John Smithson

Upgrading High School Mathematics Instruction: Improving Learning Opportunities for Low-Achieving, Low-Income Youth

Low-achieving, low-income students are typically tracked into dead-end math courses in high school. In this article, the authors evaluate the success of “transition” math courses in California and New York, which are designed to bridge the gap between elementary and college-preparatory mathematics and to provide access to more challenging and meaningful mathematics for students who enter high school with poor skills. The authors hypothesize that the transition courses—Math A in California and Stretch Regents and UCSMP Math in New York—allow students to keep pace with those who enter college-preparatory courses by covering rigorous mathematical content using a range of cognitive strategies. Data from 882 students in 48 math classes are analyzed using a three-level hierarchical linear model. The results show that growth in student achievement is significantly lower in general-track classes than in college-preparatory classes. Achievement in transition classes falls in between: not significantly lower than in college-preparatory classes, but not significantly greater than in general-track classes. More rigorous content coverage accounts for much of the achievement advantage of college-preparatory classes. The transition classes are judged a partial success in meeting their goal of upgrading the quality of mathematics instruction for low-achieving, low-income youth.

Alignment of the Intended, Planned, and Enacted Curriculum in General and Special Education and Its Relation to Student Achievement

In this initial study, the authors examined the content of the planned and enacted eighth-grade mathematics curriculum for 18 general and special education teachers and the curricula’s alignment to state standards via the Surveys of the Enacted Curriculum. The relation between alignment and student achievement was analyzed for three formative assessments and the corresponding state test within a school year. Results indicated that alignment for the planned and enacted curriculum to state standards was low with no significant differences between general and special education teachers. Significant correlations between student achievement averages for 238 students and teacher alignment indices were equal to or greater than .48. When teacher groups were examined separately, the relation between alignment and achievement remained significant only for special education, with correlations equal to or greater than .75. The study’s conceptual and methodological framework provides a model for subsequent research on alignment and opportunity to learn in general and special education.

How Well Aligned Are State Assessments of Student Achievement With State Content Standards

Coherence is the core principle underlying standards-based educational reforms. Assessments aligned with content standards are designed to guide instruction and raise achievement. The authors investigate the coherence of standards-based reform’s key instruments using the Surveys of Enacted Curriculum. Analyzing 138 standards-assessment pairs spread across grades and the three No Child Left Behind tested subjects, the authors find that roughly half of standards content is tested on the corresponding test and roughly half of test content corresponds to the standards. A moderate proportion of test content is at the wrong level of cognitive demand as compared to the corresponding standards, and vice versa. Between 17% and 27% of content on a typical test covers topics not mentioned in the corresponding standards. Policy and research implications are discussed.

Upgrading the High School Math Curriculum: Math Course-Taking Patterns in Seven High Schools in California and New York.

Previous studies have indicated that students enrolled in the general math track do not take as much math and do not learn as much math as students in college-preparatory math courses (Gamoran, 1987; Oakes, 1985; Porter, 1989). State, district, and school initiatives in California and New York have been developing mechanisms to address this problem of inequality by creating new transition math courses and eliminating the general math track. This study examines course-taking patterns of students in seven high schools in California and New York that have attempted to enroll lower level math students in more meaningful initial math courses. By examining students’ transcripts, the success of various policy options to upgrade the math curriculum are evaluated. Our data indicate that the new transition math courses meet with partial success in providing a common curriculum to students with diverse math preparation.