Tuesday / June 25

Four Steps for Increasing Teacher Clarity in Math

Teachers encounter many challenging responsibilities in their role: Learn and understand your state or provincial standards. Create a classroom that encourages reasoning and sense making. Teach each and every study in an equitable learning environment. Sift through the many different research based methodologies to learn how to improve your practice. It can be overwhelming!

However, a quick review of these responsibilities shows that they share a few commonalities. What are some of the key items that will have a great impact on your students? The four steps that follow will help you improve your practice by providing more clarity in your overall mission as a teacher:

  1. Setting goals.

Ainsworth’s Teacher Clarity starts with defining learning intentions. For example, NCTM’s Principles to Action: Ensuring Mathematical Success for All lists eight Effective Teaching Practices, the first of which is establishing mathematical goals to focus student learning. Both of these examples point to the importance of knowing the mathematical goals (for both the teacher and the students) for learning. As a teacher, this means understanding your standards and course of study. For students, it means more than reading a set of “students will be able to” statements for each class. The goals tell us what the big concepts are and what we expect students to understand.

  1. Understand the learning trajectory of your goals.

Mathematical learning is not about acquiring a set of discrete skills that have no connections. Instead, there is a progression through your mathematical goals, a building of sophistication through different strategies, reasoning, and learning experiences (Clements and Sarama, 2009). Good starting points for learning about learning trajectories include NCTM’s Curriculum Focal Points (for grade K-8) and many state and provincial standards (including the Common Core State Standards). First, you can look at a single standard, such as counting objects or citing a passage to support analysis of a text, and then look at multiple related standards to create a unit of study. All of your goals lead to this progression and the teaching strategies you will use.

  1. Set success criteria.

You need to be clear exactly what it is you want students to know and to be able to do (Fendick, 1990). Your assessments are the first thing you should be thinking about after you know your learning intentions. Then, you should be asking yourself, “How will I know my students have learned what they need to know? How can they show me?” This may be using problem based assessments, your state tests, classroom formative assessments, or anything that makes clear to the students what they need to know and why they need to know it. In other words, the success criteria are inextricably linked to your goals and the trajectories – it is the final step in the students’ learning process.

  1. Facilitate productive mathematical discourse.

Students need to struggle with mathematics and to share their thinking about mathematical problems with others. Smith and Stein, in 5 Practices for Orchestrating Mathematical Discourse, share the importance of selecting tasks that have a low threshold and a high ceiling so that all students are engaged and so that all students have access to the same material. The tasks you choose then lead to discussions among the entire class, and should also allow students to connect different solution paths and representations. When you have chosen your task for a lesson, you need to plan for what you think students will do so you have questions ready to understand where your students are and to move them forward when they are stuck (notice, this does not mean things you tell the students to get them unstuck!). The definition of a task is not limited to a mathematics problem. A task may vary from investigating a science principle, analyzing the meaning of words in different contexts, or comparing different economic theories.

These four steps can help you improve your students’ learning because improving your teaching clarity means you are focusing your teaching. (Killian, 2017)


(2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. National Council of Teachers of Mathematics.

(2014). Principles to action: Ensuring mathematical success for all. National Council of Teachers of Mathematics.

Clements, D. and J. Sarama. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.

Fendick, F. (1990). The correlation between teacher clarity of communication and student achievement gain: A meta-analysis. Unpublished doctoral dissertation. University of Florida, Gainesville.

Smith, M. and M. K. Stein. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. National Council of Teachers of Mathematics.

Written by

Frederick L. Dillon is a mathematics specialist and coach for the Institute for Learning at the University of Pittsburgh. For the Strongsville City Schools, Fred was a classroom teacher for middle and high school and was the mathematics department chair at the high school. Fred has, also, been planning and facilitating professional development for Ideastream, part of Cleveland’s PBS educational outreach program. Fred is a past member of the Board of Directors for the National Council of Teachers of Mathematics, and is a former officer for both the Ohio Council of Teachers of Mathematics and the Greater Cleveland Council of Teachers of Mathematics.  Among Fred’s recognitions are Presidential Award for Excellence in Science and Mathematics Teaching, the American Star of Teaching, the Tandy Award, and the Christofferson-Fawcett Award for lifetime contribution to mathematics education. He also received the Most Influential Educator Award from Strongsville High School students seven times. Fred is also the co-author of NCTM’s Principles to Actions: Ensuring Mathematical Success for AllTaking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12 and Discovering Lessons for the Common Core State Standards in Grades 9-12.

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