A common complaint about standardized assessments in this time of high-stakes testing is that while teachers and administrators are held accountable, students are not. Of course, teachers must be responsible, but by leaving learners out of the conversation, students often are not vested in the process.

As we implement higher standards across the country, it has become increasingly important that we identify and use a variety of strategies to assess student learning so that the appropriate interventions may be provided.

Sometimes the mathematics conversation is just as confusing to students as this collection of signs is to a driver in an unfamiliar situation. There appears to be a variety of symbols used to identify the different types of roads in the area, just as we have a variety of concepts, operations, and relations that are conveyed through symbolic notations.

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.

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.