mathematics. In the classroom if all have the opportunity to learn, and all do, then this result would bring happiness to all in the classroom. All stakeholders involved would feel satisfied. This result would have a positive result on the school, and on the community then the society at large.
According to the Ediger (1994), “In teaching mathematics humans need to reduce the inequalities, in the amount of qualified mathematics teachers and the disparity in the learning opportunities in the classroom. The bias belief that males do better at mathematics than girls must be removed under the utilitarian approach.” It is shown that the utilitarian approach provided equality learning for all in mathematics ensuring that all or most pupils’ grasping of the subject. He further stated that, “In mathematics using utilitarian approach, grouping can be encouraged but with no homogeneous grouping, but heterogeneous grouping of pupils-gifted.”
Ediger (1994) believes that “Educational literature in mathematics is quite concerned in providing for equity among pupils in ongoing learning opportunities. He believes that pupils should not be discriminated against due to race, creed, nation origin, among other items.” He believes that utilitarian approach would give rise to equal access to materials of instructions, quality teaching, quality school buildings, and classroom, as well as equipment in teaching and learning situations.
Ernst (1991) as cited in Edger (1994) states that “ a teacher working from a multicultural, social-reconstructionist approach attempts to create a learning environment that is as demanding and open as the power asymmetries of the classroom allow, but with explicit recognition of this asymmetry. He suggested that genuine discussion between students and the teacher with pedagogical process that stress the following: Cooperative group work, projects and problems solving to promote engagement and mastery. Finally, autonomous projects, problem posing, and investigative work,to afford pupil opportunities for self-directed and personally relevant activities.”
According to Ediger, (1994,) “In a multicultural social-reconstructionist approach in teaching, equity and fairness with the framework of democratic tenets should be stressed in mathematics.”He believes that through cooperative learning, students should be placed in heterogeneous grouping, therefore the talented and gifted along with slow learners will learn from each other, Ediger (1994). “He believes that quality relationship among humans and acquiring important subject matter in mathematics is being emphasized. He believes that culturally, that human should respect each other as well as have knowledge to solve problems.”
“In order to provide for individual differences, pupil individually may work on own on a project, activity, or independent study. There needs to be a rational balance groups and individual pupil endeavors in mathematics. Thus, they must learn how to work in groups and by self. Also that each person should be able to live as a member of a group and profit from being able to achieve and grow as an individual” (Ediger1994).
Based on the role of mathematics in society and culture, a lot of contribution of various cultures has contributed to the advancement of mathematics, and the relationship to the other subjects and realistic applications. According the National Council Teachers of Mathematics in their publication(1989) believes in these standards. How students’ linguistic, ethnic, racial, gender, and socioeconomic background influence their learning of mathematics. They believe that no matter which culture one belongs, all pupils need to obtain optimally in mathematics. Also that all need to have mathematics curriculum which harmonized with preferred personal ways of learning. They believe that “a pupil not speaking English in a proficient way may need a mathematics curriculum written in whole or part for use in his or her native language. They believe that racial linguistic biases of teachers must be eliminated.” They believe that “teachers can assist student to show respect for each other in the classroom by them exhibiting fairness and conscientious teaching as care and concern is important.” They believe that gender biases among male and females in developing of skills in mathematics should be reduced. When students are acquainted with the structure of academic disciplines they are more rounded individuals.
Bishop. A, (1988) believes that cultural groups generate mathematics ideas, and that Western Mathematics may be only one mathematics among many and that the value reflect in the curriculum the multicultural nature of the society.” He believes that this creates education in tune with home cultures of the society. According to Bishop (1988) “the thesis is therefore developing that mathematics must now be understood as a kind of cultural knowledge, which all cultures generalize but which need not necessarily ‘look’ the same from one cultural group to another. Bishop (1988) believes that “In the same way human cultures create religion beliefs, language, rituals, food producing techniques, etc. is the same way they are able create their own mathematics. Therefore, human needs to re-examine their traditional beliefs about the theory and practice of mathematics education.”
According to Sinclair 2008 as cited in Hardy (1940), “Beauty is the first test: There is no permanent place in the world for ugly mathematics.” According to Sinclair(2008) as cited in Dewey (1934) argues that aesthetic is a pervading quality of human reasoning and experience. Sinclair (2008) argues that aesthetic seems very pertinent to important questions in mathematics and anxiety. Sinclair states that Deweyan approach cares more about the roles that aesthetic plays in inquiry, rather than if a given theorem is elegant, or what criteria of mathematics beauty looks like. “Humans have predictable, innate aesthetic preferences they use in making sense of their environment” (Wilson 1998).
According to Sinclair (2008) aesthetic involves not only in choice of structure (and this, the choice of mathematics objects, relationships and problems) but also in the communication of results about these structures. Styles is crucial in mathematical communication, as can be seen in the various guides provided by journals and professional societies (AMS, 1990 ). According to Sinclair (2008) as cited in Krull (1930, 1987), “The rhetorical nature of mathematical writing depends strongly on aesthetic devices. Mathematics are not concerned with the findings and proving theorems, they also want to arrange and assemble the theorems so that they appear not only correct but evident and compelling.”
According to Sinclair (2008) “the aesthetic dimension of mathematics has also remained more or less on the side of the research mathematicians, though with intermittent forays into the school mathematics. In one sense, it seems natural to leave it in its place, given its tight connection with published mathematics, that is, with the production of theorems and proofs that characterize the mathematician’s work.” Poincare (1865) as cited in Sinclair (2008) believes that good mathematicians have a special aesthetic sensibility. According to Sinclair (2008) as cited in Krull (1930, 1987), “the primary goals of mathematicians are aesthetic, and not epistemological.
According to Sinclair (2008), mathematics education is one of the few disciplines that can (and sometimes does) play an interpretive role in explaining the nature, purpose and goal of mathematics to the ‘outside’ world, which are infused with aesthetic values. According to Corfield (2003), this interpretive role is crucial to the health of mathematics as a discipline and as monitory of the impact of mathematics on society. "Aesthetic is related to pedagogical issues, and can be argued that it is deeply connected to learning; not just to artistic production or appreciation” (Sinclair 2008). Sinclair opines that a stronger two-way interaction in which the discipline of aesthetics has much to contribute both to understanding the rationality of mathematics itself, and to enriching existing theories in mathematics education.
It is important to note that integrating culture, aesthetic and utilitarian approach in mathematics education is very important as they will make students grasp the concepts of mathematics better.
Bishop, A. J. (1988). Mathematics Education in its cultural context. Mathematics Education and Culture, 19, 179-191.
Ediger, M. (1994).Current concepts in Teaching Mathematics. Teaching Mathematics in Elementary Schools
Sinclair, N. (2008). NOTES ON THE AESTHETIC DIMENSION OF MATHEMATICS EDUCATION. Retrieved from https://www.unige.ch/math/EnsMath/Rome2008/WG5/Papers/SINCL.pdf