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

there must be teacher and student action on the information. For example, the teacher must review answers, sort the results into groups (got it, almost got it, not yet), and then give each group a specific problem to begin the lesson the next day.

      Figure 2.1 provides some prompts and sample responses from virtual exit slips in the mathematics classroom that teachers can administer virtually using Google Docs or other technology.

       Guided Reciprocal Peer Questioning

      Formative assessments should not only provide teachers with quick and ongoing checks for understanding but should also provide students with opportunities to learn while being assessed. During guided reciprocal peer questioning, students build inquiry skills while they go through the process of constructing questions. At the same time, they also develop metacognition skills through reflection. Teachers can provide scaffolding for this strategy by first issuing question prompts for students to choose from and then eventually asking students to create their own prompts. To aid in question generation, it’s useful to refer to the learning protocol of building probing questions. Former economist and educator Charlotte Danielson (2011) developed a framework for teaching that includes five mediational questions that teachers can use for guided reciprocal peer questioning.

      Source: Kanold, Larson, Fennell, Adams, Dixon, Kobett, & Wray, 2012.

Figure 2.1: Prompts and sample responses using virtual exit slips.

      1. Why do you think this is the case?

      2. What would you have to change in order for …?

      3. What do you assume to be true about …?

      4. How did you conclude …?

      5. How did your assumptions about _____________ influence how you thought about …?

      For guided reciprocal peer questioning, teachers provide prompts during small-group collaborative learning and the appropriate amount of time (ten to fifteen minutes) to conduct the assessment. As students are discussing the prompts, the teacher circulates and records observations. Another key component of this strategy is capturing student reflection and thinking. Students can answer using voice recording, collaborative digital documents, notecards, and so on.

       Respond, Summarize, Question, Connect, and Comment

      RSQC2 is another formative assessment strategy that builds student thinking and learning while also providing teachers with evidence to check for learning. This protocol is unique in that it is structured to emulate the levels of Bloom’s taxonomy (remember, understand, apply, analyze, evaluate, and create; Bloom, 1956). Additionally, the strategy to assess student knowledge is more effective because it not only focuses on connecting new concepts but also on building on previously learned concepts. It drives learning and captures progress. Following are the five steps for RSQC2.

      1. Recall: Students make a list of what they recall as most important from a previous learning.

      2. Summarize: Students summarize the essence of previous learning.

      3. Question: Students ask one or two questions that still remain unanswered or that they are unclear about.

      4. Connect: Students briefly explain the essential points and how they relate to their overall mathematics learning goals.

      5. Comment: Students evaluate and share feedback about the previous learning.

      Figure 2.2 shows a sample of potential responses from a student engaging with this protocol.

Figure 2.2: RSQC2 informal assessment responses.

      This strategy is well suited for virtual use in the mathematics classroom. Virtual collaboration allows for synchronous recording of thoughts and feedback from the teacher. Students can use a collaborative, shared document, such as OneNote Online or Google Docs, that the teacher and students have access to. Teachers can also encourage students to use social media tools, such as Twitter, Instagram, Edmodo, Google Classroom, and so on, to express their thinking. This is a motivational strategy, as most students enjoy expressing their thoughts on social media. Although formative-assessment data should be kept private, teachers should encourage students to reflect on their thinking and refine it. Sharing thoughts publically can encourage others to rethink how to approach and solve problems.

      Figure 2.3 presents the self-rating scale for element 4, using informal assessments of the whole class, so teachers can gauge their professional performance.

Figure 2.3: Self-rating scale for element 4—Using informal assessments of the whole class.

      Element 5: Using Formal Assessments of Individual Students

      Mathematics teachers create and utilize formal assessments to reliably record student learning data, provide feedback on student work, and create dynamic portfolios of student progress and growth. Formal assessments via performance tasks and portfolios inform teaching and learning while using strategies that take a comprehensive snapshot of where a student is in his or her learning.

      For this element, we examine two formal assessment tools for teachers to use in the mathematics classroom for individual student assessment. These tools fit within the The New Art and Science of Teaching framework strategies for element 5 for student demonstrations (students generate presentations that demonstrate their understanding of a topic, usually with skills, strategies, or processes) and student generated assessment (where students devise ways they will demonstrate competence on a particular topic at a particular level of proficiency).

      1. Performance tasks: A performance task is an assessment that prompts students to research and analyze information, weigh evidence, and solve meaningful problems, allowing them to demonstrate their new learning. These can be used as common formative assessments, exit tickets, or as a problem to further develop a concept.

      2. Learning portfolios: A learning portfolio is a dynamic assessment that allows students to demonstrate their learning. Learning portfolios can be traditional or digital, taking the form of a website, blog, or video documentary, just to name a few.

       Performance Tasks