What Mathematical Knowledge is Needed for Teaching Mathematics ?

Abstract

Abstract

Concern about Padangsidimpuan City students’ mathematics achievement has grown; evidence makes plain that the teaching and learning of mathematics in the Padangsidimpuan City needs improvement. This is not the first time that this country has turned its worried attention to mathematics education. However, past efforts have consisted of effort more than effect. We are not likely to succeed this time, either, without taking into account what has led to the disappointing outcomes of past efforts and examining factors that contribute to success in other countries. Consider what research and experience consistently reveal: Although the typical methods of improving instructional quality have been to develop curriculum, and especially in the last decade to articulate standards for what should students should learn, little improvement is possible without direct attention to the practice of teaching. No curriculum teaches it self, and standards do not operate independently of professionals’ interpretations of them. The efforts of the past decade have shown that good instruction can make a difference, and that teachers can learn from and for their work with curriculum materials. But clearer now is that using curriculum effectively and working responsibly with standards depend on understanding the subject matter. How teachers know mathematics is central to their capacity to use instructional materials wisely, to assess students’ progress, and to make sound judgments about presentation, emphasis, and sequencing. The last decade has made that plain. We cannot afford to keep re-learning that improvement of students’ learning depends on skillful teaching, and that skillful teaching depends on capable teachers and what they know and can do.