and was department chair for fifteen years. An active member of the National Council of Teachers of Mathematics, he is president-elect of the Maryland Council of Supervisors of Mathematics. Nolan is also a consultant for Solution Tree and the Resident Teacher Professional Preparation Program at the University of Central Florida, where he provides support for preservice teachers and their in-service mentors on the Common Core State Standards for mathematics.
Nolan has been published in the Banneker Banner, a publication of the Maryland Council of Teachers of Mathematics, and Mathematics Teaching in the Middle School, a publication of the National Council of Teachers of Mathematics (NCTM), and he has conducted professional development at the state, regional, and national levels, including webinars for NCTM and TODOS: Mathematics for ALL. His research interests lie in supporting students in developing algebraic thinking and reasoning. In 2005, Nolan won the Presidential Award for Excellence in Mathematics and Science Teaching.
He is a graduate of the University of Maryland. He earned a master’s degree in educational administration from Western Maryland College.
To book Juli K. Dixon, Thomasenia Lott Adams, or Edward C. Nolan for professional development, contact [email protected].
Introduction
You have high impact on the front lines as you snag children in the river of life.
—Tracy Kidder
Your work as an elementary school mathematics teacher is one of the most important, and at the same time, one of the most difficult jobs to do well in education. Since the release of our 2012 Solution Tree Press series Common Core Mathematics in a PLC at Work™, our authors, reviewers, school leaders, and consultants from the Mathematics at Work™ team have had the opportunity to work with thousands of grades K–5 teachers and teacher teams from across the United States who are just like you: educators trying to urgently and consistently seek deeper and more meaningful solutions to a sustained effort for meeting the challenge of improved student learning. From California to Virginia, Utah to Florida, Oregon to New York, Wisconsin to Texas, and beyond, we have discovered a thirst for implementation of K–12 mathematics programs that will sustain student success over time. A focus on the elementary grades is a significant component of the K–12 effort toward improved student learning.
Certainly, the Common Core State Standards (CCSS) for mathematics have served as a catalyst for much of the national focus and conversation about improving student learning. However, your essential work as a teacher of grades K–5 mathematics and as part of a collaborative team in your local school and district takes you beyond your state’s standards—whatever they may be. As the authors of the National Council of Teachers of Mathematics (Leinwand et al., 2014) publication Principles to Actions: Ensuring Mathematical Success for All argue, standards in and of themselves do not describe the essential conditions necessary to ensure mathematics learning for all students. You, as the classroom teacher, are the most important ingredient to student success.
Thus, this K–5 mathematics teaching and assessing handbook is designed to take you beyond the product of standards themselves by providing you and your collaborative team with the guidance, support, and process tools necessary to achieve mathematics program greatness within the context of higher levels of demonstrated student learning and performance.
Whether you are from a state that is participating in one of the CCSS assessment consortia or from a state that uses a unique mathematics assessment designed only for that state, it is our hope that this handbook provides a continual process that allows you to move toward a local program of great mathematics teaching and learning for you and your students.
Your daily work in mathematics begins by understanding that what does make a significant difference (in terms of high levels of student achievement) are the thousands of instructional and assessment decisions you and your collaborative team will make every year—every day and in every unit.
The Grain Size of Change Is the Teacher Team
We believe that the best strategy to achieve the expectations of CCSS-type state standards is to create schools and districts that operate as professional learning communities (PLCs), and, more specifically, within a PLC at Work™ culture as outlined by Richard DuFour, Robert Eaker, Rebecca DuFour, and Tom Many (2010). We believe that the PLC process supports a grain size of change that is just right—not too small (the individual teacher) and not too big (the district office)—for impacting deep change. The adult knowledge capacity development and growth necessary to deliver on the promise of standards that expect student demonstrations of understanding reside in the engine that drives the PLC school culture: the teacher team.
There is a never-ending aspect to your professional journey and the high-leverage teacher and teacher team actions that measure your impact on student learning. This idea is at the very heart of your work. As John Hattie (2012) states in Visible Learning for Teachers: Maximizing Impact on Learning:
My role as a teacher is to evaluate the effect I have on my students. It is to “know thy impact,” it is to understand this impact, and it is to act on this knowing and understanding. This requires that teachers gather defensible and dependable evidence from many sources, and hold collaborative discussions with colleagues and students about this evidence, thus making the effect of their teaching visible to themselves and to others. (p. 19)
Knowing Your Vision for Mathematics Instruction and Assessment
Quick—you have thirty seconds: turn to a colleague and declare your vision for mathematics instruction and assessment in your school. What exactly will you say? More importantly, on a scale of 1 (low) to 6 (high), what would be the degree of coherence between your and your colleagues’ visions for instruction and assessment?
We have asked these vision questions to more than one thousand mathematics teachers across the United States since 2011, and the answers have been consistent: wide variance on assessment coherence (low scores of 1, 2, or 3 mostly) and general agreement that the idea of some type of a formative assessment process is supposed to be in your vision for mathematics instruction and assessment.
A favorite team exercise we use to capture the vision for instruction and assessment is to ask a team of three to five teachers to draw a circle in the middle of a sheet of poster paper. We ask each team member to write a list (outside of the circle) of three or four vital adult behaviors that reflect his or her vision for instruction and assessment. After brainstorming, the team will have twelve to fifteen vital teacher behaviors.
We then ask the team to prepare its vision for mathematics instruction and assessment inside the circle. The vision must represent the vital behaviors each team member has listed in eighteen words or less. We indicate, too, that the vision should describe a “compelling picture of the school’s future that produces energy, passion, and action in yourself and others” (Kanold, 2011, p. 12).
Team members are allowed to use pictures, phrases, or complete sentences, but all together, the vision cannot be more than eighteen words. Often, in our workshops, professional development events, conferences, institutes, and onsite work, we have been asked a simple, yet complex question: “How?” How do you begin to make decisions and do your work in ways that will advance your vision for mathematics instruction and assessment in your elementary school? How do you honor what is inside your circle? And how do you know that your circle, your defined vision for mathematics instruction and assessment, represents the “right things” to pursue that are worthy of your best energy and effort?
In our Common Core Mathematics in a PLC at Work (2012) grades K–2 and grades 3–5 books, we explain how
