by Lee V. Stiff, NCTM President 2000-2002
NCTM News Bulletin, October 2001
Principles and Standards for School Mathematics is a comprehensive and coherent set of goals for improving mathematics teaching and learning in our schools. For most of us, achieving the goals of the Standards is a professional journey. The mathematics teaching and learning envisioned by the Standards require shifts in the mathematics students are asked to learn, the pedagogy teachers are required to provide, and the assessments used to inform the teaching and learning of mathematics that is taking place.
Each shift is reflected in the instructional materials we use, and we frequently find ourselves asking, "How do I identify textbooks, mathematics programs, and other resources that will help me implement the Standards in my classroom?" The answer to this question is straightforward: select teaching materials that will move you and your students closer to the realization of the goals established in the Standards documents.
We want students to be able to do mathematics and understand the underlying concepts on which their mathematical know-how is based. We want assessments to be more than merely assigning grades at the end of a term; assessments should help us as teachers provide better learning opportunities for all students. We strive to employ developmentally appropriate instructional materials and teaching practices equitably for all the students we serve. We want our classrooms to become mathematical communities in which students, frequently working together, question, reason, make conjectures, share, solve problems, and connect mathematics to the world around them.
So, the question remains, "Which instructional materials will help me do this?" To answer the question, we must recognize what it means for students to understand school mathematics.
I tell my students, "If you cannot explain it, you don't understand it!" This is my way of stating that one of the final stages of incorporating knowledge into one's own cognitive structures of understanding is the ability to talk about it. However, before students are challenged to articulate their understanding, they must participate in lessons and activities designed to foster relationships between existing knowledge, experiences, and skills and the new knowledge that they have acquired. Lessons and activities must be carefully crafted to introduce students to new mathematical ideas and then extend and apply their existing mathematics knowledge to accommodate the new.
Teachers craft these lessons and are the central figures in the implementation of the NCTM Standards. However, we frequently rely on instructional materials, such as textbooks, mathematics programs, and other resources as a starting point for the development of lessons. Thus, instructional materials have a great effect on our ability to implement the Standards. Teaching materials may also serve as learning tools for teachers, allowing us to deepen our understanding of the content, broaden the nature of interactions in our classrooms, and expand our evaluation of students' mathematics knowledge.
There are certain requisites that our teaching materials must meet if they are to move our students and ourselves closer to realizing the goals of the Standards. The sequence, timing, developmental appropriateness, and complexity of mathematical tasks described in these materials have a direct impact on the quality of the mathematical content students receive. To evaluate the mathematical content in instructional materials, we should ask, "Do the teaching materials ask students to perform at high cognitive levels? Do the materials help teachers understand the content for themselves and foster a better understanding of the teaching and learning of the mathematics? Do the materials integrate assessment into the teaching and learning process?"
Not only must we look for teaching materials that have sound and appropriate mathematical content, we must also seek materials that help bridge the gap between traditional approaches and reform-based pedagogies. In order to provide access to the road of reform, textbooks, mathematics programs, and other resources must build on the strengths of most teachers in our district and effectively address their weaknesses. When considering materials that challenge mathematics educators, we should ask, "Can these materials be used effectively by teachers? Do teachers in our district receive adequate support and enough ongoing professional development to effectively use these materials? Can these teaching materials build on the Standards-based improvements already realized by most teachers in the district or will they stall our progress?"
In order for curriculum materials to advance the vision of reform in classrooms they must meet several requirements. They must provide sound and developmentally appropriate mathematics content. They must build on and expand the content knowledge and pedagogical behaviors of teachers without being either too difficult for teachers to understand and implement or too traditional to promote the vision of the Standards. They must use assessment as a teaching and learning tool. They must help teachers increase their understanding of mathematical content and best teaching practices.
There is no one correct way to teach mathematics. As the journey of teaching and learning mathematics continues, the need to identify instructional materials that complement teachers' personal and professional development in the understanding and implementation of the NCTM Standards will always be with us. The key to making good decisions about the selection of teaching materials is recognizing that teachers must be challenged to take manageable steps over time toward the vision of a high-quality mathematics education for every child.