Peter Kloosterman

Students' Beliefs about Learning School Mathematics

In this study we considered the mathematical beliefs and achievement of 62 students in grades 1-6 from 1 school where teachers were participating in a project to improve mathematics teaching. Students, most of whom were from lower and lower-middle socioeconomic families, were interviewed about whether they liked school and mathematics, whether their parents helped them with schoolwork, whether they were confident of their abilities in mathematics, whether they felt mathematics was useful, and whether they felt all children had the ability to learn mathematics. Students were also tested for computation and problem-solving ability. Trends that emerged for this sample included (a) students in the upper-elementary grades were able to articulate their beliefs more clearly than students in the lower grades, (b) students who enjoyed mathematics were also confident of their ability in mathematics, (c) students with moderate achievement were just as confident of their abilities as high achievers, (d) most students believed that it was important to learn mathematics and that anyone who tried could learn mathematics, and (e) there was little evidence of a relation between parental support and student achievement.

Mathematics Skills of Nine-Year-Olds: 1978 to 2004

Using recently released data from the Long-Term Trend Assessment of the National Assessment of Educational Progress, this study analyzed the mathematics performance of 9-year-old students between 1978 and 2004. The study goes beyond overall results by describing the assessment items and the change over time on each of those items. The data indicate that there have been substantial gains in ability to read and interpret tables and graphs and in calculating perimeter and area. Performance increased on most place-value and computation items, although performance on the majority of items involving measurement or money was relatively stable. The periods of greatest gain varied by item. As a general rule, however, improvement on items was greatest from 1986 to 1990 and again from 1999 to 2004—periods that had the largest gain on the assessment as a whole.

Using NAEP to Analyze Eighth-Grade Students’ Ability to Reason Algebraically

After describing the content and scoring of NAEP mathematics assessments, this chapter focuses on performance on individual NAEP items as a means for documenting the algebraic reasoning skills of eighth-grade students. In general, performance on algebraic reasoning is similar to performance on the grade 8 mathematics NAEP in recent years—performance was stable on the majority of items and increased modestly in the remainder. Many eighth graders can understand and explain relationships between two variables in different settings and formats. Many are also able to plot points but few are able to use slope and intercept or determine which points to plot to connect an equation and a graph. When it comes to solving word problems involving linear relationships, it appears that many students employ intuitive strategies such as guess and check although some are able to use formal algebraic methods. Logistical and methodological issues that arise when using NAEP data are also addressed. These issues include adjusting analyses to account for the sampling method used by NAEP and limitations in statistical power when working with subsets of the NAEP data. The chapter closes with examples of the types of statistical techniques we are using to determine whether clusters of items developed by analysis of item content are valid from a measurement perspective.