What are the components of effective mathematics instruction?

Why is this question important? The acquisition of math skills by American children has lagged behind expectations for years. The long-term trend in the National Assessment of Educational Progress (NAEP) of student achievement in mathematics, going back to 1970, shows a persistent lack of progress for all age groups. This is especially troubling in light of the data suggesting that the majority of students test below proficiency, The Nations Report Card Mathematics 2011. In 2011 only 40% of fourth students could be classified as being at or above proficiency in mathematics. The data are more disappointing for 12th graders. As of 2009 only 23% of 12th graders could be said to be proficient in mathematics skills. This picture is reinforced when one examines the Program for International Student Assessment (PISA) test results that compare American student performance to children of other nations. By 2009 American students ranked 25th in the world in mathematics competency and during the period 2000 to 2009 student scores, in fact, were observed to drop by five points. These data are a good indication that we need to improve the instructional practices commonly used to teach mathematics in American schools. It is unacceptable that American schools continue implementing practices that are clearing failing to achieve the desired results.

See further discussion below.


Source(s): Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools

Result(s): The report, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools, was commissioned by the What Works Clearinghouse (WWC). The WWC panel recommends that the practices outlined in the practice guide be in the repertoire of mathematics instructors and instruction be implemented in conjunction with a multi-tiered system wide Response to Intervention (RtI) model for student support.

Tier One

  1. 1. Screen all students for potential mathematics difficulties and provide interventions to students at risk. – Moderate level of evidence supporting the practice

Tier Two and Three

  1. Instructional materials should focus on in-depth treatment of whole numbers in K-5 and on rational numbers in grades 4-8. - Low level of evidence supporting the practice
  2. Instruction should be explicit and systematic. (Provide models of proficient problem solving, verbalize thought processes, employ guided practice, offer corrective feedback, and practice frequent cumulative review) - Strong level of evidence supporting the practice
  3. Instruction should provide training in solving word problems. - Strong level of evidence supporting the practice
  4. Materials should include opportunities for students to work with visual representations of mathematical ideas and instructors should be proficient in the use of visual representations of mathematical ideas. - Moderate level of evidence supporting the practice
  5. Instructors should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. - Moderate level of evidence supporting the practice
  6. Monitor the progress of students receiving supplemental instruction and other students who are at risk. - Low level of evidence supporting the practice
  7. Utilize motivational strategies in tier 2 and tier 3 interventions - Low level of evidence supporting the practice

Implication(s): The What Work Clearing House Practice Guide offers a well-reasoned alternative to many of the methods employed for the past 40 years. Basing their practice guide on the best available evidence, the assembled panel of researchers and practitioners outline a useful plan readily accessible to educators that combines systematic use of seven sound practices to be implemented within the framework of RtI. Although the guide was designed with a focus on students who are experiencing challenges in meeting mathematics proficiency, the practice offered within the guide are well suited for instruction of all children.

Author(s): What Works Clearinghouse, 2009

Publisher(s): Institute of Education Services (IES)

Study Description: Practice Guides are published by the What Works Clearinghouse, a unit of the U.S. Department of Education, that offer practical recommendations for educators to address challenges in their classrooms and schools based upon the best available evidence. The recommendations in this guide include evaluations of mathematics interventions for low-performing students and students with learning disabilities. The goal of the panel was to base recommendations on high-quality experimental and quasi-experimental studies that meet the criteria of the WWC. In certain instances research for particular practices are not available and the recommendations reflect what, in the professional judgment of the panel, are best practice. The panel also relied on the technical adequacy of batteries of screening and progress monitoring measures for recommendations relating to assessment. Studies that do not meet WWC standards have been included to offer educators practices that offer the best chance of making a difference in boosting student achievement while we await more rigorous studies to be conducted.


  1. Response to Intervention (RtI): An early prevention and support system based on a public health model of tiered interventions. RtI relies heavily on progress monitoring and the use of evidence-based interventions. RtI identifies struggling students and proscribes a cost effective approach to assist students before they fall behind and monitors performance of interventions to maximize student progress.
  2. Strength of the evidence used by the panel:
    • Strong Consistent and generalizable evidence that an intervention pro- gram causes better outcomes.
    • Moderate Evidence that allow strong causal conclusions but cannot be generalized with assurance to the population on which a recommendation is focused or evidence from studies that are generalizable but have more causal ambiguity than offered by experimental designs (statistical models of correlational data or group comparison designs).
    • Low Expert opinion based on reasonable extrapolations from research and theory and evidence that do not meet the standards for moderate or strong evidence.

Citation: Gersten, R., Beckman S., Clarke B., Foegen A., Marsh L., Star J., and Witzel B. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (NCEE 2009-4060) Washington D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/pdf/practice_guides/rti_math_pg_042109.pdf December 4, 2012