Closing the Gap between Teaching and Learning

Abstract For years critics have scrutinized poor performance in mathematics education. The National Council of Teachers of Mathematics, responding to this concern and anticipating future criticism of the existing curriculum, developed the Principles and Standards for School Mathematics, which address how mathematics should be taught and learned. This paper will examine expectations for mathematics teachers outlined in the Teaching Principle with particular attention to content knowledge, student learning, and mathematical pedagogy. Separating the Principles creates a dichotomy between teaching and learning. An implication for educators is that they may fail to see crucial pedagogical connections, the relationship between teaching, learning, content, and context. These connections make for effective teaching. Introduction For years critics have scrutinized poor performance in mathematics education. As a result, mathematics education has been under the spotlight. The National Commission on Excellence in Education issued A Nation at Risk: The Imperative for Educational Reform in 1983 as a reform measure to hold educators accountable for student achievement (Marshall & Tucker, 1992). Since then, in 1988 with America from the Governors of the 50 states, spearheaded by Bill Clinton, people have raised questions about what mathematics content should be taught. Years later, this evolved into Goals 2000 (1994). In 1989 during the George H.W. Bush administration, there was a push for the United States to rank first in the world in mathematics and science. Still unsatisfied with the results, the George W. Bush administration reauthorized ESEA as the No Child Left Behind Act (NCLB), which has the intention that by testing students often and holding teachers and administrators accountable, student learning will improve. The National Council of Teachers of Mathematics (NCTM), responding to these initial concerns and anticipating future criticism of the existing curriculum, developed the Principles and Standards for School Mathematics (hereafter referred to as Principles and Standards). These principles and standards address how mathematics should be taught and learned. The Principles address important issues of high-quality mathematics teaching. In contrast, the Standards discuss specific mathematical content and processes that all students in grades pre-kindergarten through grade twelve should learn. The ultimate goal is a cohesive and comprehensive curriculum that focuses on the teacher, the learner, and the classroom. Even though the Standards have been developed, there have been questions about how to implement them (Askey, 2001 ; Cheney, 1997; Loveless, 2001; Wood, 2001). Concern for many is how people are teaching math itself. The results of the Third International Mathematics and Science Study (TIMSS) clearly raise these questions. This paper will take up that concern by specifically looking at the Teaching Principle in the Principles and Standards. It will examine expectations for mathematics teachers outlined in this principle with particular attention to content knowledge, student learning, and mathematical pedagogy. I will then address some of the implications for teaching in the high school mathematics classroom. For example, educators may fail to see the connections between teaching, learning, content, and context. Background The NCTM Principles and Standards were developed in 1989 as the Curriculum and Evaluation Standards for School Mathematics and then most recently revised in 2000 under the current title (NCTM, 2000). The Principles and Standards consists of six principles and ten standards which guide the teaching and learning of mathematics. Its primary purpose is to provide guidance to teachers, administrators, teacher-leaders, and teacher educators, to name a few, without dictating specific curriculum that should be taught. Curriculum writing is left to the local level, whether it is the state, district, or school, to provide the appropriate instruction for its students. …