Thurs, Feb 7

These flow maps were used as a review activity before the final assessment on techniques of integration. The day before the flow map assignment, the students worked in teams to solve as many integrals correctly as they could. When the final number of correct integrals were counted, however, an incorrect answer reset their total count to zero. Thus, they were encourgaed to be accurate as well as quick. As a follow up, I prompted students to think about how they started the process of evaluating an integral. Many students said they just think and wait for inspiration. The point of the flow map, of course, is that it encourages the students to think specifically about the process they used. Each group shared the flow maps, and it wasn't until all groups had shared that we actually had a complete flow map that did not omit any techniques. In other words, all of the flow maps were somewhat incomplete and it took the whole class to create a complete flow map.

Wed, Dec 19 #5

Here is a student generated Flow Map for graphing a rational function. We had just spent 3 days learning about essential and removeable discontinuities, vertical, horizontal and oblique asymptotes, local and global behavior, etc. The student came for extra help so I did one more example, and then I asked her to create a Flow Map in preparation for the exam. It seemed to work well for her. I know it was on her mind during the exam because when I asked a "stretch" question she let me know that it wasn't on her Flow Map!

Wed, Dec 19, # 2

After working with volumes of revolution for 3 days in my calculus class, I asked the students to create a Flow Map for the process used for these particular kinds of problems. The students took between 5 and 10 minutes to create their Flow Map. For me, it was a good way to quickly assess their understanding without having to look at the details of the calculus and algebra of how they set up and solved the problem. In other words, I got better and quicker information about their conceptual understanding from this Flow Map assessment than I do from looking at their alebra and calculus work from a solved problem. In particular, I learned that for most students, the first decision they tried to make was whether to use a disk, washer or shell despite the fact that I had emphasized repeatedly in class that the first decision should be whether or not to use a vertical or horizontal slice. That observation of mine generated some good discussion.

It was obvious the students were using higher order thinking skills, and it obviously pushed them a bit more than the standard requirement of just solving the problem. I didn't tell them to use any specific language or to use any specific number of boxes. I did require that they follow the left to right Flow Map procedure.

Mon, October 22

Teacher S and I have been working together in Geometry. We used Flow Maps last week for an algorithm for working with the formula for the area of a trapezoid. See image above.

We are going to develop the equations for the circumference and area of a circle using some hands on activities. For the circumference, I will bring in about 20 different cans and bottles. Each student will have a string and a ruler and they will measure the diameter and radius of their can or bottle. They will enter their can's diameter in List1 on Teacher S's overhead TI-83, and their can's circumference in List2. I will plot a scatterplot and line of best fit and we will discuss how to use the line to find the circumference for a can with a given diameter. I will tell them the slope of the line is 2(pi), hence C = 2(pi)r. For the area of a circle, each student will be given a circle with various sizes of pieces of pie marked. Their job will be to cut out the pieces of pie and change their circle into a rectangle. The height of their rectangle will be r, and their length will be (1/2) of the circumference. Hence Area = r*(1/2)(2)(pi)(r) = (pi)(r)^2. See the image above.

At the end of the chapter, the students will create a tree map of the areas of the shapes studied in the chapter. Instead of asking the students to create the tree map from scratch like we did in Lizzy's class, I have created a blank tree map with a list of labels. The students need to put the labels on the map in the correct places. See the two images above - one of the blank tree map and one of the scrambled labels.