Simply having a love of math yourself is not enough, though that is certainly important and desirable. How could you begin to teach something you did not truly enjoy without conveying that disinterest through a mechanical approach to the subject? Teaching most subjects requires very different skills than the skills demanded by studying the particular discipline. The world is full of extremely skilful practitioners who, for one reason or another and quite often inexplicably, cannot teach someone how they do it! The practice of something is very different from professing it in a classroom.
Planning for learning outcomes is critical. Teaching math within an established curriculum, be it high school or college, means corresponding to some Stated goals or course outline. In high school, it may be state standards, and in college, it may be a written course description in the catalog. That means you have certain learning outcomes that you must accomplish during the semester or year. To accomplish this body of learning within a set time period requires judicious planning. What will be done each day? How much time should be allowed between assignments or readings? Which materials should be required and which should only be recommended? You'll have to make countless decisions. What textbooks and ancillary materials will you use, and how will you evaluate your students?
Add to this the fact that students learn in different ways. Some are auditory learners who enjoy listening and gain most of their information in this way. Concentrated listening is how they best absorb material in the class room. If they are required to take notes and listen, something may have to give, or it may be difficult for them to retain the material. Others prefer a visual approach with board work, handouts, their own notes, diagrams, books, and many visual materials. They retain these images and can call them up to remember the material.
Others need to participate through more activity and physical involvement with the material. These learners like to participate in team projects or contests such as building a pyramid or cube, going outside and estimating the height of a building, and other activities that physically involve them. They learn best this way. These are kinaesthetic learners and they are often forgotten in planning and curriculum design. The teacher ensures that the learning styles of all students are satisfied through a judicious combination of modalities in teaching. Teachers need to analyze their own teaching style and seek to incorporate those elements that come less naturally to them in order to ensure that they reach all students.
The teaching and learning that takes place in a classroom is not static. The classroom is an emotionally charged environment for the student and instructor that may call into play questions of self esteem and competency. Students are continually exploring themselves in relation to their capabilities, values, and achievement. A good teacher understands this and encourages a risk free environment of mutual appreciation and participation. Both teacher and student are allowed to make mistakes and move on. The teacher strives to assist in establishing congruence between the real self (how we think of ourselves at that moment), the ideal self (who we want to be), and the learning environment created in the classroom. Hopefully, the classroom will be a place where the real self can rise up and begin to touch the ideal self.
While any classroom can cause us to call into question who we are or how competent we are, this is perhaps especially true for the mathematics classroom. Math is a series of building blocks, and certain skills must be mastered to move on to other, more advanced proficiencies in using math. Many people develop a strong sense of inadequacy early on about mathematics and their own levels of competence. You've heard this from your friends and family and you'll continue to hear people's "horror stories" about math every time you mention you're a math major.
One group that has been particularly hurt by this traditional resistance to math and science is young women. We now have an increasing number of genders sensitive studies describing how, frequently during middle school years, young girls seem willing to cede superiority to the boys in their classes. For many years researchers have been interested in the educational and career barriers between females and the field of mathematics. Studies (Fennema and Sherman, 1977; Fox, 1980; Armstrong, 1979; Boswell and Katz, 1980) have shown that the development of attitudes that affect a female's math achievement begin about thirteen years of age. That this attitude is due to stereotyping and not aptitude is obvious, and these studies make clear that at this age, young, talented girls begin to be rewarded for social conformity and move away from math, which is seen as more masculine. Fortunately, studies such as these have alerted not only teachers and other educators to the problem, but employers, too, are working hard to encourage women to enter fields that center on math and science skills.
Any mention of competency, self esteem, or self worth naturally suggests another sensitive subject-grading and the evaluation teachers provide on quizzes, tests, and report cards. Grades are an expected and required part of many institutional academic settings. Establishing fair and consistent standards of evaluating your students and assigning grades is a significant challenge to many teachers who otherwise feel perfectly competent in the teaching role. However, this results in a lot of work for the teacher, and much of that work is going to be done outside the classroom, during office hours or at home in the evening. Teaching is not a nine to five job, and the after hours demands of grading homework is just the tip of the iceberg in discussing the lack of boundaries in this important profession.
