Return to list of materials about "Learning how to plan a new inquiry unit"
In-service program/Methods course documentation
Learning how to plan a new inquiry unit (D7.1)
A teacher's reflections on her process of planning inquiry units (6
pages)
Note: This essay was written by Cynthia Callard, one of the teachers who planned the Olympics Games unit and the one who presented on her experience in the video "Planning a new inquiry unit: A case-study"
Previous Approaches to Planning
In order to discuss the planning of an inquiry unit, it is helpful to first consider other approaches to planning so that comparisons can be made. Oftentimes, when one first begins the job of teaching, the approach to curriculum and planning is topical in nature. In my first two years teaching I relied heavily on the textbook for my lessons and planning. This textbook provided me with a great deal of structure and I worked through it with my students fairly religiously. I was very concerned about covering all of the material in the book, and did so in a very systematic manner. The picture of building blocks in Figure 1 illustrates this idea.
This seemed like a practical approach to me at the time, as it seemed to me that learning mathematics successfully was based on mastering concepts at each level. If any of the lower building blocks were missing, more than likely the student would have a difficult time at the next level. My planning reflected these concerns.
As time went on and I became more comfortable with the material I was expected to cover, I tried to change this approach. I had heard and read material about integrating mathematics topics and helping students to make connections between branches of mathematics. As a result of this thinking, I rearranged some of the topics presented in the textbook and split apart and combined chapters so that the curriculum did not look so much like building blocks any more, but rather a mixture from a blender (see Figure 2).
Again, the main goal was to cover the curriculum, but not in such a linear fashion as before. I felt I was helping students to see how different areas of mathematics were connected by breaking down some of the dividers between chapters. However, the focus was still on the curriculum, and not much changed for students.
The third approach to planning that I have tried in the past is an "enrichment" approach. At the middle school level, the approach to the curriculum presented in most textbook series and which teachers have generally "bought into," is a spiral approach. Students see the same topics in 6th, 7th and 8th grade. Each year they spend the majority of their time reviewing the topic and the minority of the time extending it to new material. Although many of the students feel challenged by the material because they do not remember it from the year before, there is minimal learning of new material. So I tried another approach. I tried broadening the curriculum to include topics that were not traditionally covered in 8th grade mathematics. A staircase represents this idea of extending the curriculum (see Figure 3).
I did more algebra and introduced simplifying square roots during the real number unit, for example. I made trade-offs by, for example, not spending as much time on fractions. By approaching the curriculum this way, I felt like I was helping students to grow mathematically. However, as before, the focus was still on the curriculum. My planning had not changed (although I might have felt like it had because I was not necessarily following the topics provided in the textbook). I was still approaching things very linearly and my instructional goals for the students had not changed. I was not paying explicit attention to helping students communicate mathematically, reason mathematically, see the value of mathematics, etc. I was simply rearranging or adding onto the existing curriculum.
A Model for Planning an Inquiry Unit
When Denise Anthony and I became involved in the "Supporting Middle School Learning Disabled Students in the Mainsteam Mathematics Classroom" Project, however, things changed dramatically. With the new "inquiry approach" to teaching and learning that the project supported came a new approach to planning. Denise and I found that our focus now was not so much on the curriculum and the textbook, but on developing a unit or theme. We found ourselves shifting our focus from content to rich activities and questions for students to explore. Our approach shifted from a focus on moving from point A to point B in the curriculum, to having an encompassing idea and then developing activities and questions that students could be involved in in order to generate a great deal of mathematics. Denise Anthony and I came up with the model of an umbrella to help us illustrate this new approach (see Figure 4).
The umbrella is the rich topic or overarching theme or idea. From it fall interesting activities, questions and projects. From these activities, questions and projects, the mathematics develops.
But how does this type of planning actually take place and how is it different from the more "traditional" approaches discussed? While I have tried to summarize the key elements of this below (see the videotape "Planning an Inquiry Unit" for more details), I think it is important to clarify two things up-front. First, this is simply one way to approach planning of this type of inquiry unit. It is not meant to be seen as the "way to do it" but rather an example of a feasible process for planning inquiry units. Secondly, it is truly a process. When written down, this model seems very straightforward and linear in its approach. However, it is not. It is a difficult process and goes through many stages and loops, not neat little steps 1, 2 and 3.
