Why Differentiation Matters: Learning from Mistakes
For the first half of the year I worked almost exclusively with my first graders in small groups or one-on-one. Differentiation should have been easier in this context than it would have been if I were teaching the whole class. It was during this semester, however, that I realized just how difficult it is to differentiate instruction, even just for one student! I made my fair share of mistakes. In reflecting on these mistakes and their implications, even small, on my students’ academic growth and confidence, I have learned how and why differentiation is so important.
A Lesson that Was Too Challenging
As part of my Term II Child Study I had a number of one-on-one discussions and lessons with a student that I will call Jay. In an effort to get to know Jay as a reader, I planned to assess his level of comprehension through a read-aloud and follow-up assessment. I chose The Relatives Came by Cynthia Rylant because it had been one of my favorite books as a child. I read it to him, pausing to ask questions throughout, and then asked him to draw a picture and write a sentence showing me something that he liked about the book.
Jay had a difficult time responding to the story. As you can hear in the audio clip at right, when I asked him to draw a picture of something that he learned or something that he liked from the book, his first reaction was to say, “I don’t know how to write…I don’t wanna write this…a picture of that.”
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This is a clip from the end of the read-aloud that I did with Jay. (Artifact 3).
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When I reiterated that he could draw anything he wanted from the book, Jay said that he was going to draw the car, which was a source of much amusement as we were reading because of how poorly it was driven. But then he started to draw a set of stairs, which baffled me because it had nothing to do with the story. Later, he drew a tree, which again had nothing to do with the story. When I realized that he was having trouble coming up with something relevant, I tried to redirect him through a series of questions. He ended up just drawing a picture of the car and writing, “I like a car.”
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I walked away from this lesson feeling pretty discouraged. I knew that Jay had understood more from the story than was represented in his response. I felt like I had not set him up to succeed. After reflecting on this lesson, both on my own and with one of my professors, I realized that I could have done a lot of things differently. First, while The Relatives Came is a fantastic story, it was not the best choice for a first grader whose reading and comprehension skills are still developing. It doesn’t have a clear plot or a lot of deep character development—it is just a portrait of a quirky family that loves each other. A true understanding of this book relies on an ability to draw inferences, which is a rather difficult skill. Second, I realized that I didn’t know what exactly what I was looking for him to do--what “success” would look like on the open-ended assignment that I gave him, so I wasn’t clear with my expectations. I didn’t know what kinds of questions to pose in order to get a sense of his level of comprehension.
The biggest source of my mistake was that I violated one of Tomlinson’s key principles—I did not know Jay well enough as a reader to be able to anticipate such difficulties. I also didn’t know enough about the developmental appropriateness of certain books given the skills that they require. If I had it to do over again, I would have differentiated both the content (picked a different book with a more concrete plot) and the product (come up with a less open-ended, more structured response).
The biggest source of my mistake was that I violated one of Tomlinson’s key principles—I did not know Jay well enough as a reader to be able to anticipate such difficulties. I also didn’t know enough about the developmental appropriateness of certain books given the skills that they require. If I had it to do over again, I would have differentiated both the content (picked a different book with a more concrete plot) and the product (come up with a less open-ended, more structured response).
A Lesson that Was Too EasyOne of the small-group lessons that I taught for Term III was designed to develop students’ number sense and understanding of grouping. I started with a number talk using a dot array, which I figured be a good warm-up/introduction to the idea of grouping because I asked the students how they ‘saw’ (grouped) the dots. I held up an image and asked the students how they ‘saw’ (grouped) the dots. Unfortunately, math was not taught consistently in my classroom in the Fall. Therefore, given how little I knew about my students as mathematicians, I wanted to provide this scaffolding before jumping right into using the five-frames.
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In this clip you can see part of the number talk I did to introduce the concept of grouping (Artifact 6).
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I then modeled the use of a five-frame, telling a story about a combination of 5 boys and girls going to an ice cream store, the girls being the yellow side of the double-sided counters and the boys being the blue side. Eventually I gave them each a five frame and five double-sided counters, and each of them came up with a combination of five boys and girls that was different from the one that I had modeled. Finally, they shared their combinations by writing an equation on our chart paper.
As I planned and revised this lesson I realized that nearly all of the procedures or activities were going to be new. My students had never seen a dot array or done a number talk; they had never used a five frame or double-sided counters; they were totally unfamiliar with discourse; and they had not had much practice in writing number sentences. |
For this reason (and because I had not seen them do enough math to have a great sense of their understanding of these concepts) I decided to reduce the cognitive workload slightly from what I had originally planned. I took out the largest section of independent practice, which was a worksheet that I had developed. In the lesson that I taught we came up with multiple combinations of 5 as a group, but they each came up with only one independently. The worksheet would have asked them to generate multiple combinations of 5 independently.
In hindsight I wish that I had included the worksheet. I think that my lesson could and should have been a bit more challenging. In this case I believed that I violated two of Tomlinson’s principles: 1.) I did not know my students well enough in terms of their mathematical understanding; 2.) I was not prepared well enough to be able to be flexible and adapt to my students’ readiness. I had the worksheet prepared, but I did not bring it with me to the lesson, so I was not able to use it when I realized that my students probably could have handled it. I didn’t have a challenge ready! The worksheet (Artifact 7).
In hindsight I wish that I had included the worksheet. I think that my lesson could and should have been a bit more challenging. In this case I believed that I violated two of Tomlinson’s principles: 1.) I did not know my students well enough in terms of their mathematical understanding; 2.) I was not prepared well enough to be able to be flexible and adapt to my students’ readiness. I had the worksheet prepared, but I did not bring it with me to the lesson, so I was not able to use it when I realized that my students probably could have handled it. I didn’t have a challenge ready! The worksheet (Artifact 7).