2009/11/02

Journal Entry #6

Today’s lesson was one of the lecture ones again. Well, that what I thought at first. It was not a usual lecture but rather a work through a work sheet where students needed to apply previously learned material in order to find out about characteristics of disjoint and independent sets. Interesting was that Ms. Ringquist correctly recognized a confusion among students about notation of intersections and she realised that the next time she should do the notation before introducing (or in the process of introducing) binomial random variables. Each lesson is individually specific to a classroom setting (i.e. level and forms of students’ understandings) and it is crucial that a teacher keeps revising her lesson plans for future improvements. Ms. Ringquest told me she will change the order of her syllabus for the next year. Furthermore, I could clearly see an example of an appropriate recommendation for students wondering about performance. When multiplying especially these examples of geometric probabilities, it is important to write down multipliers since partial credit can be given for correct understanding but incorrect result.

After we have been done with the work sheet, we moved onto the textbook questions. The most intellectually striking one was the one about drawing M&M’s of different colours from a general population of all M&M’s. We were given particular probabilities for each colour and asked for probabilities of different colour combinations (haha, the author of the text book even included a “striped” M&M as a question – that is logically impossible, i.e. 0% probability, because M&M’s have only one specific colour by nature). As far as the calculating process is concerned, technically, it matters that we are drawing without the replacement because each time we draw out one M&M out of “n” M&M’s, the probability for the next one is calculated from the total number of (n-1) M&M’s. Practically, however, we can pretend that we are drawing without the replacement because the population of all M&M’s is massive. And that makes it easier. Students needed to think thoroughly through the setting of each question in order to realise what type of drawing should be used. Well done!

Moreover, reading the Venn diagrams raised some questions and the teacher correctly offered both logical/verbal and mathematical explanations. Anytime the class asked why, this space for questions was answered through a conversational way such that the teacher asked a few other questions until students reached own conclusions. Here I realised I was not in a lecture-type class at all. Ms. Ringquist looked at the students and saw they did not seem convinced by the verbal reasoning. Thus she started again and wrote the mathematical proof down in a exact way and then everybody had “thumbs up” (i.e. was comfortable). For a particular dilemma about independent events not being able to be when disjoint events are defined, the class could not digest the reasoning to complete comprehension. Therefore, the teacher promised she would explore a better (i.e. easier to understand) explanation that night and tell the class tomorrow. Receiving the real-time feedback from the class is important so that a teacher can accommodate students’ needs.

Lastly to mention, as an indirect effect of discussion class, the time run out and we did not manage to get to the concept of tree diagrams. Therefore, naturally, the homework was altered by excluding such questions.