Beyond the Common Core. Juli K. Dixon
Unit
In chapter 1, we provide insight into the work of your collaborative team before the unit begins, along with the tools you will need in this phase. Your collaborative team expectation should be (as best you can) to complete this teaching and assessing work in preparation for the unit.
There are five before-the-unit high-leverage team actions for collaborative team agreement on a unit-by-unit basis.
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
Once your team has taken these action steps, the mathematics unit begins.
During the Unit
In chapter 2, we provide the tools for and insight into the formative assessment work of your collaborative team during the unit. This chapter teaches deeper understanding of content, discussing Mathematical Practices and processes and using higher-level-cognitive-demand mathematical tasks effectively. It helps your team with daily lesson design and study ideas as ongoing in-class student assessment becomes part of a teacher-led formative process.
This chapter introduces three during-the-unit high-leverage team actions your team works through on a unit-by-unit basis.
HLTA 6. Using higher-level-cognitive-demand mathematical tasks effectively
HLTA 7. Using in-class formative assessment processes effectively
HLTA 8. Using a lesson-design process for lesson planning and collective team inquiry
The end of each unit results in some type of student assessment. You pass back the assessments scored and with feedback. Then what? What are students to do? What are you to do?
After the Unit
In chapter 3, we provide tools for and insight into the formative work your collaborative team does after the unit is over. After students have taken the common assessment, they are expected to reflect on the results of their work and use the common unit assessment instrument for formative feedback purposes.
In addition, there is another primary formative purpose to using a common end-of-unit assessment, which Hattie (2012) describes in Visible Learning for Teachers: “This [teachers collaborating] is not critical reflection, but critical reflection in light of evidence about their teaching” (p. 19, emphasis added).
From a practical point of view, an end-of-unit analysis of the common assessment focuses your team’s next steps for teaching and assessing for the next unit. Thus, there are two end-of-unit high-leverage team actions your team works through on a unit-by-unit basis.
HLTA 9. Ensuring evidence-based student goal setting and action for the next unit of study
HLTA 10. Ensuring evidence-based adult goal setting and action for the next unit of study
In Principles to Actions: Ensuring Mathematical Success for All, NCTM (2014) presents a modern-day view of professional development for mathematics teachers: building the knowledge capacity of every teacher. More importantly, however, you and your colleagues can intentionally act 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