Teaching mathematics in a different perspective

TEACHERS frequently regard mathematics as a fixed body of facts and procedures that are learned by memorization, and that view carries over into their instruction. Many have little appreciation of the ways in which mathematical knowledge is generated or justified.

Although teachers may understand the mathematics they teach in only a superficial way teachingmath to children is far different from what teachers were taught in college. The evidence on this has been consistent, although the reasons have not been adequately explored. To develop teachers’ understanding of the mathematics they will teach, careful attention must be given to identifying the mathematics that teachers need in order to teach effectively, articulating the ways in which they must use it in practice and what that implies for their opportunities to learn mathematics. This sort of attention to teachers’ mathematical knowledge and its central role in practice is crucial to ensure that their study of mathematics provides teachers with mathematical knowledge useful to teaching well.

Conventional wisdom asserts that student achievement must be related to teachers’ knowledge of their subject. That wisdom is contained in adages such as “You cannot teach what you don’t know.” For the better part of a century, researchers have attempted to find a positive relation between teacher content knowledge and student achievement. For the most part, the results have been disappointing: Most studies have failed to find a strong relationship between the two. Teachers are unlikely to be able to provide an adequate explanation of concepts they do not understand, and they can hardly engage their students in productive conversations about multiple ways to solve a problem if they themselves can only solve it in a single way.

According to an article Helping Children Learn Mathematics, “Just as mathematical proficiency itself involves interwoven strands, teaching for mathematical proficiency requires similarly interrelated components. In the context of teaching, proficiency requires: conceptual understanding of the core knowledge required in the practice of teaching; fluency in carrying out basic instructional routines; strategic competence in planning effective instruction and solving problems that arise during instruction; adaptive reasoning in justifying and explaining one’s instructional practices and in reflecting on those practices so as to improve them; and a productive disposition toward mathematics, teaching, learning, and the improvement of practice”.

Effective programs of teacher preparation and professional development cannot stop at simply engaging teachers in acquiring knowledge but they must challenge teachers to develop, apply, and analyze that knowledge in the context of their own classrooms so that knowledge and practice are integrated as well.