Supporting Mathematical Proficiency for ALL Students

Annotated Bibliography

Supporting Mathematical Proficiency for ALL Students

Last updated: April 15, 2010

Works Cited

Beaton, A.E., et al. 1996. Mathematics Achievement in the Middle School Years: IEA’s Third International Mathematics and Science Study (TIMSS). Chestnut Hill, Mass.: Boston College, Center for the Study of Testing, Evaluation and Educational Policy.

Bell, A. (1993). Some experiments in diagnostic teaching.Educational Study of Mathematics, 24(1), 115-117. Nottingham, England: Shell Center for Mathematical Education, University of Nottingham.

This article reports on three teaching experiments which study aspects of a diagnostic teaching methodology based on identifying and focusing on key conceptual points and misconceptions, giving substantial open challenges, provoking cognitive conflict, and resolving it through intensive discussion. An experiment in the field of directional quantities showed a positive correlation between the intensity of discussion and amount of learning. Students in classes where teachers utilized this methodology retained concepts over a period of two months. The comparison group with individualized booklets showed very low retention.

Black, P., & Wiliam, D. (1998) Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139-144.

Firm evidence shows that formative assessment is an essential ingredient of high-quality classroom work and that its development can improve achievement. Achieving this goal necessitates a four-point scheme for teacher development: learning from development, a slow yet steady dissemination process, reduction of obstacles, and substantive research efforts.

Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D.(2004). Working inside the black box: Assessment for learning in the classroom.Phi Delta Kappan, 86(1),8.

The authors report on a follow-up project to their 1998 study that has helped teachers change their practice and students change their behavior so that everyone shares responsibility for the students’ learning.

Boston, M. D., & Smith, M. S., (2009). Transforming Secondary Mathematics Teaching: Increasing the Cognitive Demands of Instructional Tasks Used in Teachers’ Classrooms. Journal for Research in Mathematics Education, Vol. 40, No. 2, 119–156.

Daro, P. (2008). Catching Up: What We Can Do For Students Behind In Mathematics. PowerPoint Presentation. Available at

This PowerPoint presentation describes intervention strategies to support students who have fallen behind in mathematics. Daro draws upon the latest research and student achievement data to support his arguments.

EdSource Report: Math and Science Education for the California Workforce: It Starts with K-12, EdSource Report: Algebra Policy in California: Great Expectations and Serious Challenges, May 2009

This report defines the current status of algebra in the state of California. It summarizes Algebra 1 CST data, the legal status of the State Board of Education’s decision to require Algebra 1 in eighth grade, the latest numbers on qualified math instructors needed, and other pertinent issues related to student achievement in Algebra 1.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., March, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools: A practice guide Washington, D.C.: Institute of Education Sciences, U. S., Department of Education.

This Institute of Education Sciences (IES) Practice Guide proffers an evaluation of the effectiveness of seven recommendations for supporting students in learning mathematics within the framework of Response-to-Intervention. Because Tier 1 mathematics interventions vary depending on the math topic and student grade level, all but one of the recommendations address Tier 2 and Tier 3 interventions. Each of the recommendations includes a brief summary of supporting evidence, instructions on implementation, and a list of possible roadblocks and solutions. All IES Practice Guides judge their recommendations as having either a low, moderate, or strong level of evidence supporting a causal relationship between their recommendations and the desired outcome.

Loveless, Tom. “The Misplaced Math Student: Lost in Eighth Grade Algebra”, Brown University, September 2008

NAEP website

National Math Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, D.C., U.S. Department of Education. Retrieved October 30, 2009, from

The National Math Panel's final report, issued on March 13, 2008, contains 45 findings and recommendations on numerous topics including instructional practices, materials, professional development, and assessments.

Stein, M.K., Engle, R.A., Smith., M.S. & Hughes, E.K. (2008) “Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell.” Mathematics Teaching and Learning. 10(4)4:313-340.

Teachers who attempt to use inquiry-based, student centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique, sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task, but also begin to align students’ disparate ideas and approaches with canonical understandings about the nature of mathematics. This paper presents a pedagogical model that specifies five key practices teachers can learn in order to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses.

Swan, M. For a summary of how his work, “Improving Learning in Mathematics: Challenges and Strategies” has influenced the research and discussion on the importance of rich tasks in mathematics:

The site focuses on Mathematics Knowledge Networks-Exploring rich mathematical tasks. Swan contrasts simple and rich tasks noting that: “Textbooks often assume that we should begin topics with solving simple questions and the move toward more complex questions. While this may appear natural, we find that learners ten to solve simple questions by intuitive methods that do not generalize to more complex problems. When the teacher insists that they use more generalisable methods, learners do not understand why they should do so when intuitive methods work well. Rich tasks allow learners to find something challenging and at an appropriate level to work on.”

Webb, N.L. (2007). Issues related to judging the alignment of curriculum standards and assessments. Applied Measurement in Education, 20(1), 7-25.

This article presents a process for measuring the alignment between curriculum standards and assessments. Using four alignment criteria: categorical concurrence, depth of knowledge consistency, range of knowledge correspondence, and balance of representation, the article discusses options for the acceptable levels of alignment. It identifies five issues related to decision making on setting standards. The issues discussed arise from a change in the underlying assumptions and from considering variations in the purpose for an assessment. The existence of such issues reinforces the subjective nature of the definition of “well-aligned standards and assessments.”

Other Resources

Allensworth, E.M., and T. Nomi. ”College-Preparatory Curriculum for All: The Consequences of RaisingMathematics Graduation Requirements on Students'Course Taking and Outcomes in Chicago.“ Paper presented at the Second Annual Conference of the Society for Research on Educational Effectiveness, March3, 2009, Arlington, VA.

Boaler, J., (2008). What’s math got to do with it? Helping children learn to love their most heted subject and why it’s important for America. Viking, NY: NY.

The Center for the Future of Teaching and Learning: California's Math Instruction Still Doesn't Add Up. Available at

National Research Council. (2001) Adding it up: Helping children learn mathematics. Washington,DC: National Academy Press.

Seeley, Cathy L. Faster Isn’t Smarter. Sausalito, CA: MathSolutions, 2009.