(that you can teach in the allotted time)
• Create ownership among all teachers required to teach the intended curriculum
It might be surprising, but in a PLC at Work, teacher teams build mathematics units from the standards, not from the chapters in a textbook. Too often, textbooks include more learning than your state or province may require, or the textbooks may be missing content that you need to supplement to better match the standards and local curriculum expectations. Thus, your team starts with making sense of the standards students must learn in each unit of study, and then utilizes the most effective resources for teaching and learning.
Part 1 consists of two chapters. Chapter 1 (page 9) describes the mathematics content and skills students must learn in grades preK–2. Your team’s work begins by understanding what mathematics students must learn in each of the primary grades, preK, K, 1, and 2. Chapter 2 (page 15) provides protocols and tools your grade-level collaborative team can use to plan for the student learning each mathematics unit requires. Together, your team’s understanding of the mathematics content students must learn and your framework for units allows for a backward-design approach to ensuring every student learns mathematics.
CHAPTER 1
Planning for Student Learning of Mathematics in Grades PreK–2
Mathematics is a conceptual domain. It is not, as many people think, a list of facts and methods to be remembered.
–Jo Boaler
The first critical question of a PLC is, What do we expect all students to know and be able to do? (DuFour et al., 2016). As your collaborative team successfully answers this question for each unit of study, members build a common understanding of the mathematics students learn in your grade level. What is the mathematics story that unfolds as student learning progresses from one mathematics unit to the next? How do the units fit together and build on one another within and across the primary grades from preK to second grade?
Guaranteed and Viable Curriculum
Your preK, kindergarten, first-, or second-grade team effectively backward plans the year by grouping essential mathematics standards into units to create the guaranteed and viable mathematics curriculum students must learn. The order in which you teach the mathematics units provides the framework for your grade-level mathematics story. Within each unit, your daily lessons create the beginning, middle, and end for that part of the story.
Thus, evidence of your team’s guaranteed and viable curriculum includes (1) a yearlong pacing plan of standards and benchmarks throughout the year of spiraled standards (proficiency map or pacing guide), (2) unit plans, and (3) daily lessons. The graphic in figure 1.1 illustrates these three areas of team planning for a mathematics guaranteed and viable curriculum.
Figure 1.1: Mathematics guaranteed and viable curriculum plan.
Together, the mathematics units of study tell the story of the primary grade-level standards teachers expect students to learn throughout the year and from one year to the next.
As figure 1.1 (page 9) shows, your grade-level team’s guaranteed and viable curriculum is first defined by a district yearlong pacing guide or proficiency map (showing a time line for student proficiency with each mathematics standard). Your team then determines a time frame appropriate to each mathematics unit, typically two to four weeks in duration in the primary grades. This process eliminates the potential risk of running out of time and skipping units or essential standards that fall at the end of the year.
If your collaborative team does not have a yearlong plan with standards in clearly defined units, see appendix A (page 137), “Create a Proficiency Map,” for additional support. Helping each teacher on your team become comfortable with the progression of mathematics units throughout the school year will support your students’ understanding of the mathematics story arc for various standards.
Mathematics Unit Planner
Once your team determines the mathematics units for your grade level (detailing the standards and time line for each unit) for the year, your collaborative team can plan for student learning on a unit-by-unit basis (see figure 1.2; Kanold & Schuhl, 2020).
The Mathematics Unit Planner in figure 1.2 provides a template your team can use as you develop a shared understanding of what students are expected to learn in each unit of study. The numbered sections in the Mathematics Unit Planner correspond with the seven elements of unit planning. Throughout this book, you will see numbered headings that correspond with these seven areas. (Find completed examples of unit planners for preK in figure 3.12 [page 58], kindergarten in figure 4.11 [page 79], first grade in figure 5.11 [page 105], and second grade in figure 6.11 [page 129].)
Once the elements of the Mathematics Unit Planner (see figure 1.2) are complete, your team can use the information to plan for common assessments and daily lesson design (see Mathematics Assessment and Intervention in a PLC at Work [Kanold, Schuhl, et al., 2018] and Mathematics Instruction and Tasks in a PLC at Work [Kanold, Kanold-McIntyre, et al., 2018]). Additionally, you and your collaborative team can reference the unit planner for each successive unit in the year and from one year to the next as your team continues to deepen its own understanding of the required student learning.
In Principles to Actions, the National Council of Teachers of Mathematics (NCTM, 2014a) shares, “Effective mathematics teaching begins with a shared understanding among teachers of the mathematics that students are learning and how this mathematics develops along learning progressions” (p. 12). Therefore, before diving into each individual unit plan for the year, as a team, first consider the mathematical content students are learning in your grade. Additionally, make sense of the mathematical content trajectories, or progressions, that students are learning across your preK–2 band.
Mathematics Concepts and Skills for Grades PreK–2
Students in grades preK–2 develop their understanding of number, place value, and addition and subtraction. They grow their knowledge related to geometry and measurement. Throughout these foundational primary years, students first learn to count sequentially and read, write, and name numbers. They determine how to quantify a group of objects using a number. They compare numbers and learn to conceptualize the differences in value represented by two or more numbers. They also develop flexibility with numbers and use patterns to grow place-value understanding. In geometry, students identify, describe, compose, decompose, and analyze two- and three-dimensional shapes and, by second grade, create arrays for early multiplication
