Improving Middle School Math: Lessons from TIMSS Research

Introduction

Ensuring American students receive a world-class education is an increasingly important topic, especially as the world becomes more globalized. The social and economic implications of this education are profound. This paper reviews Edward Silver's article, Improving Mathematics in Middle School: Lessons from TIMSS and Related Research, and provides support for the underlying principles found in his analysis using corroborating research literature.

Overview of Silver's TIMSS Analysis

Silver (1998) reviews the results from the Third International Mathematics and Science Study (TIMSS). The findings were not encouraging. In general, Silver identified "a pervasive and intolerable mediocrity in mathematics teaching and learning in the middle grades and beyond." Children in middle school — and even those graduating from high school — were found to perform significantly below their peers in other countries. This poor performance reflects a mathematics curriculum and set of instructional methods that are simply not as challenging as those found in other nations.

Silver (1998) summarizes the major findings of the TIMSS with respect to student achievement. American 8th-grade students have performed below the international average in mathematics, including in comparison to countries that are direct economic competitors of the United States. However, performance varies by topic: in algebra, data representation, fractions, probability, and analysis, American 8th graders perform at approximately the international average, while in geometry, proportionality, and measurement they perform below average.

Silver (1998) further argues that American schools' curricula are too broad in scope and lack sufficient depth. They were also found to be repetitive and insufficiently demanding when compared internationally. The structure of classroom teaching was found to be lacking in rigor and not geared toward conceptual understanding or intellectual challenge. Disturbingly, Silver notes that the results of the TIMSS were not surprising given what was already known about American mathematics education.

Silver (1998) identifies important insights into the characteristics of the American mathematics curriculum and classroom environment. The challenges revealed by the TIMSS are rooted in deeply entrenched educational practices; as such, significant commitments of resources and time will be required before meaningful changes can occur. Silver offers three recommendations. The first is to "make a serious national commitment to improved mathematics learning by all students" and to raise expectations for all students. The second is that the American curriculum should become more ambitious and that classroom instruction should be substantially enhanced. The third recommendation is that the United States invest in teacher professional development, specifically by expanding the content knowledge of teachers at higher grade levels to meet the additional demands of those courses.

Student Beliefs, Instruction, and Algebra Achievement

House and Telese (2008) also drew on the TIMSS to "simultaneously examine relationships between mathematics beliefs, classroom instructional strategies, and algebra achievement of adolescent students in the United States and Japan" (p. 101). The authors highlight the importance of mathematical skills for students' future career options, noting that algebra is a particularly critical component of middle school mathematics. Students must master foundational algebraic skills in order to succeed in higher-level mathematics courses (p. 102).

According to House and Telese (2008), there are eight modes of teaching algebra: question-and-answer, lecture, demonstration, discussion, individual student projects, laboratory work, technology-based activities, and supervised practice. Previous research has demonstrated that the use of informal knowledge, real-world settings, and opportunities to apply mathematical thinking are effective instructional approaches for introductory algebra. For this reason, instructional factors are meaningfully related to algebra achievement (p. 102).

When comparing test scores from Japan and the United States, House and Telese (2008) found a correlation between students' positive beliefs about their mathematical ability and their test performance. Students who believed they could do well in mathematics performed better than those who expressed negative views of their own skills. In addition, students who worked problems independently tended to achieve higher test scores. These findings support Silver's (1998) conclusion that a significant part of the reason American students perform below their international peers is attributable to classroom instructional practices. Teachers are currently not sufficiently fostering students' confidence in their mathematical abilities, which negatively affects achievement.

Conclusion

Today's increasingly globalized world means heightened competition not only for American businesses, but also for American students. Those entering the workforce must now compete for jobs with candidates from around the world, whether through direct hiring or through the growing outsourcing of job functions. For this reason, the educational competitiveness of United States students carries both societal and economic implications.

Upon reviewing Silver's (1998) analysis of the TIMSS data, it becomes clear that American students are significantly behind their international peers, including those from countries with which the United States is in direct economic competition. Silver offers three recommendations for improvement: making mathematics a meaningful national priority with the expectation that all students can succeed, strengthening the mathematics curriculum, and investing in teacher professional development. These proposed reforms are supported by the findings of both House and Telese (2008) and Falco, Crethar, and Bauman (2008), both of whom identify instructional format and the cultivation of students' mathematical self-confidence as key factors in improving American students' academic performance.