Chapter 7 - Engaging in Scaffolded Instructional Innovation

Many successful programs working toward school mathematics reform include scaffolded field experiences. That is, opportunities for participating teachers to experiment with instructional innovation while receiving support. However, there is great variation in the kind of innovative instructional experiences that teachers undertake and in the kinds of support that can be offered. As we examine this kind of professional development experience we will often refer to it as “scaffolded instructional innovation.”

Research conducted in several areas supports the value of scaffolded instructional innovation. First, studies of teachers’ beliefs point out that the relationship between pedagogical beliefs and practices is not unidirectional (Thompson, 1992). That is, while teachers’ beliefs clearly inform their practices, we might also expect experiencing “alternative practices” to challenge their existing beliefs. This change is especially apparent when teachers observe their own students demonstrating a higher level of learning and thinking in non-traditional instruction than they did in traditional instruction.

The importance of scaffolded field experiences is also emphasized in Simon’s (1994) learning cycles model of teacher development introduced in Chapter 3. Simon identified the planning and implementation of innovative instruction as a possible catalyst for the fifth and sixth stages of a teacher’s learning cycle.

At the same time, putting novel instructional techniques into practice presents a considerable challenge for most teachers, and many may fail in their first attempts unless they are supported appropriately. Some initial scaffolded practice is indeed recognized as a key component in the model developed by Collins, Brown, and Newman, (1989) to shed light on the process of learning complex tasks, which we introduced earlier in Chapter 1.

While it is difficult to evaluate the effect of scaffolded field experiences alone, many successful professional development programs have used this strategy extensively. The changes in teachers’ beliefs and instructional practices reported by Simon and Schifter (1991), Schifter and Fosnot (1993), and Borasi, Fonzi, Smith, and Rose (1999), for example, document the success of combining experiences-as-learners with scaffolded field experiences. Furthermore, the latter two studies include case studies and anecdotal evidence that point to the specific contributions of scaffolded field experiences.

Indirect evidence in support of scaffolded field experiences is found in the positive outcomes reported by projects that implemented one of the NSF-funded comprehensive curricula (these data can be found in each project website, listed earlier in Figure 7). These projects showed long-term gains in student achievement in schools that implemented these curricula, especially when high-quality professional development helped teachers use these exemplary instructional materials appropriately (Russell, 1997).

We derived this illustration from the Making Mathematics Reform a Reality (MMRR) project described in Chapter 2. As teachers joined the program, they agreed to participate in a week-long Introductory Summer Institute and to implement one of two illustrative inquiry units in at least one class at the beginning of the following school year.

Both illustrative units highlight fundamental features of teaching mathematics through inquiry and present “big ideas” in geometry and measurement while focusing specifically on the topics of tessellation and area. A team of researchers and teachers created and field-tested these units in a variety of middle school settings. Based on careful documentation and analysis of these experiences, instructional materials were created to support the planning and implementation of each unit at different grade levels and in different school contexts. The materials include an overview and discussion of the key components of the unit, a mathematical essay highlighting the “big ideas” addressed in the unit, a timeline, and selected artifacts (e.g., hand-outs and assessment tools) from implementations of the unit in different settings.

Scaffolding teachers’ implementation of these illustrative units began as early as the Summer Institute. First, participants engaged in two experiences-as-learners lasting 5 to 7 hours each. The activities were designed to highlight key components of the two illustrative units, both of which were adapted to challenge adult learners. The inquiry on area reported as Illustration 1 in Chapter 4 was one of these experiences. These experiences, together with the reflection on the mathematical content and pedagogy that followed, gave teachers a personal understanding of the goals, rationale and overall design of the two units. Several participants reported that the positive feelings they experienced as learners in these inquiries motivated them to take the risk to try them in their own classes.

