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Wednesday / July 8

5 Tips for Increasing Clarity in the Mathematics Classroom 

Teacher clarity is hot. And it should be. After all, who wants to be the unclear teacher or the one whose students say they don’t learn from?  We’ll focus on a few things that we have found powerful to increase clarity for your mathematics students.   

1. Identify the skills and concepts in the standards you teach.  Clarity requires a deep understanding of the content that students need to learn. That content is most often expressed in standards documents.  A cursory review of the grade level standards does not ensure that lessons have significant clarity. Rather, teachers need to understand the specific skills and concepts that students must master. There are a number of ways to do this, but we find a simple way is to look at the nouns and verbs contained within the standard.  Consider the following standard from grade 6:  

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 

There are a number of concepts that students need to understand, and which are most often expressed as nouns or noun phrases. In this standard, the concepts are: measurement units and quantities.  The skills are most often expressed as verbs or verb phrases.  In this standard, the skills are: Use ratio reasoningconvertmanipulatetransformmultiplying, and dividing.  This simple analysis indicates that there are a few concepts but lots of skills within this standard. This knowledge helps teachers plan instruction, select instructional materials, and monitor students’ understanding. Importantly, it assists teachers in understanding the relationship between content knowledge and the skills needed to utilize them.  

2. Communicate learning expectations daily.  Students should know what they’re expected to learn each day. We did not say that they needed to know this at the outset of the lesson, but we do believe that they should know what they are learning at some point in the lesson.  To ensure this, teachers should communicate learning intentions to students.  Of course, students can also identify their own learning goals. But teacher clarity requires that students know what they are learning.  And we think that they should know what they are learning each day.  When the same learning intention is use over and over again, students don’t pay attention to it. In this case, novelty matters.  And the lessons should build on one another in a logical way toward mastery.  For example, using the sixthgrade standard above, one learning intention might be:  I am learning about converting volume measurements.  There may be days with other units (e.g., time or distance).  Each day contributes to students’ understanding.    

3. Understand what success looks like.  Learning intentions are important, but we don’t think that they are sufficient to ensure teacher clarity.  Students also need to know what success looks like.  In the planning of success criteria, teachers have to consider the cognitive complexity of the learning they need on a given day.  And they need to think about the need for procedural knowledge, conceptual understanding, and the ability to apply learning.  These don’t all necessarily happen in the same lesson, but they are important considerations for teacher clarity.  Consider the following success criterion for the learning intention above, again aligned with the sixth-grade standard: I can convert pints, quarts, and gallons using ratio reasoningIn addition, or as an alternative, success might be measured if students can solve mathematical problems involving ratio using double number line diagrams.  Importantly, students can use the success criteria to monitor their progress toward goals and to reflect on their learning. 

4. Align instructional approaches with the phases of learning. Teacher clarity is more than learning intentions and success criteria. It’s also the meaningful experiences students have with the content.  In the figure below, we have organized a number of common instructional routines by three phases of learning: surface, deep, and transfer.  Clarity requires that you match instructional approaches with the appropriate phase of learning.  Importantly, these phases can occur within a single lesson or across multiple lessons. Surface learning is not superficial, it’s foundational or introductory.  And there are tools teachers have to build students’ surface learning. But we can’t leave students there. When we change our instructional approaches and our tasks, we can move to deep learning, during which time students make connections, see relationships, and develop schema. Our goal is not adult-dependent learners but rather students who self-regulate and continue learning. At the transfer level, students can apply their learning in new situations. As we have noted before, it’s the right approach, at the right time, for the right kind of learning. 

5. Check for understanding frequently. We have all taught lessons that we thought were clear only to find out too late (often during a summative assessment) that the students didn’t understand or apply the information. Clarity requires that teachers check for understanding frequently so that they can adjust their lessons to ensure that students understand the content.  There are a host of ways to check for understanding, but questioning is used most frequently. We did not say that it was the most effective, but rather that it was the most common. Writing is probably a more effective way to check for understanding. When students explain their thinking in writing, the teacher gets a glimpse inside the learner’s mind. When this happens, the teacher can identify errors or misconceptions that still need to be addressed. To continue with the sixth-grade example, asking students to choose a problem set and write to explain their thinking provides the teacher with far more insight than simply knowing if it was correct or incorrect.  

Clarity is worth our time and efforts. In fact, we believe that teacher clarity is the gateway to a lot of learning. When students know what they are supposed to learn and the tasks line up with those expectations, the potential impact is increased.  And don’t we all want to increase our returns on investments.  Investing time in teacher clarity pays dividends in learning for students.    

Source: Almarode, J., Fisher, D., Assof, J., Hattie, J. & Frey, N. & (2019).  Teaching mathematics in the visible learning classroom: High school classroom companion.  Thousand Oaks, CA: Corwin. 

Written by

Douglas Fisher, Ph.D., is Professor of Educational Leadership at San Diego State University and a teacher leader at Health Sciences High & Middle College. He is the recipient of an IRA Celebrate Literacy Award, NCTE’s Farmer Award for Excellence in Writing, as well as a Christa McAuliffe Award for Excellence in Teacher Education. He is also the author of PLC+, The PLC+ Playbook, This is Balanced Literacy, The Teacher Clarity Playbook, Grades K-12, Teaching Literacy in the Visible Learning Classroom for Grades K-5 and 6-12, Visible Learning for Mathematics, Grades K-12The Teacher Credibility and Collective Efficacy Playbook and several other Corwin books.  Nancy Frey, Ph.D., is Professor of Literacy in the Department of Educational Leadership at San Diego State University. The recipient of the 2008 Early Career Achievement Award from the National Reading Conference, she is also a teacher-leader at Health Sciences High & Middle College and a credentialed special educator, reading specialist, and administrator in California. She has been a prominent Corwin author, publishing numerous books including PLC+The PLC+ PlaybookThis is Balanced LiteracyThe Teacher Clarity Playbook, Grades K-12Engagement by DesignRigorous Reading, Texas EditionThe Teacher Credibility and Collective Efficacy Playbookand many more.  To view Doug and Nancy’s books and services, please visit Fisher and Frey Professional Learning. 

Latest comment

  • Very good article. Looking forward to the Corwin Institute on Clarity at the end of July.

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