An Administrator’s Six Spheres of Influence in Mathematics Teaching and Learning: Part 5

Structures For Intervention 2 Gradient4

As an administrator and instructional leader in your school or district, you are well positioned to positively impact teaching and learning in mathematics. The ways in which you empower educators to engage in best practices in mathematics teaching are reflected in your Six Spheres of Influence.

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 this fifth post focused on unpacking the spheres, I will share my views on intervention. In particular, I will discuss intervention in the form of small-group math instruction.

The Structures You Have in Place for Intervention

When you think about small group instruction that you have observed in the past, what comes to mind? Typically, the vision is of a teacher sitting at a kidney-shaped table with four students all facing him or her. The students are usually grouped by ability; in fact, they are often a group of students who did not understand the whole group lesson. The teacher may model the solution to a problem or ask students to compute something. The teacher then begins questioning students one at a time with low-level questions. There is very little student-to-student interaction.

Now, think about best practices in mathematics teaching. Are they evident in what I just described? They are not. So, if you are requiring teachers to use small group instruction on a regular basis and it looks like what I described, your sphere of influence related to intervention is likely not leading to increases in student achievement. Worse, this structure may promote an issue of access and equity.

Here are some suggestions for you to share with teachers in an effort to make intervention through the use of small group instruction more productive and equitable. When the learning goal for small group instruction is conceptual, students should be grouped moderately heterogeneously—not with outliers in one group but some differences across learners to enhance the discourse. When small group instruction is used as a form of intervention, there should still be moderate differences in learners. If the group is homogeneous the discourse in that group may be limited. We know that discourse supports building understanding for students, especially when they talk together in their group. If the discourse is limited, students may not be able to develop a conceptual understanding of mathematics. This is not as crucial when the learning goal is procedural.

Tasks should be worthwhile, and the questions that support them should engage students in reasoning. Teachers need to use the time in small group instruction to collect evidence of what students know as well as their gaps in understanding. What I describe here is applying the TQE Process to the small group. The TQE Process is the topic of my next blog so I won’t go into more detail about that here, other than to say that TQE refers to tasks, questions, and evidence.

For now, let’s wrap up our focus on intervention. As an administrator, it is within your sphere of influence to impact how intervention is provided. If intervention is delivered during small group instruction, take a close look at what that looks like in your classrooms, schools, and district. If you want to explore the topic of small group instruction in mathematics more deeply according to what I discussed here, you might find the book Making Sense of Mathematics for Teaching the Small Group that my colleagues Lisa Brooks, Melissa Carli, and I just wrote valuable.

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


Dr. Juli K. Dixon is an author of Into Math. Learn more about the HMH program for K-8 students here.

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