These experiences-as-learners were then supplemented by images of what the two units might look like in middle school classrooms. Excerpts of an implementation of the tessellation unit were presented in a 2-hour-long video while a 50-page narrative provided a detailed story of an implementation of the area unit. After participants watched the video and read the story, they had opportunities to share their impressions and to question teachers who had already implemented the units. Their concerns ranged from the management of materials and group work to information about student outcomes and potential pitfalls. Mostly, participants emerged from these conversations with more experienced teachers reassured that these experiences could work in middle school and encouraged by their colleagues’ enthusiasm.

During the Summer Institute, the facilitators introduced participants to the instructional materials created to support the implementation of the two units. Selected readings from these materials were assigned for homework and later discussed. When facilitators asked teachers to comment on the value of these readings, they said that encountering the materials for the first time when trying to plan their unit would have been truly overwhelming because of their unusual content and structure and might have easily discouraged them from using them. Thus, assigning the readings in the Summer Institute was an important way to enable teachers to benefit from the instructional materials intended to support their first field experience.

As teachers began to plan their unit at the beginning of the school year, facilitators encouraged them to consult individually with mathematics teacher educators on the project staff or with a lead teacher at their school site. Although not everyone took advantage of these opportunities, those that did found them very helpful. In some cases, especially when the teacher felt overwhelmed by the novelty and complexity of the task, these sessions involved brainstorming and writing an overall plan together. In addition, the teacher received help writing lesson plans for the first few days of the unit. In other cases, teachers came to these meetings with drafted lesson plans that were then discussed and refined. In all cases, these consultations made it possible to address teachers’ possible misconceptions and resulted in lessons that offered much better learning opportunities for the students.

As teachers began to implement their units, they could request further support from project staff or lead teachers. This support usually took the form of classroom visits followed by debriefing meetings. Whenever possible, support staff visited classrooms for a few consecutive days in order to observe how suggestions and decisions made during previous debriefing meetings played out. The teacher educator’s role in the classroom visits and the nature of the follow-up meetings varied considerably, depending on the personality and needs of each teacher. In most classroom visits, the teacher educator simply observed the class, moving around to help individuals and small groups during the lesson. This strategy allowed the classroom teacher to spend more time with other students and enabled the teacher educator to report observations about students’ work and thinking that the teacher might not have known otherwise. Other times, the teacher educator played a more direct role in the instruction, perhaps introducing selected activities, demonstrating the use of certain materials or recording on the board the key points of a discussion the teacher was facilitating. In either case, the debriefing meetings that followed the lesson played a key role. These meetings focused not so much on providing feedback on the teacher’s performance, but rather on discussing students’ work and what had been observed about their learning and thinking. This kind of knowledge helped teachers to consider in more depth the mathematical concepts they were working on and to plan for future lessons.

Occasionally, two or three teachers from the same school who were teaching the same mathematics courses worked as a team. In that case, they usually planned the units together and met regularly to discuss the outcomes of specific activities and to make revisions to the original plan. These teams were encouraged to observe each other if possible, but few managed to put this suggestion into practice.

Finally, in November, after everyone had concluded the implementation of the first inquiry unit, all Summer Institute participants were called back together for a day-long meeting. To prepare for the meeting, teachers were asked to look back at their experience and to identify at least one success and one concern that they would like to share with the rest of the group. The meeting began with each teacher briefly sharing these reflections.

Overall, the reports were quite positive, and in most cases, even enthusiastic. Most of the successes had to do with student accomplishments; several teachers reported their surprise at seeing some of their weakest students blossom during this unit and reveal abilities they had never imagined!

This sharing also revealed some common concerns and challenges. Several teachers reported feeling panicked when students came up with solutions they could not understand or questions they had no idea how to answer. Others were worried about being able to follow through, given the enormous amount of time and energy this way of teaching requires. In the second half of the meeting, these common concerns were addressed in small groups. While the small groups did not always reach satisfactory solutions, teachers generally agreed that it was helpful just to know that other people had encountered similar problems or worried about the same issues.

