2009/11/30

Journal Entry #10

This was my last observation in the class which review sample distribution and use of confidence intervals on calculators. I tried to distinguish clearly metacognitive processes of the teacher and students. While Ms. Ringquist was lecturing on sample distributions by using technology (screening on the white board), the students were paying attention in order to process information presented. Other topics included Central Limit Theorem and taking sample averages, both already covered. Ms. Ringquist gave them always enough time to copy from the white board, but not too much so that they could lose their attention. The students were not interacting a lot with the exception of participating during the lecture. Therefore, they were happy to play the Greedy Pig in the middle of the lesson. Another exam is approaching and therefore no new material was explored today and the students had time to work through homework examples.

The example of sample statistics, for example, revised the standard error idea and the confidence interval. If the confidence interval is exactly 95%, the multiple of standard deviation is not 2 but 1.96 (because of the shape of Normal distribution). Therefore, I found it very interesting to solve an example illustrating that, in order to have 3% margin of error (1.5% to each side of a mean value) for big sample size, it is necessary to chose the sample size of 1,068 at most. This example was presented through an application of presidential elections. If each candidate has certain probability to be elected (and the is the chance to be not elected), and if that is 0.5 (so the product with the other probability is the biggest possible, i.e. 0.5×0.5=0.25), then by the definition of standard deviation, sampling large samples and confidence intervals, it is enough to ask a sample of 1,068 random people to be 95% sure about the 3% interval for the event of being elected. Up until now, I was wondering why back home in Slovakia statistic companies always used a (somehow magic to me) number 1,068. And here the explanation was. J

Overall, I would say that this revising lesson had a pretty standard format the teacher, students and even I are used by now – revision of main ideas presented by the teacher and then students’ questions about previous homework examples. It is for sure that this lesson was not designed to engage students by its activities, but rather by the content presented that is interesting enough to think about.

2009/11/23

Journal Entry #9

Do you remember the student I named Matúš and I mentioned earlier? Well, when I walked to the classroom today, the class has just started and he was sitting aside on a special seat. While all the other students were behind desks, he was occupying a small lecturing chair with a small desk mounted on it. I do not know the exact reason for that but I assume that some discipline issues might have occurred. If I was a teacher and I agreed with students on their seating preferences as long as they are fine, and some students breaks the deal, then fair enough – s/he has to bear consequences. And this temporary warning for Matúš should work because he is a confident student who is not going to suffer his ego. If he was a different type of a student, let´s say a shy person who barely speaks, this kind of a punishment would be definitely inappropriate. That student could suffer a trauma from public humiliation, as s/he could see it. But for our Matúš, it was certainly not going to be a problem, as I have already said. He seems to be a very intellectually gifted student who is aware of his own misbehaviour. And he needs a strong authority showing him when enough is. I wish I could have seen what had to happen a class before. The individual seating had a positive effect and, actually, Matúš kept making some jokes during this lesson too. But nothing too extreme happened; he behaved as usual. He had leave a lesson in the middle because of his other commitments.

This lesson was about expanding the knowledge on the model of Central Limit Theorem (CLT). Ms. Ringquist first revised the conditions that there is a random sample with some probability and with large enough repetitions/trials. Together with students, she worked through a example on the whiteboard that revised how to normalise a Normal Random Variable with bell-shaped symmetrical curve. I saw that students worked through a project recently – they individually got some random values that actually composed into a Normal r.v. They stick sticky notes on the blackboard on the back side of the classroom and that is what I could see. There were in multiple groups and those with small sample sizes had, naturally, big variation.

Today, similarly, the students were working individually to illustrate that if we repeat a certain random event multiple times, we can be quite confident about predicting its results (the CLT). Yet today, the students expanded their knowledge and got to know about confidence intervals. Ms. Ringquist prepared an investigation task that consisted of a table where we (yes, I was participating as well J) could enter our results. We, individually, were supposed to toss thumbtacks fifty times and record whether they ended up down or up. Then we calculated cumulative proportion of ups (let´s say 3 out of 5 or 25 out of 43 in my case) and answered a sheet of logically connected questions. First we saw what probability value the thumbtacks approach, then that they seem to follow the Normal model of which we could calculate standard deviation and finally defining our confidence interval as the interval of the Mean plus-minus two standard deviations (Mean in this case is the probability that a thumbtack ends up “up”). But why 2 standard deviations? The Normal distribution covers 95.5% of all outcomes and, in other words, we can be 95.5% sure that the real Mean is in that confidence interval. After all the students got a certain confidence interval, we could compare them on the blackboard in the back of the class and see where approximately our true probability (Mean) should be. Of course, there were a few cases when the thumbtacks behaved way too off from all other cases. That could have been due to the fact that Ms. Ringquist mixed two boxes that might have included some defected (or off-centred) thumbtacks. Therefore, not only had the students learnt new knowledge and skill, the teacher also found out what to do the next time better.