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Can we assume all mathematic teachers to know it all?
Oleh ENG KIAN SENG
KUMPULAN DEVLIN KOHOT 10
SM-WB 10 :
Menggunakan ICT Dalam Pengajaran Pembelajaran Matematik Menengah
Yang Berkonsepkan Sekolah Bestari
It is an attractive proposition: Find young, smart people with arts and science degree and put them in classrooms. The underlying assumption, of course, is that these well-educated people know enough to teach effectively. They may not know much about teaching, but they will learn when they teach in class. Think again, can they really learn to teach from teaching experiences.
What should teachers know about their subject matter? Are there essential concepts or ideas? Are there certain qualities of knowing that are important to teachers? Are there certain aspects of mathematical knowledge that all mathematics teacher should possess? Alternately, can some concepts go untaught on the assumption that teachers will develop that knowledge later in their career?
The analysis presented in an article by Michigan State University shows that many new teacher lack of fundamental knowledge of mathematics. The Teacher Education and Learning to Teach Study (TELT) which sponsored by the National Center for Research on Teacher Education (NCRTE, 1988) studied the learning of teachers over a 4-year period. They investigated teacher education in 11 sites, selected to represent structural and conceptual variation among teacher education programs. 306-item questionnaire were administered to all participants at 11 sites. It was designed to tap respondents' beliefs about and knowledge of diverse learners, mathematics and writing, teaching and learning, learning to teach, and the role of social context. Some of the question involved the knowledge of Rules of Thumb included:
Out of 55 (teachers with degree in Mathematic) participants' responses to these question show that 87% correctly rejects the 1st rule, 95% correctly rejects 2nd rule, 86% correctly accepts 3rd rule and 40% correctly rejects 4th rule. In this case, we can assume that some of the teachers with degree do memorize the rule without understanding.
After all, teacher cannot learn all the mathematics they need to know before they enter the classroom. However, they will learn from teaching mathematics. After all, isn't that the best way to learn anything? Teaching means that to understand, explain it the correct way and to apply it correctly in term of mathematic. They should not explain that there is really no logical reason to explain certain rule in mathematic but just memorize it. By asking "Why?" teacher must find the reason behind these rules.
As the authors of the National Council of Teachers of Mathematic (NCTM, 1989) Standards explained, teachers who teach for understanding will need to (a) understand mathematical concepts, structures, procedures and their relationship; (b) identify and interpret representations of mathematical concepts, structures and procedures; (c) reason mathematically, solve problems, and communicate mathematics; (d) understand and appreciate the nature of mathematics and the role of mathematics in culture, and (e) develop a disposition to do mathematics.
Many of the teachers in TELT sample appeared tethered to an older view of mathematical competence that depends on the mastery of rules. Even among those who had earned degrees in mathematics and had entered teaching through an alternative route, a number believed that key mathematical ideas cannot be explained but simply must be memorized. They did not know how to represent the meaning of particular algorithms. They did not know how to reason through the problems they encountered in the interviews.
In order to improve class teaching, we must have the skill of reflective, pedagogical reasoning and problem solving. Teacher should think reflectively and solve classroom problems rather than simply to accept principles without evaluating their rationale. Self evaluation was emphasized as an important cognitive function perform after a teaching episode. One must comparing goals, intents, and images of teaching to teaching outcome.
Pedagogical reasoning can be categorized in three categories of beliefs about teacher responsibility: (a) student affect, (b) student cognition, and (c) learning environment. Student affect including student motivation and attitude toward learning. Student's cognitive performance, level of achievement and degree of learning were coded as student cognition. The third category of teacher beliefs was used for statements about responsibility for establishing and maintaining a positive learning environment, including promoting respect and fairness in the classroom.
As for problem solving, teacher must identify the problem occur, generating alternative plans/ solutions, anticipating outcomes, regulation or monitoring and lastly evaluating your solution. Problem identification was defined as describing and clarifying the problem. Generating alternative referred to generating and considering several alternative solution to the problem. Anticipating outcomes involved reflecting on the consequences of one's action. self-regulation or monitoring was defined as self-awareness or metacognitive activity. A systematic plan to reflect on and critique teaching was coded as evaluative skill. Group discussion with other teacher is an alternative way to solve some of the problem rather than working alone. Get opinion from those experiences one will help generate more alternative solution.
Teachers must have teaching perspective, personal attitude, values, beliefs, principles, and ideals that help a teacher justify and unify decision and action. The outcome will still depend on those teachers who tried to follow the wind of change or those in a stagnant pool.
References
Ball, D. L., & Wilson, S. M. (1990). Knowing the subject and learning to teach it: Examining assumptions about becoming a mathematics teacher. (Research Report 90-7). East Lansing, MI: Michigan State University, National Center for Research on Teacher Education.
Journal Of Teacher Education Vol 42-2, 1991. American Association Of Colleges For Teacher Education.
Journal Of Teacher Education Vol 42-4, 1991. American Association Of Colleges For Teacher Education.
National Center for Research on Teacher Education.(1988). Teacher education and learning to teach: A research agenda. (Issue Paper 88-7). East Lansing, MI: Michigan State University, National Center for Research on Teacher Education.
National Council of Teachers of Mathematics.(1989). Curriculum and evaluation standards for school mathematics. Reston.