Paraphrase of Cathy Seeley in Algebra for the 21st Century

NCTM, 1993.

The movement to offer more meaningful mathematics courses to all students will challenge the instructional skills of many teachers. As students who in the past enrolled in General Mathematics courses begin to take algebra and geometry, teachers are likely to react in two ways, both detrimental to the education of students:

1. some teachers will teach their courses using methodologies appropriate for students with high motivation and practiced in abstract reasoning and
2. other teachers will lower expectations and water-down content to accommodate the wider range of students.

The former will result in inadequate preparation of students and the latter will lead to high rates of student failure.

The use of concrete manipulative materials is one critical technique for making abstract concepts more accessible to a wider audience.