In my previous blog, I argued for a dual topic approach to curriculum design. The framework outlined in that blog is based on a variety of research.

Some of this research is drawn from psychology and studies of human learning. These involve the development of automaticity and controlling cognitive load. Other design elements are associated with what we have learned over the years from international research, particularly the way successful countries focus on fewer topics with greater depth in their math curricula. Still other research is a synthesis of what we believe are best instructional practices in remedial and special education.

Defining a High-Standards Math Curriculum for Struggling Students, Part 2 of 2

I made the case in my previous blog that adjusting the pace of instruction for struggling students in a high-standards curriculum is imperative. We all have different aptitudes for a given endeavor—from music to mathematics—and it is unrealistic to expect that all students can learn the same set of complex ideas in the same, fixed period of time.

Adjusting the pace of instruction does not mean that we should teach topics like fractions or integers in “twice the time” as much as it means that we need to sequence carefully the flow of concepts within these topics. It also means trade-offs such as not teaching every standard. There is little reason to believe that every standard is equally weighted in its importance, particularly if time is an issue.

Defining a High-Standards Math Curriculum for Struggling Students, Part 1 of 2

It takes time for research to be translated into practice, particularly when it comes to textbooks. For example, it was nearly 20 years ago when U.S. math educators examined the textbooks and instructional practices of highly successful countries around the world, only to determine what we already knew. American math textbooks were “a mile wide and an inch deep.” In contrast, international curricula typically contained fewer topics that were addressed in greater depth.¹

The traditional structure of math textbooks as you move across the grade levels has been unfortunately predictable. James Flanders’ analysis of elementary and middle school texts in the late 1980s characterized the typical text as bloated with all kinds of review and extra content.² Almost 30 years later, we still have the same problem in many of our math textbooks.³ This problem remains in spite of the fact that efforts like the National Council of Teachers of Mathematics (NCTM) standards to infuse more conceptual understanding and problem solving in textbooks occurred in the intervening years.

One of the biggest impacts of the No Child Left Behind (NCLB) legislation has been the infusion of the word “research” into the language and thinking about education. Teachers are encouraged to ask, “Is my classroom curriculum research based?” “What about specialized interventions for students with disabilities?” It is a short step to asking the same question about today’s mathematics standards, and prominent researchers at Vanderbilt University have done just this in a series of randomized control studies.¹

What the researchers described as “very low achieving” fourth grade students were randomly assigned to either inclusive or specialized intensive classrooms. Instruction in both conditions was guided by grade-level standards for fractions. It wasn’t a major surprise that the students in the inclusive classrooms performed poorly over the three years of the study as teachers fully implemented the Common Core State Standards. Researchers, however, were dismayed to find that the performance of students in specialized intensive settings also decreased over time, despite the use of their intervention curriculum in these studies.

• Are high standards appropriate for struggling students?
• If they are not appropriate, are they even relevant?