Continued




	Engaging in Scaffolded Instructional Innovation Many successful programs working toward school mathematics reform include scaffolded field experiences. That is, opportunities for participating teachers to experiment with instructional innovation while receiving support. However, there is great variation in the kind of innovative instructional experiences that teachers undertake and in the kinds of support that can be offered. As we examine this kind of professional development experience we will often refer to it as “scaffolded instructional innovation.” Theoretical rationale and empirical support Research conducted in several areas supports the value of scaffolded instructional innovation. First, studies of teachers’ beliefs point out that the relationship between pedagogical beliefs and practices is not unidirectional (Thompson, 1992). That is, while teachers’ beliefs clearly inform their practices, we might also expect experiencing “alternative practices” to challenge their existing beliefs. This change is especially apparent when teachers observe their own students demonstrating a higher level of learning and thinking in non-traditional instruction than they did in traditional instruction. The importance of scaffolded field experiences is also emphasized in Simon’s (1994) learning cycles model of teacher development introduced in Chapter 3. Simon identified the planning and implementation of innovative instruction as a possible catalyst for the fifth and sixth stages of a teacher’s learning cycle. At the same time, putting novel instructional techniques into practice presents a considerable challenge for most teachers, and many may fail in their first attempts unless they are supported appropriately. Some initial scaffolded practice is indeed recognized as a key component in the model developed by Collins, Brown, and Newman, (1989) to shed light on the process of learning complex tasks, which we introduced earlier in Chapter 1. While it is difficult to evaluate the effect of scaffolded field experiences alone, many successful professional development programs have used this strategy extensively. The changes in teachers’ beliefs and instructional practices reported by Simon and Schifter (1991), Schifter and Fosnot (1993), and Borasi, Fonzi, Smith, and Rose (1999), for example, document the success of combining experiences-as-learners with scaffolded field experiences. Furthermore, the latter two studies include case studies and anecdotal evidence that point to the specific contributions of scaffolded field experiences. Indirect evidence in support of scaffolded field experiences is found in the positive outcomes reported by projects that implemented one of the NSF-funded comprehensive curricula (these data can be found in each project website, listed earlier in Figure 7). These projects showed long-term gains in student achievement in schools that implemented these curricula, especially when high-quality professional development helped teachers use these exemplary instructional materials appropriately (Russell, 1997). Illustration 7: A scaffolded implementation of an illustrative inquiry unit We derived this illustration from the Making Mathematics Reform a Reality (MMRR) project described in Chapter 2. As teachers joined the program, they agreed to participate in a week-long Introductory Summer Institute and to implement one of two illustrative inquiry units in at least one class at the beginning of the following school year. Both illustrative units highlight fundamental features of teaching mathematics through inquiry and present “big ideas” in geometry and measurement while focusing specifically on the topics of tessellation and area. A team of researchers and teachers created and field-tested these units in a variety of middle school settings. Based on careful documentation and analysis of these experiences, instructional materials were created to support the planning and implementation of each unit at different grade levels and in different school contexts. The materials include an overview and discussion of the key components of the unit, a mathematical essay highlighting the “big ideas” addressed in the unit, a timeline, and selected artifacts (e.g., hand-outs and assessment tools) from implementations of the unit in different settings. Scaffolding teachers’ implementation of these illustrative units began as early as the Summer Institute. First, participants engaged in two experiences-as-learners lasting 5 to 7 hours each. The activities were designed to highlight key components of the two illustrative units, both of which were adapted to challenge adult learners. The inquiry on area reported as Illustration 1 in Chapter 4 was one of these experiences. These experiences, together with the reflection on the mathematical content and pedagogy that followed, gave teachers a personal understanding of the goals, rationale and overall design of the two units. Several participants reported that the positive feelings they experienced as learners in these inquiries motivated them to take the risk to try them in their own classes. These experiences-as-learners were then supplemented by images of what the two units might look like in middle school classrooms. Excerpts of an implementation of the tessellation unit were presented in a 2-hour-long video while a 50-page narrative provided a detailed story of an implementation of the area unit. After participants watched the