These include: question/answer, lecture, demonstration, discussion, individual student projects, laboratory, technological 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 instruction methods for introductory algebra. For this reason, instructional factors are related to achievement in algebra (p. 102).
When comparing the test scores from Japan and the United States, House and Telese (2008) found a correlations between positive beliefs in the students mathematical ability and their test scores. Those who believed they could do well in math performed better than those who expressed a negative opinion about their skills, when compared to their peers. In addition, students who worked problems on their own had higher test scores. This supports Silvers (1998) analysis that much of the reason why American students have poorer test scores than their international peers is due to the classroom instructional practices. Teachers, currently, are not instilling confidence in their students, in their math skills, which negatively affects their test scores.
Falco, Crethar and Bauman (2008) also agree that a middle school students attitudes towards mathematics affects their learning and test scores. In their study, students received a Skill Builders curriculum, which was school counselor-led and geared toward improving students attitudes towards mathematics. The authors note that although there is an increased emphasis on the importance of mathematics for the American economy, there is a significant decline in students pursuing math-related degrees and occupations. Of particular concern is the widening gender gap in mathematics interest (p. 231).
The Skill Builders curriculum was developed to increase student competence beliefs. This includes improving their self-efficacy and self-confidence, towards mathematics. Falco, Crethar and Baumans (2008) study found that students who took part in this program scored significantly higher on their post-test scores.
Females also improved significantly more than males in the study. This also supports Silvers (1998) analysis that teachers and curriculums have a significant effect on improving test scores.
Todays increasingly globalized world means increased competition not only for American businesses, but also for American students. Americans entering the workforce now must often compete for jobs with candidates from other parts of the world, whether through direct hires or through increasingly outsourced job tasks. For this reason, there are both societal and economic impacts to the educational competitiveness of United States students. Upon reviewing Silvers (1998) analysis of the TIMSS data, it becomes clear that American students are significantly behind their international peers, including countries which the United States is in competition with. Silver offers three recommendations for improving this situation, including: making mathematics a significant national priority with the encouragement that all students can be good at mathematics, improving the mathematics curriculum and an investment in teacher professional development. These theories in how to improve the scores of American students are supported by both House and Telese (2008) and Falco, Crethar and Bauman (2008). Both note that the instructional format and facilitating students self-confidence in their abilities in mathematics are key factors to improving American students test scores.
Falco, L., Crethar, H. & Bauman, S. (Apr 2008). “Skill-builders: Improving middle school students self-beliefs for learning mathematics.” Professional School Counseling, 11(4). p. 229-235.
House, D. & Telese, J. (Feb 2008). “Relationships between student and instructional factors and algebra achievement of students in the United States and Japan: An analysis of TIMSS 2003 data.” Educational Research & Evaluation, 14(1). p. 101-112.
Silver, E. (Mar 1998)..