Effective Mathematics Instruction: Development, Instruction, and Programs

We see effective instruction as having three important characteristics:1.It is based on empirical evidence about development and use of the knowledge and skills that comprise the area to be taught.2. It is delivered using instructional procedures that have been shown to have positive effects on pupil outcome.3. It uses programs that have been empirically validated.At a minimum, providing content instruction requires some way of delivering that content.But, to the extent that we can incorporate knowledge about the ways people act and think when correctly and efficiently handling that content (point 1), we can make instruction more effective.Of course, other things being equal, we assume that people (teachers, parents, administrators, students, and others) would prefer to have students taught by teachers who use effective instructional techniques to deliver the content (point 2).Similarly, we assume that people would prefer to have students taught using the most effective instructional programs available (point 3); that is, we presume that people would favor instructional materials that have a demonstrated record of success.Along these lines, our purpose in this article is to illuminate what is known about providing effective instruction in mathematics.We begin with some illustrations about the growing understanding of children's thinking in mathematics, follow that with a discussion of the application of effective teaching procedures, and conclude with an examination of research about effective procedures and programs.