video and read the story, they had opportunities to share their impressions and to question teachers who had already implemented the units. Their concerns ranged from the management of materials and group work to information about student outcomes and potential pitfalls. Mostly, participants emerged from these conversations with more experienced teachers reassured that these experiences could work in middle school and encouraged by their colleagues’ enthusiasm. During the Summer Institute, the facilitators introduced participants to the instructional materials created to support the implementation of the two units. Selected readings from these materials were assigned for homework and later discussed. When facilitators asked teachers to comment on the value of these readings, they said that encountering the materials for the first time when trying to plan their unit would have been truly overwhelming because of their unusual content and structure and might have easily discouraged them from using them. Thus, assigning the readings in the Summer Institute was an important way to enable teachers to benefit from the instructional materials intended to support their first field experience. As teachers began to plan their unit at the beginning of the school year, facilitators encouraged them to consult individually with mathematics teacher educators on the project staff or with a lead teacher at their school site. Although not everyone took advantage of these opportunities, those that did found them very helpful. In some cases, especially when the teacher felt overwhelmed by the novelty and complexity of the task, these sessions involved brainstorming and writing an overall plan together. In addition, the teacher received help writing lesson plans for the first few days of the unit. In other cases, teachers came to these meetings with drafted lesson plans that were then discussed and refined. In all cases, these consultations made it possible to address teachers’ possible misconceptions and resulted in lessons that offered much better learning opportunities for the students. As teachers began to implement their units, they could request further support from project staff or lead teachers. This support usually took the form of classroom visits followed by debriefing meetings. Whenever possible, support staff visited classrooms for a few consecutive days in order to observe how suggestions and decisions made during previous debriefing meetings played out. The teacher educator’s role in the classroom visits and the nature of the follow-up meetings varied considerably, depending on the personality and needs of each teacher. In most classroom visits, the teacher educator simply observed the class, moving around to help individuals and small groups during the lesson. This strategy allowed the classroom teacher to spend more time with other students and enabled the teacher educator to report observations about students’ work and thinking that the teacher might not have known otherwise. Other times, the teacher educator played a more direct role in the instruction, perhaps introducing selected activities, demonstrating the use of certain materials or recording on the board the key points of a discussion the teacher was facilitating. In either case, the debriefing meetings that followed the lesson played a key role. These meetings focused not so much on providing feedback on the teacher’s performance, but rather on discussing students’ work and what had been observed about their learning and thinking. This kind of knowledge helped teachers to consider in more depth the mathematical concepts they were working on and to plan for future lessons. Occasionally, two or three teachers from the same school who were teaching the same mathematics courses worked as a team. In that case, they usually planned the units together and met regularly to discuss the outcomes of specific activities and to make revisions to the original plan. These teams were encouraged to observe each other if possible, but few managed to put this suggestion into practice. Finally, in November, after everyone had concluded the implementation of the first inquiry unit, all Summer Institute participants were called back together for a day-long meeting. To prepare for the meeting, teachers were asked to look back at their experience and to identify at least one success and one concern that they would like to share with the rest of the group. The meeting began with each teacher briefly sharing these reflections. Overall, the reports were quite positive, and in most cases, even enthusiastic. Most of the successes had to do with student accomplishments; several teachers reported their surprise at seeing some of their weakest students blossom during this unit and reveal abilities they had never imagined! This sharing also revealed some common concerns and challenges. Several teachers reported feeling panicked when students came up with solutions they could not understand or questions they had no idea how to answer. Others were worried about being able to follow through, given the enormous amount of time and energy this way of teaching requires. In the second half of the meeting, these common concerns were addressed in small groups. While the small groups did not always reach satisfactory solutions, teachers generally agreed that it was helpful just to know that other people had encountered similar problems or worried about the same issues. Continued