I’ve been selected to be on my district’s textbook adoption committee as we select new materials to be used for the implementation of common core. We were given High School publisher’s criteria to help us implement the standards as we review the materials. We may use new materials, modify or combine existing resources, and/or analyze existing materials for strengths and weaknesses. We will also be investigating digital and online materials to make sure that they follow the standards.
It is very important that the materials follow the standards as written and track the structure in the standards. Connections and clusters that are in the standards need to be preserved, even when tackling specific learning objectives. Content standards are designed to support focus and coherence. It is important to recognize that the standards are not all of uniform size and will require different amounts of time to master.
The idea is that fewer skills will be targeted, but those skills will be taught in a more in-depth and open-ended way. There are three aspects of “Rigor” that are equally important: (1) conceptual understanding, (2) procedural skill, and (3) applications. These three aspects don’t always have to be together, although two or more may be.
It is important that all materials provide support for special populations, such as English learners or students with disabilities. This would also include low skilled or remedial learners, who should deal with incomplete understanding of concepts taught in earlier grades inside the course level work, rather than in separate remediation.
There is a great emphasis on preparing students with prerequisite skills for postsecondary work, which, interestingly, can come from Grades 6-8. These skills are developed and extended in high school-level work and form the backbone of student’s conceptual understanding and problem solving abilities.
The materials should have a variety of problems, such as conceptual problems with low computational difficulty and those that require identifying correspondences across different mathematical models and representations, leading students to observe structure. Students will be spending considerable classroom time communicating reasoning, and as such, the teaching the language of mathematics and argument is supported in the materials, even for English learners or remedial students.
The materials need to support both problems, which teach specific mathematics concepts, and exercises, which build fluency and are performed in deliberate progressions. It is also essential that the amount of both problems and exercises be balanced for optimal focus, concentration and coherence. There should be a regular linking of conceptual understanding and exercising for proficiency. Students should produce a variety of output such as explanations, diagrams, and models.
The teacher materials should support modeling of new methods, prompting broad student reasoning, anticipating a diverse array of student responses, and what mathematical behavior is desired from students, in addition to designing lessons that flow logically from unit to unit with strong correlation to the standards.
So overall, an immense task, but one that I am very interested to see unfold. I feel very grateful to have this opportunity to be a part of this process.
Humble Pi 