on information22. Organizing students to interactSource: 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.
PART I
Feedback
CHAPTER 1
Providing and Communicating Clear Learning Goals
The New Art and Science of Teaching framework begins by addressing how teachers will communicate with students about what they need to learn. It addresses the teacher question, How will I communicate clear learning goals that help students understand the progression of knowledge in mathematics they are expected to master and where they are along that progression?
This design area includes three elements related to tracking students’ progress and celebrating their success. Together, these three elements—(1) providing scales and rubrics, (2) tracking student progress, and (3) celebrating success—create a foundation for effective feedback. In this chapter, we describe specific strategies for implementing these elements in a mathematics
