Student Activities from Lecture 6

October 10, 2005

This was a student submission based lecture on graph theory. The majority of the students had seen the material before, so the goal was to remind the students of concepts, and to ensure that there was a consistent use of terminology. The lecture was designed with the theme of "finding cycles" - first in undirected graphs, then in directed graphs.

Five student activities were included in the lecture. Roughly twenty five students were present for the lecture, along with two observers. All participants used HP TC1100 Tablet PCs on an Ad Hoc network. There were no technlogy issues.

Activity 1 - Draw a picture

Activity Type: Engagement

Activity Goals: Allow students to gain familiarity of the student submission process, establish an atmosphere of student participation, and describe the workflow of student submissions.

Planned Use: Show all of the student submission, so students would see their solutions displayed.

Actual use: This went very much as planned. Students immediately figured out how to use the system, and there was a very high rate of participation.

Evaluation of activity: Variations on this activity have been used regularly, and it consistently achieves its goals. The variation "Draw Notkin" (the department chair), worked well.

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Activity 2 Determine if an undirected graph has a cycle

Activity Type: Assessment, Pedagogical Point

Activity Goals: Start class with an activity to have students thinking about the lecture topic

Planned Use:Find algorithms of different types to talk about, first a algorithm based on counting edges, then maybe BFS and DFS based solutions

Actual use: A solution counting edges was identified - although it actually was counting vertices - students pointed this out. Then a second solution was displayed based on a graph search.

Evaluation of activity: The solutions were very difficult to evaluate in real time. After class analysis show many solutions in the right direction. The activity may have been useful in getting the students to work with cycles - but I do not feel I was able to take advantage of the solutions.

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Activity 3 How do you detect a cycle with DFS

Activity Type: Assessment, Pedagogical Point

Activity Goals: There were a couple of points I wanted to make around this - how to express algorithmic ideas simply, and the structural information provided by depth first search.

Planned Use: The hope was that there would be several solutions with concisely expressed results

Actual use:THe solutions were longer, and more algorithmic than I had hoped. THe majority of the solutions looked basically right, so I showed just a single solution and then made some general points.

Evaluation of activity: I was not happy with this activity. I had hoped to be able to use the activity to talk about how to concisely express algorithmic ideas. However, I don't think I articulated this goal in the activity discussion. This activity was devised late in the design of the lecture, when I discarded an earlier one because I realized it would have been too contrived. It would have been useful to discuss several of the solutions in more detail. Since the solution I was looking for was not provided, I should have presented it

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Activity 4 Find the Strongly Connected Components

Activity Type:Activity and Assessment

Activity Goals:I wanted to students to work through an example to find strongly connected components to reinforce the idea. I also wanted to verify that students understood the concept

Planned Use: Show a correct solution, and possibly incorrect solutions if they existed

Actual use: Solutions were very close to being correct. A few solutions were missing a minor detail - which allowed a (minor) point to be made about strongly connected components of size one.

Evaluation of activity:I felt this worked well. Students were able to demonstrate they understood the concept, and I believe that this was more valuable for the students then me working through an example. The discussion about strongly connected components was helped by having the student drawn versions. The timing on this example went well

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Activity 5 Topological Sort

Activity Type:Discovery and Pedagogocial Point

Activity Goals:The activity was to have students do a Topological sort on a graph with a cycle. The goal was to have students discover the obstruction.

Planned Use: Show some incorrect solutions, and then put a solutions that showed there was no solution

Actual use: This worked pretty much as planned - with students discovering the problem with the cycle. Several incorrect solutions were displayed, followed by a series of correct solutions. I wanted to show a lot of correct solutions just so students would be able to see their own results.

Evaluation of activity: I felt this was very successful, in that a large number of students were able to make the discovery of the cycle problem, in contrast to the usual way I would have done this where the first student to answer would probably identify the issue. The activity engaged students, and was easy for me to analyze.

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