Following the long break since our last class, we reviewed some basic ideas in Probability, mainly the concepts of a procedure or outcome, a simple event, equal likelihood, and sample space. We then discussed the three main approaches to probability (Relative Frequency, Classical, and Subjective) in the light of several different scenarios (e.g. lottery wins, genders of babies born, plane and car crashes) and how certain approaches suit certain situations better than others.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Ditto what I said for Algebra 2. A bit more difficult today, but I'm sure it will pass, like it has before.
As I mentioned in the previous Session Summary, Jared had asked to review these algebra topics, and so I took advantage of the fact that he himself requested to delve deeper into these subjects. Jared worked very hard in both hours.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
We will pick up with Statistics after the break, but I'm less worried about that topic seeing Jared's intense curiosity on the subject, and intuitive understanding of many of the concepts.
Probability - Relative frequency and classical approaches
Lesson Outline
We're beginning to formalize (mathematically) the earlier lessons in which we discussed probability, and probable outcomes and scenarios. Today we discussed the concept of calculating how probable an outcome is based on previous trials versus the probability of an outcome based on the sample space. As in the Algebra class, Jared fully participated in class.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Again, Jared was delightfully engaged for this class. A real pleasure.
I substituted for Diana. We started looking at a TED talk of Jim Simons who used statistics to run one of the worlds largest hedge funds. This started the discussion about how to run a conglomerated business, getting trademarks, financing, etc.
I wanted to review some of the topics in last Friday's math test. I could see that Jared was a bit unsure in solving some of the problems, so we worked through them together. I wanted to iron out any doubts Jared may have had with regard to these concepts, so that he can build solidly on them when we progress. Jared cooperated very nicely in class, and worked very hard (especially considering we had a double lesson of Algebra (see next session summary).
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Jared genuinely appeared to want to understand how to solve the problems he had missed on Friday. He started by being a tad argumentative (in a friendly way, though!) by saying he used 'his method' but was very quick to listen when I showed him how to actually work the problems. His main areas of uncertainty were three-variable systems (although we had worked on them quite a lot last week), mainly he insisted on trying to solve them in his head. I then realized he was hiding the fact that he wasn't all too sure of how to tackle the problems (substitution or elimination) ... so we reviewed the idea behind both methods, and he appeared to absorb what I was showing him. I had started class by giving him a bit of a pep talk, in the sense that I recognize his mental acuity when it comes to (especially) math, and that it's not something to be ashamed of (I used different, gentler words, but I don't remember them now!) if one doesn't immediately know how to tackle something - that's why we have learning. And the point of these problems is not so much to get the right answer (although that is important, too!) but it's to build a set of methodical analytical skills that can translate to all areas of life.
Jared and I systematically recorded the flipping of a coin three times in order to see if certain sequences have more probability of occurring before another sequence. We saw that our results pretty much coincided with the calculated probabilities. I also discussed various real-world scenarios in which the term 'probability' is not taken to mean the layman's interpretation (i.e. 'odds') but instead represents a physical situation, such as one often finds in quantum mechanics. We shall be exploring more of these examples in lessons to come.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Despite having just sat the test in the previous class, Jared was very cooperative and engaged in Statistics. As always, he showed a great deal of interest when we discussed physics, especially our tentative first dip into quantum mechanics.
We briefly discussed what Jared had discovered about the Michelson-Morley experiment, and I was very happy to see that he had researched the subject and had some very relevant questions pertaining to it. We then discussed experimental errors in a larger context (e.g. the consequences of having to combine the signal from multiple elements in an array, such as a radio telescope interferometer) and talked about how propagating errors need to be taken into account. We concluded by discussing the difference between a layman's interpretation of 'probability' and an experimentalist's, or a statistician's.
Assignment
Start thinking about an extended project involving data collecting – to be discussed
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Ditto to the Algebra comments. Jared was much less tense than yesterday. I would like to switch the order of Algebra and Stats tomorrow, Friday, so he gets the Algebra test done and over with. His reward for focusing on classes today, and so demurely agreeing to the test tomorrow, is Probability exercises/games for class tomorrow.
Wrap-Up: Standard Deviation, Variance, Populations and Samples
Lesson Outline
In order to complete the section on Statistics for Describing and Comparing Data and Datasets, we reviewed the principal concepts involved, such as Standard Deviation, Variance, and went further back and discussed the definitions – and implications – of the mean, median, midrange, and mode of a dataset. Today's lesson wrapped up the chapters on the basics of statistical tools, and as of tomorrow we shall put these tools to use in exploring other fields of Statistics.
Assignment
Research the Michelson-Morley experiment and report what were the statistical issues with their experiment
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Jared was far less focused today than he was yesterday. I managed to get him to concentrate partially by engaging him in another game that involves probabilities. But it was a game with which he was familiar, and it was a tad difficult to get him to follow the rules that would highlight how the rules of probability work. I then tried to conclude class by wrapping up the statistical tools section.
We reviewed the importance of the concept of standard deviations, trying to understand the full meaning behind the equation. The standard deviation on its own is a very good representation of the internal spread of a dataset, but its relevance really stands out when interpreting Bellcurves. I illustrated the importance of quoting a result at different significances using the real-life example of the announcement of the discovery of the Higgs boson.
Assignment
Research the history of the press conference announcing the Higgs boson; Express 4s,5s, 6s, 7s as percentages
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We only fully tackled one topic today, but Jared was really focused (albeit for a short time) on the topic. I think we can move on now to the next topics, since I think he has a good handle on standard deviations.
