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

correctly in three minutes, the winner of math drills, or how well students perform on a standardized test. While there may be benefits to these types of celebrations, they are not as conducive to reliable measurement as progress on a proficiency scale, which allows the teacher to celebrate knowledge gain—the difference between a student’s initial and final scores for a learning goal. To celebrate knowledge gain, the teacher recognizes the growth each student has made over the course of a unit. Mathematics teachers can also use the strategies of status celebration (celebrating students’ status at any point in time) and verbal feedback (emphasizing achievement and growth by verbally explaining what a student has done well) throughout the unit.

      Figure 1.14 presents the self-rating scale for element 3, celebrating success.

Figure 1.14: Self-rating scale for element 3—Celebrating success.

      GUIDING QUESTIONS FOR CURRICULUM DESIGN

      When teachers engage in curriculum design, they consider this overarching question for communicating clear goals and objectives: 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? Consider the following questions aligned to the elements in this chapter to guide your planning.

      • Element 1: How will I design scales and rubrics?

      • Element 2: How will I track student progress?

      • Element 3: How will I celebrate success?

Summary

      Providing and communicating clear learning goals involves three elements: (1) providing scales and rubrics, (2) tracking student progress, and (3) celebrating success. In the mathematics classroom, how teachers state these learning goals can make the difference between students reaching proficiency or not. They can support students in thinking in complex ways about mathematics, but only if they are communicated in a way that students understand and that inspires them to solve problems. Tracking student progress and celebrating success is not only important in the classroom but crucial in mathematics, as students are continually pursuing perseverance in problem solving and need support and affirmation to help them along the way.

      CHAPTER 2

      Using Assessments

      The second design area from The New Art and Science of Teaching framework involves the use of effective assessments. Some mathematics teachers use assessments only as evaluation tools to quantify students’ current status relative to specific knowledge and skills. While this is certainly a legitimate use of assessments, the primary purpose should be to provide students with feedback they can use to improve. When mathematics teachers use assessments to their full capacity, students understand how their test scores and grades relate to their status on specific progressions of knowledge and skills teachers expect them to master.

      Element 4, using informal assessments of the whole class, and element 5, using formal assessments of individual students, together allow teachers to monitor student progress, provide useful feedback, and ensure that all students are moving toward mastery of the content. Here, we describe how these elements might manifest in a mathematics classroom.

Element 4: Using Informal Assessments of the Whole Class

      In the mathematics classroom, teachers create and use informal formative assessments to monitor student progress in order to differentiate instruction, reteach concepts and skills, address misconceptions, and to provide meaningful feedback. In this section, we describe the use of three specific strategies for informal assessment of the whole class in the mathematics classroom.

      1. Virtual exit slips

      2. Guided reciprocal peer questioning

      3. Respond, summarize, question, connect, and comment (RSQC2)

      Teachers can use these tools as response strategies for students when students are to address a question or prompt and for the strategy of unrecorded assessment, in which teachers use the assessment for feedback but not to score students.

       Virtual Exit Slips

      Exit slips are student responses to questions teachers pose at the conclusion of an instructional activity in which students reflect on the learning. Exit slips are an effective way to quickly assess students’ level of understanding and set up for the next learning opportunity. Marzano (2012) articulates at least four ways teachers can use exit slips, each having a different intended outcome.

       1. To rate students’ current understanding of new learning

      2. To analyze and reflect on students’ efforts around the learning

      3. To provide feedback to teachers on a respective strategy

      4. To provide feedback about the instruction and instructional resources

      Virtual exit slips—those that use technology—can transform the way formative assessments take place in the mathematics classroom. Virtual exit slips provide the teacher with a more effective way of assessing student learning, because the feedback is immediate, interactive, and can be more efficiently tracked and saved. As with traditional exit slips, with virtual exit slips, teachers pose a question or prompt at the conclusion of a learning block or lesson, and students have the opportunity to respond. The difference is that rather than using paper and pencil, students respond through a variety of virtual tools, such as WeVideo, Flipgrid, Adobe Spark, and Canva, to name a few.

      • WeVideo (www.wevideo.com): A creativity platform that allows students to create videos to deepen learning experiences

      • Flipgrid (https://flipgrid.com): An online tool for sharing and discussion that facilitates students recording videos and replying to one another

      • Adobe Spark (https://spark.adobe.com): An online platform that allows students to create beautiful presentations

      • Canva (www.canva.com): An online tool that makes it possible to design anything and publish anywhere with thousands of customizable templates.

      With these tools, students are able to reflect on mathematical thinking, create visual representations of mathematics concepts, or create mathematics videos. Students then post their responses through a district-approved and Children’s Online Privacy Protection Act (COPPA)-compliant platform with teacher guidance, such as on the class learning management system (LMS), or share their responses via district-approved social media outlets (such as Twitter, Facebook, Instagram, and so on). Virtual exit slips using tools such as those listed tap into student creativity. Students are intrinsically motivated to respond because they have choices (responding digitally in a medium they prefer) in the visual and text creation and they feel pride in sharing their creations online.

      Virtual exit slips also allow mathematics teachers to provide input and feedback quickly to individual students (because cloud-based feedback tools allow for real-time, synchronous feedback), and teachers can then appropriately adjust instruction, properly scaffolding and sequencing the next day’s content in meaningful