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An Integrated Approach to Teaching Mathematics and Science

An Integrated Approach to Teaching Mathematics and Science

Introduction

The field of math education, both the teaching of mathematics and the preparation of math teachers, remained constant during much of the twentieth century. Yet, since the 1960s, reforms in math education have raised questions and caused debate about best practices in the teaching of mathematics and the preparation of math educators. These questions and debates have sparked a series of changes in the nature of the public school and college curricula and the focus of research on the teaching and learning of mathematics. The rise of technology for instruction, the standards and accountability movement, and new national and international measures of comparative assessment have further fueled the debates and continue to shape the evolution of the field of math education.

Mathematics and science are important for success in school, but learning mathematics and science can be a difficult task to some students. Efforts to improve students' learning of school mathematics and science have led to reform efforts in curriculum and instruction over the past decades (e.g., National Council of Teachers of Mathematics [NCTM], 2000; National Research Council [NRC], 1996). Yet, "In the 2000 National Assessment of Educational Progress, only 17 per cent of grade 12 students nationally performed above a basic level of competence." (Bali, 2003, p. xi)As the improvement of mathematics and science learning is an extremely complex activity that requires coordinated efforts from multiple resources, good research support is very important. In particular, research on students' learning difficulties should help lay a foundation for developing effective interventions, and thus hold much promise for the improvement of teaching and learning school mathematics and science.

An Integrated Approach to Teaching Mathematics and Science

Today, the downplaying of basic memorization and computational skills during the twentieth century has surfaced as a serious problem in the P-16 curriculum evidenced by international comparisons of student performance on standardized tests. Students in the United States consistently perform below that of their counterparts in highly developed countries. Since the mid-1980s, international comparison studies, such as the Third International Mathematics and Sciences Study (TIMSS), show that mathematics instruction in many developed nations, particularly Eastern Asia, is definitely richer in comparison to math instruction in American classrooms. The TIMSS study, the largest cross-national, multiyear research study conducted in the history of math education, included 41 countries across five continents and compared over 500,000 students' scores in mathematics and science.

Students' learning difficulties can be presented in the form of errors. But not all the errors that students make are the same. Some errors in procedures can simply be due to students' carelessness or overloading working memory (Lemaire, Abdi, & Fayol, 1996). Some errors in procedures can be caused by faulty algorithms or "buggy algorithms" (e.g., Brown & Burton, 1978). Other errors can have certain conceptual basis and can be termed as "'misconceptions". What follows is an example used to illustrate the subtle differences among errors, buggy algorithms, and ...

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