Unfinished Learning in the Spotlight
Recent conversations regarding unfinished learning in mathematics have brought topics related to intervention supports into the spotlight. This attention is long overdue. What follows is a culmination of many years focusing on this topic. My thoughts are informed by best practices in mathematics teaching and learning as well as insights gained from my experiences with my daughter and my work with students, teachers, and administrators in schools. You can learn more about how I developed first-hand knowledge related to students who struggle by reading about my family’s story at www.astrokeofluck.net. This will also clarify the genesis of my twitter handle (@thestrokeofluck). This story goes back many years – my daughter, Alex, is now 25 and works as a public-school paraprofessional in a pre-kindergarten class. I am a proud mama! I have been developing a concept of productive intervention since Alex was 12.
As we examine mathematics intervention, I think we will see that it needs to be reinvented. Imagine a scene where an interventionist is working with a small group of students in grade 4. The students are ability grouped; all having demonstrated struggle with multiplying multidigit numbers. The teacher shares the following multiplication problem and helps students to step through the process of the standard multiplication algorithm.
The teacher says to multiply the 2 by each digit in 486 and then to put down a zero as a place holder and then to multiply the 1 by every digit in 486. Students follow along and then the teacher has students practice with two more problems. The teacher provides immediate feedback if students make errors like forgetting to put down the zero while solving the problems. There is very little student talk other than to provide short answers to the teacher. Students are mostly successful following the steps, but when they encounter this in class again, not too much later, they struggle.
To recap, the intervention is highly structured and highly procedural, and is only minimally supported by student discourse and conceptual understanding. These sorts of scenarios are described in detail in Making Sense of Mathematics for Teaching the Small Group (Dixon, Brooks, & Carli, 2019) and suggestions for changing the tasks, structures, and general experiences in small group instruction are provided. What I am discussing here is more specific. The focus here is on intervention groups and can be identified with many different names. What I am talking about here is pulling small groups to support those who are significantly far behind. The argument I will attempt to make is that, with best intentions, we are trying to do too much and ultimately accomplishing too little.
The first step in transforming intervention is to embrace the idea that students who struggle in mathematics likely do so because there are foundational gaps in their conceptual understanding of prerequisite content knowledge. Those gaps widen as more content is addressed. The urge is often to “pre-teach” upcoming content so that when the learners who struggle encounter the content, they are more familiar, and ultimately more successful, in class. Returning to the fourth-grade example, we can imagine that this intervention might occur in preparation for a lesson on the same topic so that students may be more likely to experience success with the topic in class. The flaw in this plan is that the pre-teaching is often necessarily procedural because the conceptual understanding is elusive without the foundational knowledge the students lack. Confounding the issue is that many people who are tasked with providing the intervention lack access to professional development on best practices in mathematics teaching and learning.
What does this mean? It means that we are using precious instructional time with close proximity to a teacher (in a small group setting) in a manner that will likely not lead to desired outcomes. What do we do about it? We need to re-invent intervention.
The reimagining of intervention must involve a multifaceted approach. What I will share over the next several blogs are six features required for reimagining intervention. These features, when taken together, support the re-invention of intervention.
Six Features for Re-inventing Intervention
Productive intervention must:
1. Focus on conceptual development,
2. Provide a clear connection between concepts and procedures,
3. Prioritize a strategic selection of content,
4. Support discourse through engaging tasks and targeted questioning,
5. Elicit and linger on common errors, and
6. Include professional development focused on content knowledge for teaching for all interventionists.