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ОглавлениеIntroduction
The New Art and Science of Teaching (Marzano, 2017) is a comprehensive model of instruction with a rather long developmental lineage. Specifically, four books spanning two decades precede and inform The New Art and Science of Teaching and its use in the field.
1. Classroom Instruction That Works: Research-Based Strategies for Increasing Student Achievement (Marzano, Pickering, & Pollock, 2001)
2. Classroom Management That Works: Research-Based Strategies for Every Teacher (Marzano, Marzano, & Pickering, 2003)
3. Classroom Assessment and Grading That Work (Marzano, 2006)
4. The Art and Science of Teaching: A Comprehensive Framework for Effective Instruction (Marzano, 2007)
The first three books address specific components of the teaching process, namely instruction, management, and assessment. The final book puts all three components together into a comprehensive model of teaching. It also makes a strong case for the fact that research (in other words, science) must certainly guide good teaching, but teachers must also develop good teaching as art. Even if they use precisely the same instructional strategies, two highly effective teachers will have shaped and adapted those strategies to adhere to their specific personalities, the subject matter they teach, and their students’ unique needs. Stated differently, we can never accurately articulate effective teaching as a set of strategies that all teachers must execute in precisely the same way.
The comprehensive model in the book The New Art and Science of Teaching (Marzano, 2017) reflects a greatly expanded and updated version of The Art and Science of Teaching (Marzano, 2007). One of the unique aspects of The New Art and Science of Teaching is that it focuses on student learning, rather than being teacher focused, as we depict in figure I.1:
Source: Marzano, 2017, p. 5.
Figure I.1: The teaching and learning progression.
According to figure I.1, the intervening variables between effectively applying an instructional strategy and enhanced student learning are specific mental states and processes in the minds of learners. If teachers do not produce these mental states and processes as a result of employing a given strategy, then that strategy will have little or no effect on students. This implies that teachers should heighten their level of awareness as they use instructional strategies for maximum efficacy.
The Overall Model
At a basic level, the model in The New Art and Science of Teaching (Marzano, 2017) is a framework that educators can use to organize the majority (if not all) of the instructional strategies that research and theory identify. The model has several parts: three overarching categories, ten design areas, and forty-three specific elements.
Three Categories
At the highest level of organization, the model has three overarching categories.
1. Feedback refers to the all-important information loop teachers must establish with students so that students know what they should be learning about specific topics and their current level of performance on these topics.
2. Content refers to the sequencing and pacing of lessons such that students move smoothly from initial understanding to applying knowledge in new and creative ways.
3. Context refers to those strategies that ensure all students meet these psychological needs: engagement, order, a sense of belonging, and high expectations.
Embedded in these three overarching categories are more specific categories of teacher actions (design areas).
Ten Design Areas
In The New Art and Science of Teaching framework, each of the ten design areas is associated with a specific teacher action, as follows.
1. Providing and communicating clear learning goals
2. Using assessments
3. Conducting direct instruction lessons
4. Conducting practicing and deepening lessons
5. Conducting knowledge application lessons
6. Using strategies that appear in all types of lessons
7. Using engagement strategies
8. Implementing rules and procedures
9. Building relationships
10. Communicating high expectations
Table I.1 shows the ten teacher actions within the three categories and describes the desired student mental states and processes for each. For example, when the teacher conducts a direct instruction lesson (the third design area), the goal is that students will understand which parts of the content are important and how they fit together.
