on that knowledge and transfer what you learn into daily classroom practice through the ten high-leverage teacher team actions presented in this handbook. For more information on the connection between these two documents, visit go.solution-tree.com/mathematicsatwork.
Although given less attention, the difficult work of collective inquiry and action orientation has a more direct impact on student learning than when you work in isolation (Hattie, 2009). Through your team commitment (the engine that drives the PLC at Work culture and processes of collective inquiry and action research), you will find meaning in the collaborative work with your colleagues.
In Great by Choice, Jim Collins (2011) asks, “Do we really believe that our actions count for little, that those who create something great are merely lucky, that our circumstances imprison us?” He then answers, “Our research stands firmly against this view. Greatness is not primarily a matter of circumstance; greatness is first and foremost a matter of conscious choice and discipline” (p. 181). We hope this handbook helps you focus your time, energy, choices, and pursuit of a great teaching journey.
CHAPTER 1
Before the Unit
Teacher: Know thy impact.
—John Hattie
The ultimate outcome of planning before the unit begins is for you and your team members to gain a clear understanding of the impact of your expectations for student learning and demonstrations of understanding during the unit.
In conjunction with the scope and sequence your district mathematics curriculum provides, your collaborative team prepares a roadmap that describes what students will know and be able to demonstrate at the conclusion of the unit. To create this roadmap, your collaborative team prepares and organizes your work around five before-the-unit-begins high-leverage team actions.
HLTA 1. Making sense of the agreed-on essential learning standards (content and practices) and pacing
HLTA 2. Identifying higher-level-cognitive-demand mathematical tasks
HLTA 3. Developing common assessment instruments
HLTA 4. Developing scoring rubrics and proficiency expectations for the common assessment instruments
HLTA 5. Planning and using common homework assignments
These five team pursuits are based on step one of the PLC teaching-assessing-learning cycle (Kanold, Kanold, & Larson, 2012) shown in figure 1.1 (page 8). This cycle drives your pursuit of a meaningful formative assessment and learning process for your team and for your students throughout the unit and the year.
In this chapter, we describe each of the five before-the-unit-begins high-leverage team actions in more detail (the what) along with suggestions for how to achieve these pursuits (the how). Each HLTA section ends with an opportunity for you to evaluate your current reality (your team progress). The chapter ends with time for reflection and action (setting your Mathematics at Work priorities for team action).
Source: Kanold, Kanold, & Larson, 2012.
Figure 1.1: Step one of the PLC teaching-assessing-learning cycle.
HLTA 1: Making Sense of the Agreed-On Essential Learning Standards (Content and Practices) and Pacing
An excellent mathematics program includes curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.
—Steven Leinwand, Daniel J. Brahier, DeAnn Huinker,
Robert Q. Berry III, Frederick L. Dillon, et al.
In most K–5 grade levels, there will be eight to ten mathematics units (or chapters) during the school year. These units may also consist of several learning modules depending on how your curriculum is structured. An ongoing challenge is for you and your team to determine how to best make sense of and develop understanding for each of the agreed-on essential learning standards within the mathematics unit.
The What
Recall there are four critical questions every collaborative team in a PLC asks and answers on an ongoing unit-by-unit basis.
1. What do we want all students to know and be able to do? (The essential learning standards)
2. How will we know if they know it? (The assessment instruments and tasks teams use)
3. How will we respond if they don’t know it? (Formative assessment processes for intervention)
4. How will we respond if they do know it? (Formative assessment processes for extension and enrichment)
|
|
= Fully addressed with high-leverage team action |
This first high-leverage team action enhances clarity on the first PLC critical question for collaborative team learning: What do we want all students to know and be able to do? The essential learning standards for the unit—the guaranteed and viable mathematics curriculum—include what (clusters and standards) students will learn, when they will learn it (the pacing of the unit), and how they will learn it (often via standards such as the Common Core Standards for Mathematical Practice). The Standards for Mathematical Practice “describe varieties of expertise that mathematic educators at all levels should seek to develop in their students” (National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], 2010, p. 6). Following are the eight Standards for Mathematical Practice, which we include in full in appendix A (page 149).
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning. (NGA & CCSSO, 2010, pp. 6–8)
While different school districts use many names for learning standards—learning goals, learning targets, learning objectives, and so on—this handbook references the broad
