2009/11/16

Journal Entry #8

The students are going to have a test on Wednesday and so no new material was taught. Instead, we started with the homework check and proceeded to the complete review of current chapter. The main idea was to identify the difference in between a geometric random variable (having trials until a success occurs) and binomial random variables (having a specific number of successes among a fixed number of trails. Ms. Ringquist used various examples to which the students had to answer immediately out loud. The most evoking one was a personal example from the teacher’s family: “What is the probability that there are two girls among seven siblings?” Not only the students learnt that their teacher has six sibling, they also figured out that there was 16.4% chance of such occurrence (assuming that there is an equal probability for a girl or a boy being born). Building of the personal relationship among the teacher and students is important in order to establish the level of mutual trust, partnership and cooperation. But of course, there are always limits so that the teacher maintains authoritative status. For example, Ms. Ringquist only presented an interesting mathematical concept that occurred in her family, but she did not share any more private details such as names or personalities of her siblings.

Furthermore, the students correctly figured out that both geometric and binomial random variables share initial characteristics of constant probabilities, two different outcomes, independent trials not affecting each other, and having sample size at least 10% from the general population. After this, the class asked for a short intellectual break in the form of another attention-asking game: “Greedy Pig”. The teacher was rolling a dice and summing up the numbers until the number 5 appeared. Each student stood up and could decide to sit down before each roll, securing the previous cumulative sum. If the number 5 appeared, the bank burst and a standing student earned no points. The point was to keep a geometric random variable on mind and try guessing this random event correctly. I had a feeling that not so many students realised that there was a 20% chance on having NO 5 at all nine times in a row (geometric) and though about simple 1/6 chance of getting five instead. Also, certain level of self-control and gambling was included as well. Some of the students kept risking several rounds in a row, while others secured their bank after the fifth or sixth row.

After this short application, we started working through a review sheet in groups of two to three students. They had to reason to each other what and why they were doing, in order to solidify knowledge before upcoming exam. Also, the teacher distributed the previous test with all problems and solutions for detailed review so that students could follow up directly from previously learnt material.

2009/11/09

Journal Entry #7

It is a flu season and many students are missing. There were just one half of the students (eight) present on the beginning of this class. Moreover, only two guys were actually present during the last lesson on Friday of the previous week. And the major dilemma arose – what to do? Although the AP system pushes forward to utilize each classroom due to highly demanding expectations, Ms. Ringquist decided to use this lesson for catching up. First, the class went over the previous quiz/test in order to clarify any previous misconceptions. Then they recapitulated random variables and reminded the key concepts. At this point, a few more students arrived from a theatre play they were organizing for underclassman. Thus more students could benefit from this lesson which did not include any new material but solidified all previous concepts. We also read a sample example from the book and went over examples of calculating expected values, variances and standard deviations. Homework problems were also reassigned and the emphasis was on material revised during the class (expected values, variances and standard deviations).

One could argue that a teacher should always proceed ahead in curricular, but I agree that under certain circumstances I have just witnessed today there is no point to do so. Considering the fact that only two students were present the last time and some of them might have no problems catching up, there would be a majority of students who would lose the connection of syllabus´ progress. It is crucial for students to recognize the perspective of material taught and anticipate upcoming development of ideas (like walking on a path) instead of rushing through unknown trails of dark forest.