The New Art and Science of Teaching Mathematics. Robert J. Marzano

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 classroom.

      Scales and rubrics are essential for tracking student progress, and tracking progress is necessary for celebrating success. The desired joint effect of the strategies associated with these three elements is that students understand the progression of knowledge they are expected to master and where they currently are along that progression. When learning goals are designed well and communicated well, students not only have clear direction, but they can take the reins of their own learning. As Robert J. Marzano (2017) articulates in The New Art and Science of Teaching, students must grasp the scaffolding of knowledge and skills they are expected to master and understand where they are in the learning, and this happens as a result of the teacher providing and communicating clear learning goals.

Element 1: Providing Scales and Rubrics

      Scales and rubrics articulate what students should know and be able to do as a result of instruction. The content in a scale or rubric should come from a school or district’s standards. As an example of how teachers might do this, we include the learning progression for mathematics from Achieve the Core (n.d.) in figure 1.1 (page 12) and in figure 1.2 (page 13) for secondary-level mathematics.

      For element 1 of the model, we address the following two specific strategies in this chapter.

      1. Clearly articulating learning goals

      2. Creating scales or rubrics for learning goals

      Source: Achieve the Core, (n.d.).

Figure 1.1: Learning progression for mathematics, grades K–8.

      Source: National Governors Association Center for Best Practices & Council of Chief State School Officers, 2013.

Figure 1.2: Learning progression for mathematics, secondary level.

       Clearly Articulating Learning Goals

      Mathematics learning goals are most effective when teachers communicate them in a way students can clearly understand; however, students must also feel as though they “own” the goals. Student ownership is the process of allowing students the freedom to choose their goals and take responsibility for measuring their progress toward meeting them. Student ownership occurs most effectively when students are able to connect to mathematics using natural, everyday language. Stephen Chappuis and Richard J. Stiggins (2002) explain that sharing learning goals in student-friendly language at the outset of a lesson is the critical first step in helping students know where they are going. They also point out that students cannot assess their own learning (see element 2, tracking student progress,