NOTE: The Briefing Book from Meeting 8 included many readings on Algebra Instruction in the U.S. and Language and Mathematics. We encourage you to review the priority readings from the Meeting 8 briefing book. In this section we provide additional literature on mathematics curriculum and opportunities to learn, and on middle school grades.
Mathematics Curriculum
**Schmidt, W., Houang, R. & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 10-26, 47-48. Not available online.
In this article, the authors compare the K-8 mathematics curriculum in the U.S. to that of top-achieving countries on the Third International Mathematics and Science Study (TIMSS). They find that the curriculum in top-scoring countries is coherent, and transitions steadily from arithmetic in early grades to algebra and geometry in grades 7-8. The U.S. curriculum, in comparison, is incoherent with much repetition of content across all grades. The authors suggest that incoherence in content across schools contributes to gaps in achievement between the most- and least-advantaged schools.
Schmidt, W.H. (2008, spring). What’s Missing from Math Standards? Focus, Rigor, and Coherence. American Educator. Available at http://www.aft.org/pdfs/americaneducator/spring2008/schmidt.pdf
This brief article highlights similar themes to the Schmidt, Houang, & Cogan article above. The article is based on findings from the Third International Mathematics and Science Study (TIMSS), and speaks to three aspects of math curricular expectations that are important for student learning: focus, rigor, and coherence. The author contends the mathematics standards in the U.S. are lacking in all three of these qualities. He attributes this to the political nature of standards setting. In order to increase coherence he proposes working together in a cooperative manner across states, districts, and the federal government to establish national math standards.
Mathematics Opportunities to Learn
Abedi, J., Courtney, M., Leon, S., Kao, J., and Azzam, T. (2006, November). English Language Learners and Math Achievement: A Study of Opportunity to Learn and Language Accommodation. (Technical Report 702). Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing. Available at http://files.eric.ed.gov/fulltext/ED495848.pdf
This study investigates the interactive effects between measures of students’ opportunity to learn (OTL) in the classroom (including content coverage, teacher content knowledge, and class prior math ability) and language proficiency, and how these variables impact mathematics performance. The study found that all three class-level OTL components were significantly related to math performance, after controlling for prior math ability. Results of the study provide some evidence that English learners can learn and demonstrate algebra content knowledge when provided with sufficient mathematics content delivered by strong math instructors in a classroom of students who are proficient in math.
Hill, Heather C. (2007, June). Mathematical Knowledge of Middle School Teachers: Implications for the No Child Left Behind Policy Initiative. Educational Evaluation and Policy Analysis, 29, 95-114. Available at http://dx.doi.org/10.3102/0162373707301711
This article provides findings from a survey of middle school teachers’ mathematical knowledge. A quantitative analysis of the relationship between teachers’ mathematical knowledge and their subject matter preparation, certification type, teaching experience, and students’ poverty status revealed that teachers with strong subject matter preparation and high school teaching experience had higher mathematical knowledge for teaching. In addition, the author found that more affluent students are more likely to have more knowledgeable teachers, confirming that inequities exists in the distribution of teacher knowledge across student populations.
Middle Grades
Studier, C. & Perry, M. (2004, March). California’s Middle Grade Students. Palo Alto, CA: EdSource. Available at http://eric.ed.gov/?id=ED485363
This report examines how middle grade students are performing against California’s academic standards, based on state and national tests. It includes an in-depth examination of progress on getting more students to take and master algebra in 8th grade. It also addresses some middle school student achievement issues, including strategies for engaging the age group, debates on how best to handle transitions into and out of middle school, and the extra resources needed to help all students be more successful. Finally, the report looks at the qualifications of California middle school educators.
Southern Regional Education Board (2002). Academic Achievement in the Middle Grades: What Does Research Tell Us? A Review of Literature. Atlanta, GA: Author. Available at http://publications.sreb.org/2002/02V47_AchievementReview.pdf
This report reviews the literature on academic achievement, strategies for reform, and educational practices in the middle grades. The mathematics research reviewed suggests that middle-grade students could benefit from an accelerated curriculum and placement in higher tracks. In addition, findings suggest that U.S. mathematics teachers need to focus more deeply on fewer and more advanced topics.
**This document is considered a priority reading.