Editor's Note: This is part 1 of a 3-part series on Math PD

Professional development researchers have told us for a long time principals need to be instructional leaders. That prescription entails visible support for new instructional strategies as well as the need for persistence, follow-up, and even the use of data to sustain or refine new practices. Unquestionably, all of this is important. But where does a principal start today in a world awash with new teachers, many of whom struggle to teach to state or national standards? As co-authors of the K-8 mathematics professional development program, NUMBERS, Michele Douglass, Mary Stroh and I have done a lot of thinking about how principals can orchestrate successful change.

A Two-Day In-Service Isn’t Enough

There is a beginning truism we all agree upon: a two-day in-service isn’t enough. However, it can be an important starting point if it is linked intentionally to subsequent services. Furthermore, those services should be cost effective given the limited time and funds school districts have for PD. We believe professional development services in mathematics should satisfy these criteria:

• Be standards based
• Be aimed at appropriate grade levels
• Be filled with the big ideas in a mathematics domain that improve instruction
• Be complete with a concrete vision of tasks and teaching techniques
• Be readily transportable to the classroom

To be sure, the list could go on, but let’s unpack these features for now and use PD in fractions and decimals, as an example. New state and national standards provide a clear roadmap for what needs to be taught in grades 3-6. Yet, a close look at the standards, associated mathematical practices, as well as sample items from high-stakes assessments can be daunting for teachers and administrators.

Big Ideas

The NUMBERS module for Fractions and Decimals translates national standards into a sequence of big ideas, ones that not only are comprehensible to teachers, but are orchestrated in a way that allows third-grade teachers to see where to start and why rich, initial instruction in part to whole relationships or number magnitude sets a critical foundation for subsequent instruction in the intermediate grades. Teachers at the other end of this continuum—even seventh- and eighth-grade teachers—can achieve a better understanding of what their incoming students know and what areas need review. Knowing more about the big ideas across grades 3-6 enhances a teacher’s diagnostic skills.

It’s also essential that mathematical practices are core to the PD. That leads directly to an emphasis on high-level tasks, the kinds of activities that are not typically part of daily instruction but need to be there if students are to better understand a topic and improve their performance on today’s demanding, high-stakes tests.

For example, today’s standards expect students actually understand what it means to divide a fraction by a fraction. NUMBERS presents a range of activities using area and length models to help students visualize and make sense of this operation in the context of everyday contexts. Moreover, this element of the Fractions and Decimals module builds off a visual and conceptual treatment of all of the operations on fractions, thus enabling students to better understand why denominators need to be converted for addition and subtraction, but not for multiplication and division of fractions.

As intermediate and early middle school teachers engage in critical, high-level tasks in fractions and decimals, they learn about a discrete number of tools—from Cuisenaire® Rods to 100-square grids—which can be taken back to the classroom and used with any curriculum.

All of this is the first phase of our PD. Subsequent NUMBERS PD intentionally links the initial in-service to instructional planning. Any principal today knows this is a key weakness in new teachers, ones who tend to rely solely on textbooks rather than standards and contemporary math practices to guide their classroom instruction. During this phase of NUMBERS PD, teachers also learn how to create easy-to-grade performance assessments that can dramatically change the learning targets in a classroom from computational proficiency only to higher-level skills.

Capacity Building

Further phases of NUMBERS focus on capacity building—especially training of trainers—as well as coaching and site-specific needs. The core idea behind the final phases of NUMBERS PD is to scale up new math practices and turn over further professional development to district or school specialists.

This makes NUMBERS a cost-effective alternative in professional development, and enhanced local capacity increases the likelihood of sustained change. We have thought a great deal about realistic, standards-based PD in mathematics, and we believe NUMBERS is particularly valuable for the growing number of teachers who are new to the classroom.