A Third Structure: Spiraling-Scaffolded Tasks

With open-ended problem-solving tasks that students could access at a variety of levels and tiered-tasks that provided students appropriate practice with basic skills, it certainly seemed as though I had the issue of differentiation under control.

There was only one major hitch. I still had not found a structure well-suited to the differentiation of direct instruction in mathematical algorithms. Some children may be able to develop an efficient strategy for adding multi-digit numbers simply by tackling a sheet of story problems, but the vast majority of children benefit from teacher instruction which involves the modeling and explanation of traditional algorithms accompanied by guided practice. It was the question of how to organize direct instruction that had me stymied.

At first I thought that tiered instruction would work for direct instruction as well as independent practice tasks; I would simply teach two lessons to two groups. Unfortunately, that proved to be more complicated than I anticipated. When I taught a straight first grade I would teach a lesson on multi-digit addition to the whole group, modeling the traditional algorithm of combining “ones” and combining “tens.” Then I would sent everyone off with a set of practice problems. I would circulate about the room, providing extra support to those who needed it. When I began to teach the multi-age group, I assumed that I could use this same framework, simply running two different groups. So I tried to instruct first graders while the second graders practiced, and to instruct the second graders while the first graders practiced. It seemed so straight-forward!

Unfortunately, I had not accounted for those students that needed extra support– the ones that in a straight-graded class were getting extra help when I circulated around. Now, while I was trying to teach the second graders I was also trying to manage first graders who weren’t able to complete their work independently. Travis was constantly interrupting the group I was trying to teach. If I took a minute to try and help him, the group of students sitting around me would chit-chat and lose focus. If I tried to shoo him back to his work or ignore him, his behavior inevitably fell apart. He would be scribbling on his neighbor’s paper, starting an argument, or dancing around to make others giggle. Soon, I was punishing him, but I knew that this wasn’t fair. He needed help, and I wasn’t offering it. I felt that I was cheating him out of the support that he deserved. Sarah, too, was struggling. While she was not causing disruptions, she was quietly sitting in her seat doing nothing. Knowing that some of these children needed help, I tried to have stronger students help those who were struggling. Travis’s comedy routine only became more elaborate. Not only were Travis and Sarah getting nothing done, but now I was distracted, the group I was teaching was distracted, and the helpers were distracted. When I compared the experience that students had in my straight-graded classroom with the experience that students were having in my multi-age classroom, I knew that it was not on par. Struggling students in the straight-graded class had been receiving a much higher level of support. Something else had to be done.

Since assigning independent practice was proving unmanageable, and even unfair, I decided that the practice simply had to become part of the lesson. My lesson time with each group became longer, and the work I expected students to complete independently was no longer lesson practice, but easier work that students could handle alone. This system was more manageable--Travis’s behavior improved--but it still did not seem right. I felt now I had not only dropped the level of support that I was offering to struggling students, but that I was letting down the level of rigor in the room for all students.

In an effort to meet individual student needs—both those of struggling students and those of advanced students--, I decided to throw out the tiered model for use in direct instruction. Instead of differentiating on two levels, I needed to develop a way to meet individual needs. This is how the spiraling-scaffolded task evolved. I decided that I would try teaching one brief lesson to the whole group on material that would be new for some and review for others--multi-digit addition. Then I would allow students who were comfortable to work through problems for independent practice at their own paces. Students who were new to the material or less comfortable with the material could stay with me and would receive extra support in a group.
Travis was clearly relieved to be allowed to stay for more support. Sam was thrilled to tackle the work at his own pace. In this way, I was once again supporting my struggling students, and I was providing a degree of independence that my more advanced students seemed to appreciate.

Using this format again on a second day, more students were comfortable working independently and the group of students who needed teacher support was smaller. On the third day, the bulk of the class was working independently and only Travis and Sarah remained for extra help. At this point these two could support each other, so I sent them off to work without me. To my relief they really were able to help each other through the problems. I was finally able to turn my attention to my more advanced students. Instead of circulating about, I called back the first batch of independent workers who were ready for more challenge. This group was mostly composed of older students like, but also a few like Sam who, while younger, were ready to take on something new. Together this group worked on multi-digit addition involving regrouping. In this way, everyone remained engaged with their work, and the level of rigor in the room remained high.

In describing this structure as "spraling" and "scaffolded" I’m drawing on the Jerome Bruner terms that I learned in my college ed psych class and I know it sounds jargony, but the term “spiraling-scaffolded instruction” is the best way I can think of to describe this format.

Traditionally, math curriculums do spiral, teaching a concept in first grade that will be reviewed and extended in second grade. For example, first graders might learn to tell time to the hour, while second graders might review telling time to the hour and also learn to tell time to the minute. Since my classroom is multi-age, I assume that my students are standing on the same spiral staircase, but happen to be at different locations on the stair. A lesson on telling time to the hour should be appropriate for all of my students and those who have previous experience with the concept will benefit from a lesson on telling time to the minute as well.

Scaffolding is assistance that allows a learner to perform a task that he or she is not yet ready to handle independently. Mathematical work may be scaffolded in a variety of ways, but teacher modeling or coaching and student use of manipulative materials are ways in which I generally offer students assistance. A student learning to add might first work with a teacher and blocks, then graduate to working independently with the blocks, and finally work independently without the blocks.

Now when I want to teach using direct instruction and guided practice, I set up a unit of spiraling and scaffolded tasks. For example, in teaching topics like multi-digit addition or subtraction, the whole class, including both olders and youngers, begins seated on the rug. To start, I model solving a math problem using manipulatives and recording my work on the board. Next I move on to a second problem, but this time the children participate in solving the problem and writing on the board. Then I move on to a third problem and this time I let the class “teach” me how to do the work. I pretend that I have forgotten what to do next and model typical mistakes. The children know that I am pretending, but they delight in catching my errors and explaining correct procedures! At this point the more advanced students have been reminded of familiar procedures and cautioned against potential errors, and they have articulated the concepts at hand. They are itching to dive in to this work. Other students may be fairly comfortable with what they have seen but not ready to tackle it independently while beginners have simply taken in a broad impression of the concept and are not at all ready for independent work. To ensure that each of the students has an appropriate level of support for taking on a sheet of practice problems, I ask each child to tell me if her or she would like to “stay or go.” Children who choose to “stay” grab a clipboard and a pencil and stay on the rug to work through the problems together at a pace set by the teacher. Children who choose to “go” take the work to their own seats. They are free to work at their own pace, but are accountable for completing the same amount of work at the end of the period as the “staying” group completes with teacher support. When I first introduce this structure I am clear with the children that I am not available to help those children working independently. They may whisper questions to each other, or they may return to the rug group. Children who work a few problems on the rug and realize that they are able to work independently sometimes choose to “go,” quietly leaving the group for their own seat. These students then solve problems independently, pacing themselves and working either with or without manipulatives. Other students continue to work with the support of the teacher, at the teachers’ pace. When the whole group has grown able to take on the task independently, I then work on problems involving regrouping with those students who are ready for an additional challenge.