they are expected to master.
Each of the ten design areas corresponds with a design question. These questions help teachers plan units and lessons within those units. Table I.2 shows the design questions that correspond with each design area.
Table I.2: Design Questions
| Design Areas | Design Questions | |
| Feedback | 1. Providing and Communicating Clear Learning Goals | How will I communicate clear learning goals that help students understand the progression of knowledge they are expected to master and where they are along that progression? |
| 2. Using Assessments | How will I design and administer assessments that help students understand how their test scores and grades are related to their status on the progression of knowledge they are expected to master? | |
| Content | 3. Conducting Direct Instruction Lessons | When content is new, how will I design and deliver direct instruction lessons that help students understand which parts are important and how the parts fit together? |
| 4. Conducting Practicing and Deepening Lessons | After presenting content, how will I design and deliver lessons that help students deepen their understanding and develop fluency in skills and processes? | |
| 5. Conducting Knowledge Application Lessons | After presenting content, how will I design and deliver lessons that help students generate and defend claims through knowledge application? | |
| 6. Using Strategies That Appear in All Types of Lessons | Throughout all types of lessons, what strategies will I use to help students continually integrate new knowledge with old knowledge and revise their understanding accordingly? | |
| Context | 7. Using Engagement Strategies | What engagement strategies will I use to help students pay attention, be energized, be intrigued, and be inspired? |
| 8. Implementing Rules and Procedures | What strategies will I use to help students understand and follow rules and procedures? | |
| 9. Building Relationships | What strategies will I use to help students feel welcome, accepted, and valued? | |
| 10. Communicating High Expectations | What strategies will I use to help typically reluctant students feel valued and comfortable interacting with their peers and me? |
Source: Marzano, 2017, pp. 6–7.
Within the ten categories of teacher actions, we have organized sets of strategies in even more fine-grained categories, called elements. As teachers think about each design question, they can then consider specific elements within the design area.
Forty-Three Elements
The forty-three elements provide detailed guidance about the nature and purpose of a category of strategies. Table I.3 depicts the elements that correspond to each design area. For example, the design area of providing and communicating clear learning goals involves three elements.
1. Providing scales and rubrics (element 1)
2. Tracking student progress (element 2)
3. Celebrating success (element 3)
As a teacher considers how to provide and communicate clear learning goals that help students understand the progression of knowledge he or she expects them to master and where they are along that progression (design question 1), the teacher might think more specifically about providing scales and rubrics, tracking student progress, and celebrating success. These are the elements within the first design area.
Finally, these forty-three elements encompass hundreds of specific instructional strategies, some of which we explore in this book in relation to the mathematics classroom. Table I.3 lists the forty-three separate elements in the New Art and Science of Teaching framework beneath their respective design areas.
The Need for Subject-Specific Models
General frameworks like The New Art and Science of Teaching certainly have their place in a teacher’s understanding of effective instruction. However, a content-specific model of instruction can be a useful supplement to the more general framework in The New Art and Science of Teaching. The content-specific model should fit within the context of the general framework, but it should be based on content-specific research and should take into account the unique challenges of teaching a particular content area. For mathematics, such a content-specific model should address important aspects of mathematics and mathematics instruction, such as higher cognitive thinking, reasoning, and problem solving, and address the important concept areas of number sense, operations, measurement and data, and algebraic thinking. A content-specific model for mathematics should address these aspects in depth and relate back to the general framework of instruction. We designed this book to provide just such a model. Specifically, in the following chapters, we address the three overarching categories—(1) feedback, (2) content, and (3) context—with their corresponding ten categories of instruction and the embedded forty-three elements that feature specific strategies expressly for mathematics.
Table I.3: Elements Within the Ten Design Areas
| Feedback | Content | Context |
| Providing and Communicating Clear Learning Goals1. Providing scales and rubrics2. Tracking student progress3. Celebrating successUsing Assessments4. Using informal assessments of the whole class5. Using formal assessments of individual students | Conducting Direct Instruction Lessons6. Chunking content7. Processing content8. Recording and representing contentConducting Practicing and Deepening Lessons9. Using structured practice sessions10. Examining similarities and differences11. Examining errors in reasoningConducting Knowledge Application Lessons12. Engaging students in cognitively complex tasks13. Providing resources and guidance14. Generating and defending claimsUsing Strategies That Appear in All Types of Lessons15. Previewing strategies16. Highlighting critical information17. Reviewing content18. Revising knowledge19. Reflecting on learning20. Assigning purposeful homework21.
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