Table I.1: Teacher Actions and Student Mental States and Processes
| Teacher Actions | Student Mental States and Processes | |
| Feedback | Providing and Communicating Clear Learning Goals | 1. Students understand the progression of knowledge they are expected to master and where they are along that progression. |
| Using Assessments | 2. Students understand how test scores and grades relate to their status on the progression of knowledge they are expected to master. | |
| Content | Conducting Direct Instruction Lessons | 3. When content is new, students understand which parts are important and how the parts fit together. |
| Conducting Practicing and Deepening Lessons | 4. After teachers present new content, students deepen their understanding and develop fluency in skills and processes. | |
| Conducting Knowledge Application Lessons | 5. After teachers present new content, students generate and defend claims through knowledge application tasks. | |
| Using Strategies That Appear in All Types of Lessons | 6. Students continually integrate new knowledge with old knowledge and revise their understanding accordingly. | |
| Context | Using Engagement Strategies | 7. Students are paying attention, energized, intrigued, and inspired. |
| Implementing Rules and Procedures | 8. Students understand and follow rules and procedures. | |
| Building Relationships | 9. Students feel welcome, accepted, and valued. | |
| Communicating High Expectations | 10. Typically reluctant students feel valued and do not hesitate to interact with the teacher or their peers. |
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. Elaborating on information22. Organizing students to interact | Using Engagement Strategies23. Noticing and reacting when students are not engaged24. Increasing response rates25. Using physical movement26. Maintaining a lively pace27. Demonstrating intensity and enthusiasm28. Presenting unusual information29. Using friendly controversy30. Using academic games31. Providing opportunities for students to talk about themselves32. Motivating and inspiring studentsImplementing Rules and Procedures33. Establishing rules and procedures34. Organizing the physical layout of the classroom35. Demonstrating withitness36. Acknowledging adherence to rules and procedures37. Acknowledging lack of adherence to rules and proceduresBuilding Relationships38. Using verbal and nonverbal behaviors that indicate affection for students39. Understanding students’ backgrounds and interests40. Displaying objectivity and controlCommunicating High Expectations41. Demonstrating value and respect for reluctant learners42. Asking in-depth questions of reluctant learners43. Probing incorrect answers with reluctant learners |
Source: Marzano, 2017, p. 8.
Although this text predominantly provides suggestions to support lesson planning around mathematics instruction, we encourage readers to explore the foundational book The New Art and Science of Teaching (Marzano, 2017). In doing so, they will likely infuse their content areas and grade levels with additional strategies.
About This Book
In chapters 1 through 10, we situate a mathematics-specific model within the broader context of The New Art and Science of Teaching framework. Part I, focused on feedback, begins with chapter 1, which describes how teachers can effectively articulate learning goals for mathematics content within scales and rubrics, create learning progressions (called proficiency scales), and use those scales to track students’ progress and celebrate their success. In chapter 2, we explain strategies for how to assess students’ current mathematics status using both informal and formal assessment.
Part II addresses content. In chapters 3, 4, 5, and 6, we articulate instructional strategies for teaching the mathematics content that students need to learn. Chapter 3 focuses on conducting direct instruction lessons, chapter 4 on conducting practicing and deepening lessons, chapter 5 on conducting knowledge application lessons, and chapter 6 on using strategies that appear in all types of lessons.
Part III, concentrated on context, reviews mathematics-related issues pertaining to student engagement (chapter 7), rules and procedures (chapter 8), building relationships (chapter 9), and communicating high expectations to all students (chapter 10).
Chapter 11 describes a four-step process for developing teachers’ expertise. In anticipation of chapter 11, each chapter contains self-rating scales for readers to assess their performance on the elements of the model. By doing this, they can determine their areas of strength and the areas in which they might want to improve relative to The New Art and Science of Teaching. All of the self-rating scales in this book have the same format for progression of development. To introduce these scales and help readers understand them, we present the general format of a self-rating scale in figure I.2.
Figure I.2: General format of the self-rating scale.
To understand this scale, it is best to start at the bottom with the Not Using row. Here, the teacher is unaware of the strategies that relate to the element or knows them but doesn’t employ them. At the Beginning level, the teacher uses strategies that relate to the element, but leaves out important parts or makes significant mistakes. At the Developing level, the teacher executes strategies important to the element without significant errors or omissions but does not monitor their effect on students. At the Applying level, the teacher not only executes strategies without significant errors or omissions but also monitors students to ensure that they are experiencing the desired effects. We consider the Applying level the level at which one can legitimately expect tangible results in students. Finally, at the Innovating level, the teacher is aware of and makes any adaptations to the strategies for students who require such an arrangement.
Each chapter also contains Guiding Questions for Curriculum Design to support planning and aid in reflection. Appendix A provides an overview of The New Art and Science of Teaching framework. Appendix B, Lesson Seed: Fluency With the Solute Game, provides details for a game to support student fluency in mathematics. Appendix C provides a list of tables and figures.
In sum, The New Art and Science of Teaching Mathematics is designed to present a mathematics-specific model of instruction within the context of The New Art and Science of Teaching framework. We address thirty-five elements from the general model within the context of mathematics instruction and provide mathematics-specific strategies and techniques that teachers can use to improve their effectiveness and elicit desired mental states and processes from their students.
