Mathematics: Content and Pedagogy.
The debate has gone on for some time in terms of which is more salient for the teacher to be well versed in, mathematical content versus methods and approaches in teaching. Both are salient. They cannot be separated from each other. The mathematics teacher must indeed have broad, indepth knowledge of subject matter as well as in teaching and learning. Mathematical content and pedagogy then need to be integrated. The goal of mathematics teachers is to assist pupils to achieve, grow, and develop in attaining vital facts, concepts, and generalizations. This takes teacher knowledge of content as well as of pedagogy. Teaching of Mathematics There are several needs of individuals in becoming proficient in mathematics. Thus, each person needs to be able to use mathematics in everyday transactions such as buying necessary goods and services, to buy groceries, pay utility bills and rent, and pay for needed services such as repairs and maintenance work. Functioning well, numerically, in society is a need for all citizens. Then too, a mathematics curriculum must provide for those going into higher education and will major in and teach mathematics. Also, there will be future engineers and other professionals who need to experience a high quality school curriculum. Individual differences then must be provided for in the elementary and secondary school years. Sequentially, pupils need to experience teachers who possess ample knowledge of subject matter as well as of methods of teaching mathematics (Ediger and Rao, 2000). Quality teachers are needed, as a key ingredient, in assisting optimal pupil learning. They must experience the latest, relevant trends in teaching mathematics, be it in workshops, other inservice education programs, or through personal research projects. Cooperation among teachers to conduct grade level meetings as well as school wide, and system wide endeavors at curriculum improvement should provide for provisions made for optimal achievement in mathematics of each learner. Here, content and pedagogy need integration in helping pupils achieve well. The two should not be separated from each other, nor should value judgments be made as to which is more important (Ediger, 2005). Mathematics as a language needs to be used to communicate ideas. Communication must occur in school and in society between and among individuals pertaining to quantitative topics. Precision is involved. Mathematics is perhaps the most objective of all academic disciplines whereby individuals agree, as a whole, with the quantity being discussed. It attempts to be precise with the quantity being considered. Among others, mathematical ideas may be expressed orally and in diagrams, charts, tables, formulas, library books, graphs, and written work (See Betne and Castonguay, 2008). Pupils need to make connections in terms of use of mathematical subject matter. They need to perceive how mathematics relates to the self, as well as others. Problem solving is a vital skill for all to develop. Developmentally and at increasing levels of difficulty, pupils must be able to solve personal mathematics problems. Logical thinking is necessary here as well as dealing factually with quantitative information. Critical thinking is inherent when separating facts from opinions, the relevant from the non-relevant, as well as fantasy from reality in problem solving experiences. Creative thinking, too, is necessary in determining new methods of solving a problem. Novel, unique ways of viewing and attempting solutions at problem solving are to be encouraged (See Stein, 2007). Contextual situations are needed in fostering the utilization of mathematics. Standardized tests stress the application of mathematics outside the framework of a particular context. Pupils then respond to test items which do not pinpoint a functional use. Then too, pupils are drilled much to do well on a standardized test. Generally, drill assists pupils in turning off in studying mathematics. …