2009/09/13
Write-up #1
I would like to start with mentioning my pre-class preparation. Originally, I wanted to get a textbook and pick up some major topics about the Graph Theory. Looking into multiple textbooks, however, I realised that Penelope is undoubtedly going to lack vocabulary previously introduced in the Abstract Algebra and its Group Theory. Since all of the textbooks I have seen were too complex, I decided to make a simple lecture at first. I combined information from 5 textbooks and 3 internet sources to a supposedly easy-to-understand form. Although textbooks have been proven to help with understanding of scientific concepts significantly (Adolescent Literacy Research and Practice, ADSaP, page 76), I am not still quite sure I will use a textbook at all. I believe that it is counterproductive to introduce them so early in the process of learning completely new content. Maybe, I will use some form of a textbook later during the course once I am sure Penelope has gained enough of background knowledge.
Furthermore, I thought a week ago that the pre-class preparation was not going to be such a difficult part of the project. But I was wrong. As I was reading Adolescent Literacy Research and Practice and Understanding by Design, I realised that it is equally important to “plan-revise-teach-assess-reflect-adjust” (UbD, page 8 ) and to know the expectations of a student. I spent several hours outlining an ideal lesson plan mentioning initial problems, historical background, notation and categorization. But before all of that, I began the class introducing Penelope to a KWL Know-Want-Learn concept (ALRaP, page 31) and assured myself with the decision not to bring a textbook and start from a total scratch. She had not learnt anything about the Graph Theory before. We also talked a bit about our teaching experiences and I asked Penelope, who is more experienced, to be picky and give me recommendations at any time before debriefing. Then I outlined the class and let her know that I made several variations on the end of the subject discussed, depending on time restrictions. Therefore I made her feel comfortable that there is no time pressure upon us and she can keep asking me for any clarifications, I believe. Itold her, “There is no stupid question, there are just stupid answers.”
Luckily for us, we do not have a real final exam on the end and we do not have an exact amount of knowledge to learn. I just want to make sure that Penelope absorbs whatever information I present. Thence, compared to my original lesson plan, we slowed down a bit and reassured ourselves we understand basic differences among Simple Graphs and Digraphs.
In order to help Penelope visualising those concepts, I let her solve the Three Utility Problem right on the beginning of the lesson. She was struggling but together we could reason why there was no solution. Then we moved onto historical development and Euler´s Kőnigsberg Bridge Problem. Again, there was no solution and I hope that Penelope got the idea that the graph theory was partly developed as endeavour to reason certain impossible facts. We ended the lesson by introducing Complete Graphs and planarity. Penelope´s homework is to try to figure out if there is a planar K5 graph. And as a usual part of mathematics, she has to completely reason why there is such a solution or why there is none. I am looking forward to start the next lesson and see how much of new information Penelope deep-processed and managed to apply.
Lastly to mention, I presented a few textbooks and other materials during the debriefing session. Other materials included some pictures to help us revising and also a vocabulary list I printed out from some internet sources. That one sheet of paper is our aim of six sessions: to completely understand the meaning and the context of each of those words. As I was told, Penelope is happy with the teaching style and the content so far. Therefore I am not planning to make any major changes yet and I will keep on developing ideas we have learned.