What I learned this summer: Probability and Statistics

This summer I taught something new. Statistics for middle school mathematics. I had a blast! The approach we used was to use investigations of data to build statistical reasoning. Many curricular tasks focus in hard on the vocabulary and definitions statistics and then quickly move on to the procedural instruction on how to calculate these statistics and how to create graphical representations from that data. Very little time is spent designing and enacting investigations, creating good meaty questions, and then on the other side choosing representations and interpreting the results.

I quickly realized that the separation of probability from statistics is a mistake. This may seem obvious to others, but interpreting probabilities is directly linked to interpreting results from investigations. Trends and likelihoods are the same thing. Fair games are like designing an investigation that collects data equitably and without bias as well as choosing a statistical tool that fits the question. I don't know if teachers have been teaching these as linked ideas or not. My middle school teacher group reported that in their curriculum, probability tasks are separated from statistics tasks by months in the scope and sequence, and that they purposely teach statistics right before the state test to make sure kids will remember the procedures. **SIGH**

I also realize without a strong understanding of probability (e.g. certainly is rarely guaranteed, and that chance has no memory), the general population does not understand the responsibility of science to be transparent about their predictions, and honest about the level of certainty. For example, if a study on climate change shows a 99 percent chance that a cause is linked to the effect, this is pretty certain! The slightest chance of something being one way or the other make people doubt the predicted outcome. This happens in gambling or lotteries as well. People think "Well there is a one-percent chance that the prediction/correlation could not be true (we have human influenced climate change OR you will not win money), so I am going to believe the less likely outcome instead.

Last, I learned that I LOVE box and whisker graphs and dot plots. Honestly, it is true, until you teach something you don't really know it. Yes, I have used these tools in research, but it felt different teaching it, and teaching them conceptually, created from real messy data. Below are some photos taken from my group. We collected data on the first day about the groups favorite math topic, years of experience and certification. Teachers, the next day, created an investigation based in the data (yes, I know the investigation could have begun with a question, design of data collection, blah-blah-blah, but this was truly spontaneous). One question arose as they studied this data was, "Does alternate certification have a relationship with years of experience?" Here is the table of data and the results. Does certification type predict years of experience? Why might it be related?

Next, we wondered about the relationship of favorite topic to the other two questions. What do you think? Is this a good question? Why? Why not? What kind of representation could support answering this question?

In a couple of weeks, I am teaching another teacher group, and then after that we will be interviewing middle grades students to investigate their statistical reasoning and then teach a lesson based on what we learn about them. Can't wait!