An Administrator’s Six Spheres of Influence in Mathematics Teaching and Learning: Part 2


In my last blog post, I asked about what you expect to see and hear when you walk through mathematics classrooms. Included were questions about requirements regarding what many leaders expect teachers to include on their classroom walls—such as the lesson essential question or learning objective.

In an effort to support you in being effective instructional leaders in your schools or districts, I shared what I have come to understand to be your Six Spheres of Influence in mathematics teaching and learning.

Your Six Spheres of Influence:

  • The lens through which you observe teachers
  • Your expectations regarding the posting of lesson objectives
  • Your requirements related to lesson structures
  • The ways you hold teachers accountable to provide feedback to students
  • The structures you have in place for intervention
  • How you support teacher planning

In my last contribution, I described the first sphere. Here I will share my views on the second. I will make sense of the remaining spheres over the next several weeks leading up to the 2018 Model Schools Conference. My session on June 25 will provide a window into schools and classrooms where these spheres are operating in ways that increase student achievement in mathematics.

Your Expectations Regarding the Posting of Lesson Objectives

The push for posting the lesson essential question or learning objective at the start of the lesson has been strong since Dylan Wiliam shared the importance of students knowing what they are to learn before they learn it. This just makes sense—until it doesn’t.

It truly depends on the goal of instruction. If it’s for students to learn a procedure like long division, then we should encourage teachers to share that learning goal so students will know how to attend during instruction. However, this makes less sense if a teacher’s goal is to facilitate students in “discovering” a concept. If the learning goal is inquiry-based, posting the intended outcome could undermine the inquiry process.

Consider the topic of finding the area of a rectangle. A conceptual idea within that topic is for students to understand that finding area is not limited to counting the square units that cover a rectangle, but they can also determine area by multiplying the side lengths of that same rectangle. In this case stating the essential question, “How can I use multiplication to find area?” is counterproductive. It’s more productive for students to count squares and then see that they are counting rows of the same number of squares, and finally realizing that if they know the number of squares in one row and they know the number of rows, they can multiply to find the area. When students are led to this discovery, what they learn is likely to have more traction. Topics that allow for this level of guided discovery should not be introduced with the outcome of the discovery.

The important message here is that the learning goal should influence the required structures in teaching. If the goal of the lesson is procedural in nature, then posting the essential question or learning objective is not only acceptable; it is warranted. However, if the learning goal is conceptual in nature or based in inquiry, then adhering to the rule that the objective must be posted at the start of the lesson could limit student engagement and, ultimately, student achievement.

If students already know what it is they are to discover, they are less likely to benefit from the inquiry process. I encourage you to use your influence to support teachers in making informed instructional decisions regarding how to introduce the lesson and what to post on the walls that are truly driven by learning goals. While we can all agree that we want students to be able to answer the essential question by the end of the lesson, how and when that question is revealed could have great impact on students’ experiences with the mathematics content.

Check back soon for the next installment of the Six Spheres of Influence to learn how your requirements related to lesson structures might influence mathematics teaching and learning.

The views expressed in this article are those of the author and do not necessarily represent those of HMH.


Join me and my fellow ICLE thought leaders at the 26th Annual Model Schools Conference, June 24–27 in Orlando. Each year, over 5,000 participants are inspired by innovative strategies for strengthening their teaching and leadership practices, and take away an action plan for positive change.

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