Where to begin? The first thing one needs to do is to have an idea for a topic that seems rich with interest and that would be able to generate a great deal of mathematics. The topic should be broad enough so that there could be a variety of interesting activities generated from it. Tessellations, Area, and the Olympics are just a few examples of rich topics that have been developed within this Project.
After generating an idea, it is helpful to pull out a variety of resources on this idea or topic. These may be directly related to the topic and grade level to be taught or they may be slightly different but may be helpful to generate ideas. One rarely starts in a vacuum and it is always helpful to see what others have done with similar ideas. For example, when Denise Anthony and I began planning the Tessellation Unit we obviously used the Project materials (see the booklet entitled "Investigating Tessellations to Learn Geometry: Supporting Materials for Teachers") as our starting point for ideas. We made many modifications but it was very helpful to see what other people had done and to provide us with a base to start from. For a unit on the Olympics that we did in the Spring of 1994 with our eighth graders, we used a unit previously developed for eighth graders around the 1990 U.S. Census to help us generate ideas. Although this was not directly related to what we were going to be teaching, it helped to see how another teacher had used a current event as an overarching theme to generate rich activities for students to work with mathematics.
The next stage for us was to brainstorm what mathematics, activities and goals the idea could generate. What kinds of mathematics might come up? It is important to have this in mind as possible activities students could participate in are brainstormed. How are students going to be engaged? How will students' interests be included? What are the overall goals for the unit? Developing goals for the unit, both process and content, is a crucial piece to planning, but may not be able to be done first. This may not be possible until after the mathematics that may be generated and some possible activities that students may be engaged in have been thought about. Once some goals for the unit are determined, the mathematics needs to be revisited and a focal point chosen. What general branch of mathematics is going to be the focus? An excerpt from a journal entry that I wrote at the end of my first year in the Project discusses the idea of using a theme to generate meaningful mathematics:
July 6
Another thing that struck me after completing our first unit was that it was very important for us to know what math we wanted to cover, but by carefully choosing questions and activities for students to participate in, much more mathematics was uncovered than was originally planned. I remember it being a big break through for me when I realized that it was not tessellations that I was teaching, rather I was using the topic of tessellations to teach a great deal of math! This mathematics was spread throughout all activities whether it be independent student work, small group work, large class discussion, or even a more traditional presentation. But the key was that the mathematics was presented or discovered in a meaningful way. Students were not completely left on their own to "find what they could find" nor were they dryly given random information. The mathematics was all connected under the umbrella unit idea of tessellations.
Continuing this idea about the mathematics that was covered, another important distinction to make is that this math was not presented as isolated topics in a chapter--a day on classifying triangles, a day on definitions, a day on polygons, etc. Rather, everything was integrated in the context of tessellations so that on any one day many different topics could come up. As a result, the vocabulary and concepts were a part of the everyday classroom language and hopefully helped in retention, especially for LD students. I think this was one of the keys to their success.
After some goals for the unit have been determined and a mathematical focus chosen, it is important to match the goals with the possible key activities previously brainstormed. In some cases, an idea for an activity may not be used because it may not fit with the overall goals for the unit. Or, if it seems important, a goal may be added. Also, activities may need to be generated in order to meet a particular goal, or goals may be deleted if they do not seem feasible for whatever reason. Again, this is a process. It is a flexible interchange between goals and activities, always keeping in mind the mathematical focus. Not until now can one begin to consider the overall scope of the unit and the overall timeliness.
Hopefully, by having clear goals in mind, one can avoid some of the difficulties I had my first year teaching the Tessellation Unit as the following journal excerpts illustrate:
October 2
I think that one of the things that has been difficult for me in implementing this unit for the first time, is I am still not entirely sure what my goals are! A colleague in the project was talking one day about her way of viewing lessons and when to pursue a students' thoughts and when not to, and she was saying that she makes a decision to pursue an idea based on whether pursuing it will just be a different route to help her reach the same goal or whether it will be a sidetrack that does not help her to reach her goal. That sounds great, but my trouble is I'm not completely sure what my goal is, therefore I am having a difficult time making decisions about what ideas to grab onto and what ones to let slide for a little!
