Return to list of materials about "Providing classroom support during the implementation of an illustrative unit"
In-service program documentation
Providing classroom support during the implementation of an illustrative
unit (D6.5)
Excerpts from participants' journals during the field experiences
The following journal excerpts show the participant's perspective of the very same lessons and debriefing meetings discussed in the facilitator's personal journal entry included in the Instructional materials for this section.
These excerpts were taken from the participant's journal following the two lessons testing the conjecture "all triangles tessellate".
9/26 Day 7
[…] This lesson also flowed very smoothly today. However, the team facilitator happened to stop in and observe today and noted that the students so not seem to be completely convinced that all triangle tessellate. We have not addresses the issue that all triangles can be made into strips and that these strips are formed by the three angles of a triangle, which is 1800. This proves that thee "strips" do in fact have straight lines for edges so that the strips can be places above and below each other. We did not discuss any of this explicitly and we need to before we go on to similar and congruent triangles. We will need to insert this extra day into our plans.
9/27 Day 8
[…] I thought this lesson went great. […] I also feel that if the students do not understand it completely right now, that's all right. At least they have been introduced to the idea. What is amazing is that this was such a key lesson in the conclusion to the questions "Do all triangles tessellate?" This was the mathematical justification to the question ! It was also a key point in the modeling of the research projects. And it was not in our original plans ! This is a disadvantage of being too closely tied to your plan. My partner and I just had it in our heads that the triangle lab was going to take five days. So after we had spent three days on the first part we were ready to move on to congruent and similar ! It was so good that [facilitator] happened to observe one of my classes yesterday. She helped us to stpe back and look at the fact that the students were missing some key information and were not ready to move on. So we did some quick planning and came up with today's lesson ! It was momentarily stressful planning under pressure at 3 p.m. but was definitely worth it and well needed.
This excerpt was taken from the participant's final reflections written in June of same year. This excerpt demonstrates how powerful this experience really was for this participant.
[…]
Another thing I really want to comment on is what turned out to be a very important piece to the unit. The students were towards the end of the triangle lab investigating whether all triangles tessellate (day 7). They had been doing tracings and had pretty much come to the conclusion that yes, in fact, all triangles will tessellate based on the tracings that they had done. My partner and I were getting ready to wrap that lab up and move on to working with similar and congruent triangles. That day our facilitator happened to come in and observe my 9th period class. She felt that the students were not quite ready to move on as we had not mathematically proved that all triangles will in fact tessellate. We realized that we had not really justified this result mathematically but were not sure how to approach this with the students and we were also concerned about time and keeping to our original time frame in the outline. She really encouraged us to pursue this concept and helped us to brainstorm ways to prove our result. We eventually came up with the lesson that we did on day 8 and it really was an extremely important piece. A very similar thing happened during the quadrilateral piece with the introduction of angle relationships when parallel lines are cut by a transversal (day 13). We once again wound up scratching our original plans and doing some late night, last minute planning! Although the process was a bit stressful, these were both very important activities in terms of content covered and modeling the research process. These turned out to be two of my favorite lessons! Neither my partner nor I had realized that these pieces were missing. How do we as teachers slow down enough and reflect on each lesson in order to see these key pieces? Especially in this approach, the pieces are so important. I wonder how many others we missed or how our Perimeter, Area, Volume unit could have been better if we had had someone observing our lessons.