formative assessment as a research-affirmed process for student and adult learning serves as a catalyst for successful CCSS mathematics content implementation. In the series, we establish the pursuit of assessment as a process of formative feedback and learning for the students and the adults as a highly effective practice to pursue (see chapter 4 in Kanold, Larson, Fennell, Adams, Dixon, Kobett, & Wray, 2012a, 2012b).
In this handbook, our Mathematics at Work team provides tools for how to achieve that collaborative pursuit: how to engage in ten high-leverage team actions (HLTAs) steeped in a commitment to a vision for mathematics instruction and assessment that will result in greater student learning than ever before.
A Cycle for Analysis and Learning: The Instructional Unit
The mathematics unit or chapter of content creates a natural cycle of manageable time for a teacher’s and team’s work throughout the year. What is a unit? For the purposes of your work in this handbook, we define a unit as a chunk of mathematics content. It might be a chapter from your textbook or other materials for the course, a part of a chapter or set of materials, or a combination of various short chapters or content materials. A unit generally lasts no less than two to three weeks and no more than four to five weeks.
As DuFour, Eaker, and DuFour (2008), the architects of the PLC at Work process, advise, there are four critical questions every collaborative team in a PLC at Work culture asks and answers on a 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)
The unit or chapter of content, then, becomes a natural cycle of time that is not too small (such as one week) and not too big (such as nine weeks) for meaningful analysis, reflection, and action by you and your teacher team throughout the year as you seek to answer the four critical questions of a PLC. A unit should be analyzed based on content standard clusters—that is, three to five essential standards (or sometimes a cluster of standards) for the unit. Thus, a teacher team, an administrative team, or a district office team does this type of analysis about eight to ten times per year.
This Mathematics at Work handbook consists of three chapters that fit the natural rhythm of your ongoing work as a teacher of mathematics and as part of a teacher team. The chapters bring a focus to ten high-leverage team actions (HLTAs) your team takes before, during, and in the immediate aftermath of a unit of instruction as you respond to the four critical questions of a PLC throughout the year, as highlighted in the previous feature box. Figure I.1 (page 4) lists the ten high-leverage team actions within their time frame in relation to the unit of instruction (before, during, or after) and then links the actions to the critical questions of a PLC that they address.
Figure I.1: High-leverage team actions aligned to the four critical questions of a PLC.
Visit go.solution-tree.com/mathematicsatwork to download a reproducible version of this figure.
Before the 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