November 11
I think the unit was difficult the first time around (at least for me) because I did not have really clear goals in mind. As a result, we did a lot, but I think we (and the kids) are ready to move on. Already though, I'm looking forward to doing the unit again next year. The second time around is always so much easier because of material, but I think it will also be better for me because I know the direction we're heading in.
Referring back to the umbrella analogy, at this point there is the "umbrella" theme or idea, the "droplets" with the major activities that students will engage in, and the minimum mathematics that could be generated from these activities. It is important at this point to have something in writing for a beginning structure, although this skeleton plan has a lot to be filled in and will be continuously revised. An excerpt from my first year journal, written at the end of the year, reflects this idea:
July 6
One of the things that became clear to me is the importance of having this general structure for a unit. We wound up revising, adding to, and taking away from this general plan but it was very important that we have it to start from. In a way, these unit plans are new things for teachers to create. Not that we don't have a plan for traditional topics, but that plan is usually given to us by our textbooks. Again we would revise, add to, and take away from this textbook plan, but the structure was given to us. Maybe that helps explain why this overall plan is so hard to create!
Throughout this planning process, assessment should be in the background. The "traditional" paper-and-pencil test given at the end of a chapter will probably not be enough to assess the students on the process and content goals identified for the unit. This needs to be considered at the beginning of the unit so that assessment opportunities are not missed and so that clear expectations and guidelines are given to the students. These expectations are very important as the types of activities students are engaged in may be very different than what they might be used to doing in math class. They need to know what is expected of them. I also mentioned this in the same end-of-the-year journal:
July 6
As we continued throughout the unit we began to consider how we were going to assess our students. We quickly realized that since how we were teaching and what we were asking our students to do was changing, so must our assessment. We developed a matrix for assessment that included not only a more traditional quiz and test, but also writing assignments, group presentation, and a poster project. The group presentation was an important piece of this unit. This was where we were asking students to conjecture, investigate, and draw conclusions based on their exploration about what shapes tessellate. We were putting them in the role of a mathematician. Although this was a very open-ended project, one of the things that I grew to appreciate was that simply because students are working on their own investigating does not mean that there is no structure and guidance. And as a matter of fact, structure and clear expectations became even more important for students. Denise and I spent a great deal of time establishing this structure and expectations for students in order to help them be successful in their exploration.
It is at this point that daily plans can begin to be thought through. Up until this point, there are the few key segments or activities with a general idea of how many days each will take, but no detailed daily plans. For each activity, days can now be sketched out in a few words per day so that there is a framework for how each activity will be implemented. In our planning, we also found that we spent a great deal of time planning the first few days of the unit in detail. This was very important in order for us to feel comfortable and in order to set the stage of the unit for the students. It was at this stage of the planning process where we made decisions about what we wanted to happen in the classroom, but these decisions were also affected by logistical and practical influences.
When constructing these daily plans there continues to be interaction with the overall unit goals and activities. A comment in one of my journals early in the implementation of the first Tessellation Unit contrasts this type of planning with previous approaches to planning that I had tried:
October 2
In terms of planning, the planning of this unit was done a little differently than when I usually plan alone. Instead of planning days, this unit was planned more by topics and activities. I am trying not to get too caught up in daily goals and in counting days, but to concentrate more on my overall goals for students' thinking and where they are in terms of their thinking. The latter, however, often takes much more time to reach!
As we know, however, nothing in teaching ever goes exactly as planned! Whether it be assemblies, snow days, band trips, activities that took longer than planned, activities that did not go off as planned at all, or wonderful ideas brought up in class that need to be pursued, plans change. While it is crucial to have a plan before beginning this type of inquiry unit so that one knows where one wants to go, it is also imperative that this plan be flexible enough to accommodate daily teaching "surprises."
Again, the planning process I have described is simply that--one example of an approach that Denise Anthony and I have used to plan an inquiry unit. No matter how one plans, however, it is important to note that changing the way one teaches and approaches the teaching and learning of mathematics is a difficult and unsettling process. I described it many ways in my journals over the years but I think the phrase that captures it the most is an "emotional roller coaster And although it may not make the ride easier, it is sometimes comforting to know that others have taken the ride before you!
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