Applied Abstractions

When I teach a topic I haven't taught for a while, I usually refer to some old texts, my course notes, and the internet for new ways of presenting the topic. In my statistics class we were to cover Bayes' Theorem, a topic I have always enjoyed presenting, but never felt that I got quite 'right'. Students seemed disconnected from the idea, and weren't able to answer basic questions about the idea during the first lecture. To address this I wanted to create an activity where students were to apply Bayes' Theorem in a relatively simple way. Searching the internet I found the article (an essay really) An Intuitive Explanation of Bayes' Theorem by Eliezer S. Yudkowsky, and thought it did a good job explaining the basic idea, and even includes different presentations of the same example. These different presentations are used to discuss innumeracy in health professionals, but provided me a variety of ways of presenting this example. After some self-editing a

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I've discussed what I wanted for this experiment activity, what my plan was , and now I'll talk about how it went and what to change in future activities. Overall I thought it went pretty well, but there were a few major changes that had to be made on the fly. The biggest one being the math tests themselves; I completely underestimated my student's basic math ability and we came up with useless data. Someone mentioned that they thought it was part of the activity, and was a great way to show how 'messy' statistics really is. I'm glad they thought that, because I really didn't anticipate it. The initial discussion of how to construct this experiment was useful and demonstrated a number of ideas we discussed in class. Controlling for certain variables turned into a big part of the discussion, namely how to control for people with natural math ability. We decided to do a paired sample, pairing those people of the same math ability by their score on the first

After the last post I spent some time thinking about my options for an experiment to do in-class that fulfilled all of my requirements. After some thought I decided on the following plan. Claim to the class that I have a logic puzzle that I believe will help people with their math skills. I want to be able to put something on my website saying that this puzzle helped people with their math by some incredible percentage. Walk students through how I was to do this, including samples, factors to control for, and how to create the tests. I guided the conversation so that we would also collect information on how long ago they took their previous math class, to ensure that the control and experimental groups had a variety of math ability levels (measured by an initial test), to anonymize the results, and discuss how we would use the class setting in the most appropriate manner. I created a packet with all the necessary tests, the puzzle, and data recording forms. When printed I assign

This Wednesday I've scheduled an in-class activity that relates some of the ideas we've discussed in my Statistics I class. So far they include surveys, descriptive statistics (mean, median, quartiles, and standard deviation), sampling, experiment design, and observational studies. Writing this on Tuesday morning, I have nothing written down but I have a couple ideas of what I want this activity to include: Perform an experiment and/or an observational study. I covered what these are in a lecture, but I really want them to attempt one (or both) on their own so they get a concrete idea of what they are. Doing both would be best since they would then be able to compare the methods of both. Take appropriate samples based on the research question. Ideally this would be done with students in the class so they can see how to take appropriate samples. Compute and use descriptive statistics to compare and contrast different samples. Quantitative reasoning and analysis are a core f