Math Education

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.

Prior to the twentieth century, math educators were primarily viewed as drillmasters charged with the utilitarian responsibility of teaching for the memorization of basic arithmetic skills, computation, and problem solving in mathematics. During the early part of the twentieth century, most math teachers were prepared with 1 or 2 additional years of schooling at a specialized high school called a “normal school.” After 1900, when the concept of a universal high school curriculum took hold, math educators majored in mathematics in a teacher's college and were prepared to serve as secondary content specialists. Inherent in this program design was the assumption that math teachers for the elementary and primary grades learned all the mathematics they needed during their postsecondary schooling, and because of such thinking, most elementary and middle grade math teachers received only mathematics required of an elementary education major. After World War II, however, the curriculum emphasis shifted to more modern, sophisticated levels in public schools and colleges, including the inclusion of elements of geometry and algebra in elementary curriculum, greater emphasis on functions and less emphasis on trigonometry in high school, and the introduction of calculus into the curriculum of the first year of college. This shift caused subsequent rethinking of the math curriculum in colleges and schools of education for the preparation of math educators.

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.

Other comparative assessments, such as the National Assessment of Educational Progress (NAEP), show equally alarming data. Positive press that was provided early during the release of main NAEP data occurred primarily because of the fact that fourth graders and eight graders increased overall from 1999 to 2003 by a range of 15 to 22 scale points respectively. However, a closer look at the comparisons of student performance over time as revealed on the specialized long-term-trend NAEP show that the gains portrayed by the main NAEP are 10 times larger than on the trend NAEP. In fact, in 1999 only 56% of 17-year-olds scored correctly on basic computation skills. Trend analysts blame hidden differences such [Page 648]as this one on differing curriculum frameworks. Test items for the main NAEP tests are developed from the National Assessment Governing Board (NAGB) and closely approximate changes within math instruction in the field, while the trend NAEP utilizes the same testing instruments in order to be able to make comparisons over time. Regardless of the reason, the dismal performance of American students on national measures of standardized assessment and in comparison to other developed nations has called the math curriculum and the preparation of math teachers into question. As the United States neared the end of the twentieth century, it was apparent that we would not achieve the federally legislated goal of Academics 2000 for American students to place first in math and science achievement in the world.

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