• There is indeed much known about the teaching of math, the prerequisite concepts and skills that underlie math understanding for children at different stages of development, and the instructional strategies that have proved effective in promoting success in math learning for children throughout their K-12 careers, and
• There are certain areas where the best available information is not yet of high-enough rigor and quality to draw conclusions, and that more targeted and sustained research is needed.

Ingredients for Success

• Standards of evidence

  • More than 16,000 studies were gathered, read, and assigned ratings of evidence (strong, moderate, suggestive, inconsistent, weak) based on carefully-established criteria that would allow researchers to draw conclusions. These include: whether students were randomly assigned to groups during research studies, levels of attrition (drop out), the validity and reliability of measures and procedures used, the sample size (numbers of children studied), and teacher knowledge of math and experience/qualifications.
  • Public testimony was gathered from 110 individuals, input was received from 160 organizations, and surveys were collected from 743 math (algebra) teachers. The opinions and concerns voiced were of great value to NMAP work as both a reality check (Are we asking the right questions? Will our findings and recommendations be valued by the education community?) and as a way to acknowledge the importance not only of research findings informing practice, but practice informing current and future research efforts as well.

• Learning processes

  • Perhaps the most interesting and encouraging finding is that "... even before they enter kindergarten, most children develop considerable knowledge of numbers and other aspects of mathematics" and that this early knowledge "...influences their math learning for math years... probably throughout their education."
  • "Number Sense" was identified as a key component of math learning, often acquired informally before starting school but critical to later success in math performance.
  • The NMAP report disagreed with those who might suggest that children at certain ages cannot learn math concepts because they are "too young," "not in the appropriate stage" or "not ready." The report concluded that "what is developmentally appropriate is not a simple function of age or grade" and that in great part, children gain understanding by "prior opportunities to learn."
  • Motivation counts! The report corroborated the adage "success breeds success," finding that children who gained proficiency and received positive feedback for their efforts placed greater value on math learning. The report also concluded that children who believed that math learning was related to innate ability showed less persistence than students who thought that effort was more important to their success.

• Teachers and teacher education

  • Teachers count! (no pun intended). Researchers found that 12-14 percent of the variability in student performance could be attributed to the classroom teacher, and this effect was dramatically increased when students had a series of effective or ineffective teachers.
  • While it was clear that "teachers' knowledge of mathematics was positively related to student achievement," the NMAP was not able to identify the specific areas of knowledge and expertise that would predict most effective teaching practices and student learning outcomes. This is an important (and difficult) area of need for further study.

• Instructional practices

  • This is the area from which "wars" emerge, and similar to other areas of learning (such as reading), the opposing camps have been those who advocate for "student centered" or "teacher directed" practices. The NMAP was clear that there were way too few studies (only eight) to make generalized recommendations about one approach vs. the other, and that high-quality research does not support the exclusive use of either approach.
  • The NMAP recommended that "formative assessment" (monitoring student learning and using the findings to make needed changes in instruction) was strongly recommended. It also makes note of some promising strategies (e.g., technology tools) that help teachers gather information about individual students and whole classes, some of which can be built into computer-assisted tutoring or instruction programs.

• Instructional materials

  • In general, the NMAP found that math text books are too long, contain errors and ambiguous statements and problems, and lack coherence across the grades.
  • A number of suggestions were offered about how to improve the user's experience, including eliminating photographs that are not essential to the math content and using supplements rather than the text itself to deliver review and enrichment activities.

• Assessment

  • It was the strong recommendation of the NMAP that the large-scale assessments used to track students' progress over time be of the highest quality, that test items reflect best test-design features and that that they measure what they are intended to measure. This is a huge (and important) challenge because of the different state tests being used and the different ways that decisions are made about curriculum selection, the implementation of training and support for teachers, and policy decisions that impact education practices on school, district and state levels.

Saying it Again

• There is wide-spread misunderstanding of the importance of math in everyday life and a lack of appreciation of how important math learning is for young children. Researchers have begun to look at kindergarten math skills as effective predictors of future academic achievement. Children's early math knowledge is said to be important because it fosters future abilities not only in math but also in reading. In one study, pre-math skills at kindergarten entry are said to predict math achievement as much as reading achievement  by grade three.
• .Math difficulties are more pervasive among minority children and among those from low-income families. Many of these children lag behind before they even start school. Without early and effective instruction, many of these children will face math frustration and failure throughout their school career.
• Many teachers (and parents), by their own admission, lack a conceptual understanding of math and are therefore not well prepared to teach math effectively or convey an appreciation of math to their students (many even admit to disliking or being anxious about math, a perception easily conveyed to students).
• In contrast to dyslexia, researchers have not yet identified the primary cognitive deficits that underlie math learning disabilities.
• Difficulties in math appear not to be linked to a specific disability, but rather, may be the result of weaknesses in other related cognitive skill areas such as language, attention, memory, and skills related to perceiving and imagining space.
• Math learning does not follow a predictable, step-by-step course. Interestingly, seemingly more advanced skills and concepts are possible to learn before mastering more basic numerical operations.
• There is good evidence that early prediction or identification of math difficulties, coupled with well-targeted research-based interventions, can diminish or prevent struggle with math learning for many children.
• Children with learning disabilities in math are likely to show persistent difficulties with learning over time, making it all the more important to gather reliable data about student progress beginning as early as possible in the child's school career.

Additional Resources

• Education Publications Center
  You can download copies of the NMAP reports online or order hard copies of the National Mathematics Advisory Panel Report or the Reports of the Task Groups and Subcommittees from this Web site. (Be sure to look for other valuable resources while you are there!)
• American Educational Research Association
  The December 2008 (volume 37, number 9) issue of Educational Researcher is a special issue that examines Foundations for Success: The Final Report of the National Mathematics Advisory Panel, featuring peer-reviewed articles from leading education research experts.
• National Academy of Sciences
  This two-year study on early childhood mathematics is focused on synthesizing and analyzing the past twenty years of research on early childhood mathematics. The findings will have implications for policy and practice affecting young children as they move through the preschool years and begin formal schooling. The report will provide research-based guidance to increase the numbers of young children, especially vulnerable children, getting off to a strong start in learning mathematics during their first years of schooling.

Sheldon Horowitz, Ed.D. is the Director of LD Resources & Essential Information at the National Center for Learning Disabilities. This article first appeared as a Research Roundup column in LD News.

Read all Research Roundup Columns by Dr. Horowitz in the Research Roundup Archive.