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Intervention Lenses

by Nancy Berkas and Cyntha Pattison (NCTM News Bulletin, September 2007)

As we attempt to define intervention in relation to mathematics education, we must first establish a few fundamentals, which we will call “lenses,” to use as we discuss ideas, strategies, programs, sales pitches, and the vocabulary that surrounds efforts to serve all learners.

Serving all learners is the center of the issues, ideas, inventions, and, of course, interventions that we will address in this column. We must remember that the “one-size-fits-all” approach to education that receives such bad press these days—was the result of efforts to provide a free public school education to all students regardless of economic status. This “one-size-fits-all” public schooling has evolved into Title IX classifications and, we believe, has shifted from all to every student. We believe that if we make the switch from all to every in our thinking and planning, we will begin to understand what it means to intervene on behalf of every student, as well as to find, define, invent, and refine the interventions that address every student’s
mathematical learning experience. It is from this perspective that we will create the lenses through which we will look in all future intervention columns.

First and foremost, we believe that every student, regardless of category or educational designation, is entitled to learn significant mathematics. This is our first lens. It is the lens that determines the shape of the other lenses.

The next lens is our own deep understanding of the mathematics we teach—its form and its structure, its developmental nature, and its power. Understanding the mathematics ourselves enables us, as teachers, to adapt our pedagogy to address the goals and needs of every student. Thus it follows that the intervention we provide for every student will also address the mathematical goals set for individual students.

Knowing the mathematics and the pedagogy that will work best can positively affect our goal setting only if we know what understandings the students bring with them. We need to consider intervention through a lens that is focused on assessment and data gathering. This will help us begin to identify ideas, strategies, programs, and so on, that can be considered viable mathematical interventions for each and every student.

It follows that through our focus on the learning of significant mathematics, if we know the mathematics and its appropriate pedagogy, and if we assess and gather the data needed to set appropriate goals for every student, we must have a lens through which we identify suitable and high-quality planning and delivery of the service we are offering to every student. This service is often assumed, but it can fall into the “one-size-fits-all” category as a result of numerous limitations including legislative requirements, fiscal restraints, expediency, and so on.

We have found that perhaps our greatest successes and most serious failures in serving the needs of every student have been defined by our last lens, alignment. Alignment has a number of components including (1) chronology—intervention concepts must be timely; (2) curriculum—intervention materials need to compliment the materials used in the classroom; (3) pedagogy—strategies for intervention must be based on specific needs; and (4) standards and goals—intervention materials should reflect the nature and intent of the mathematical standards and goals set for every student. We think great diligence will be required to ensure that intervention is coordinated with each of these areas.

So we have set the structure for our remaining columns by establishing our lenses. We will explore technology, manipulatives, programs, differentiation, supplemental programs, and special education by using the following lenses:

  • Learning Significant Mathematics—What guarantees the learning of every student? What provides the mathematical power that every student should expect?
  • Knowing the Mathematics—How do we know that the providers know the mathematics and the appropriate pedagogy that ensures understanding is developed by every student?
  • Assessment and Data Gathering—How do we know the understanding that every student brings to the situation? What information determines the goal setting?
  • Quality Planning and Delivery—Is the planning and delivery transparent? Are they flexible enough to address the needs of every student?
  • Alignment—What structures are in place to align the services chronologically? How is curricular alignment ensured? How have pedagogical strategies been addressed and aligned with content and needs? How are appropriate standards and goals aligned with the delivery of services for every student?

In the next seven columns, we will explore intervention(s) and the ways in which mathematics teachers, leaders, and materials providers are approaching the concept. Please contact us at or with comments or questions.

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