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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 ways.

For the exit slip to be formative, 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