Beyond the Common Core. Juli K. Dixon

= 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 mathematical concepts and understandings for the entire unit as essential learning standards. For more specific lesson-by-lesson daily outcomes, we use daily learning objectives or essential questions. We use the terms learning goals or learning targets to reference the outcome for student proficiency in each standard. The daily learning objectives and the tasks and activities representing those objectives help students understand the essential learning standards for the unit in order to demonstrate proficiency (outcomes) on these standards. The daily learning objectives articulate for students what they are to learn that day and at the same time provide insight for teachers on how to assess students on the essential learning standards at the end of the unit.

      A unit of instruction connects topics in mathematics that are naturally grouped together—the essential ideas or content standard clusters. Each unit should consist of about four to six essential learning standards taught to every student in the course. These essential learning standards may consist of several daily learning objectives, sometimes described as the essential questions that support your daily lessons. The context of the lesson is the driving force for the entire lesson-design process. Each lesson context centers on clarity of the mathematical content and the processes for student learning.

      The crux of any successful mathematics lesson rests on your collaborative team identifying and determining the daily learning objectives that align with the essential learning standards for the unit. Although you might develop daily learning objectives for each lesson as part of curriculum writing or review, your collaborative team should take time during lesson-design discussions to make sense of the essential learning standards for the unit and to consider how they are connected. This involves unpacking the mathematics content as well as the Mathematical Practices or processes each student will engage in as he or she learns the mathematics of the unit. Unpacking, in this case, means making sense of the mathematics listed in the standard, making sense of how the content connects to content learned in other grades as well as within the grade, and making sense of how students might develop both conceptual understanding and procedural skill with the mathematics listed in the standard.

The How

      As you and your collaborative team unpack the mathematics content standards (the essential learning standards) for the unit, it is also important to decide which Standards for Mathematical Practice (or process) will receive focused development throughout the unit of instruction.

       Unpacking a Learning Standard

      How can your team explore the general unpacking of content and linking the content to student Mathematical Practices for any unit? Consider the third-grade mathematics content standard cluster Understand properties of multiplication and the relationship between multiplication and division in the domain Operations and Algebraic Thinking (3.OA). This content standard cluster consists of two standards: “Apply properties of operations as strategies to multiply and divide” and “Understand division as an unknown-factor problem” (NGA & CCSSO, 2010, p. 23). For the purpose of this discussion, focus your understanding on how to apply strategies based on properties of operations to multiply. See also the CCSS website (www.corestandards.org) to explore the Mathematical Practices and standards.

      You can use the discussion questions from figure 1.2 to discuss an appropriate learning process you and your collaborative team could create for applying strategies to multiply.

       Figure 1.2: Sample essential learning standard discussion tool.

      Visit go.solution-tree.com/mathematicsatwork to download a reproducible version of this figure.

      Think about how you would expect students to demonstrate their understanding of both the standard of using properties correctly and Mathematical Practice 7, “Look for and make use of structure.”

      Share your property-based strategies to find 6 × 7 with your team members, and discuss which properties you used to find the product. For example, you may have created a web to illustrate the properties you used (such as figure 1.3, page 12). Once your team brainstorms various strategies, focus your team discussion on the connection between the strategies and properties of operations.

       Figure 1.3: Strategies for finding 6 × 7.

      Your collaborative team’s conversation