Straight Walkin' With Statistics - Day #1
Lesson 11 of 21
Objective: The students will gain further access to statistical concepts and data collection by identifying key properties of a normal distribution and extending those properties to a new setting. They will also continue their practice of critiquing a study and identifying a multitude of variables that can arise.
As the students enter the classroom, I prepare the YouTube video for viewing. This video sets the stage for the lesson investigation. Entry events like YouTube videos are nice to mix into lessons from time to time because they really peak the students interest! Plan to allow 4-5 minutes to discuss the video after its viewing. The students may have individual stories that connect to the investigation, or perhaps they have tried something similar in the past. Do you think that we can walk in a straight line when it is dark, or when we do not have the luxury of looking at landmarks?
After our conversation, I explain to the students that they will once again participate in data collection for our new study – we will be walking blindfolded (SAFETY FIRST!) through the field house. Walking blindfolded, how far can you go before you deviate from a straight line? I ask the students things that they think they will see from the data.
- What type of study is this?
- How spread out will the data be?
- What do you think the max and min will be?
- What do you think the data distribution will look like?
- How do we ensure accurate data collection?
- What variables do we need to identify and control?
- What variables do we need to identify and control?
Take time to quickly write these responses on the board. It is fun to look back at the initial guesses after the study! (HSS-ID.A.1 will also come into play here, how can we represent this data?)
Blind Walk Data Collection
Once we have talked at length (well, really 5-6 minutes) about the study that we are about to conduct, it is time to gather some data! Fortunately for me, our school has a gigantic field house that the PE classes usually vacate during the warmer months. Starting at one end, our field house is nearly 300 ft. long (obviously 100 yards). I use a large measuring tape to mark off every 5 yards. If you do not have the luxury of a field house, a hallway will work just as well as long as it is free from sound! (The absence of sound is important because it prevents the students from picking up queues from their surroundings... try it, its actually easy to do!) As the students identified in the opening activity, participants who hear sound will have a better sense of direction than those who do not!
Since I am using the wide open spaces of a field house, I also use cones from the PE department to create “out of bounds” lines. When the students step out of this 10 ft. wide zone they will be considered eliminated and a data point will be collected based on the yard marker nearest to them. Prior to this particular lesson, I ask my students to bring in old t-shirts so that we can roll them up and cover up their vision. I also bring 3-4 headbands to help hold the t-shirt over the student’s eyes. It is best to make participation completely voluntary; however, almost all students will be eager to participate!
SAFETY FIRST: Do not take this activity for granted! It may take a little more time, but I do not let more than 2 students start down the line at a time. I also pair each student up with a safety buddy to ensure that they do not bump into any walls, or trip over any cones. The safety buddy also tells them when they have left the straight line zone, so that the data point may be
collected. If you are conducting this study in the hallway, be sure the students walk with their arms out in front of them. Again, BE VERY CAREFUL and keep an eye on your students!
For the activity, I tell the students that I would be happy to keep the data collection for the class – I tell the students that their primary job is to get accurate results and stay safe. When we get back to the room, I will share the data set for the students to copy down.
Initial Dive into the Data
Once we retreat back to the classroom, I display all of our data on my Apple TV (it is REALLY handy to take down the data on my IPAD and then be able to throw it up on the screen right when we walk through the door… no time wasted!)
As we begin to look at the data, I ask the students for ways that we can check to see if the distribution is normal. Although we have not explicitly answered this question in class, the students should have an idea of the qualities of a normal distribution from previous class sessions. I am “fishing” for a few things from the students:
1) How does the mean compare to the median? These should be relatively close in a normal distribution.
2) Where does the median fall within the quartiles?
3) How does the data look in a box plot? In a histogram?
4) FINALLY: What dangers do we assume when we are trying to test a relatively small number of data points (approximately 30 is not very many) for normality?
Due to the time that it took to collect the data today, we will not end with a traditional conclusion to the lesson. As the students head home with the data set to answer the questions above, it is important that we equip them with tools to make their life easier!
A few additional points:
1) If you have extra time, revisit the student’s initial assumptions that we wrote down in Section #1.
2) Assign the worksheet as homework and tell the students to come prepared to share out their findings, as well as any cool stats aps/calculators that they came across!