The goal of this investigation is to provide students with the understanding of how normality is determined in a real world application (MP4). Traditionally, most “textbook” problems imply normal distribution right from the start, and don’t ever confront the students with this important primary thought process. That is why the ensuing discussion is so important!
I theme the introduction to our discussion in the following way: (MP2)
Baseball Player: Would you show up to your next double header with a tennis racquet?
Band Member: Would you show up to the next home football game with a basketball?
Football Player: Would you show up to Friday night’s game with pom-poms?
CLASS: Would you apply properties of the normal distribution to something that is not normal?
Soooo… THIS is why we are spending all of this time trying to figure out if our data is normally distributed! We have to know what tools to bring to the game! We have already talked about the pitfalls of using a small sample population, but it is going to be impossible for us to test everyone in the world. Although we have a limited sample size, we can still analyze the data to see if it appears normal.
But how accurate are we with our assumption of normality?
This is where I roll out the appropriately named “Confidence Interval” – and EMPHASIZE its connection to the standard deviation. A quick picture on the board is a really helpful tool for the students so that they are not overwhelmed by the calculation. If you are comfortable with your student’s level of understanding on the concept, feel free to introduce them to how they can use technology to make the calculation much simpler! Be sure to compare the answer obtained to the “by hand” answer to see how things align.
After heading to the board to "sketch an overview idea of the confidence interval" - it hit me...
#1: I don't want to run class this way! I always prefer not to be the sole provider of knowledge for my students. I want them to discover the confidence interval through inquiry and discovery - and through my scaffolding in the remainder of the unit...not because I just tell them what it is.
#2: A trip to the whiteboard (where I was the only one talking) would have killed the positive momentum of our lesson.
For these reasons, I adapted my plan. Instead of mathematically revealing the confidence interval, I simply wrote the words "CONFIDENCE INTERVAL" on the board and probed my students to define what it might mean. The result was an outstanding discussion. Through asking follow up questions like Can you give me an example of what we are talking about? the students were able to achieve a working definition of the concept without killing the momentum of the class. After calling this "audible" to my game plan, I went ahead with my original plan of attack and illustrated how this might look on a graph.
Allow the students the time to work on the above worksheet, as well as answer any questions from the previous Day #1 Worksheet. During this time, I fly around the room visiting students. I work hard to create a high-energy atmosphere with a lot of positive reinforcement. I emphasize NOT getting write answers, but being able to understand and explain mathematical thoughts. The students should finish completing the Straight Walkin’ With Statistics – DAY #2 Worksheet for homework.