Common Core Standards: Math
7. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Students should understand that when they're being asked to understand statistics, we're expecting them to understand statistics. Textbook mathematics does not equate to real-world problem solving abilities. Knowledge does not imply understanding.
It's easy to jot down a formula here and there (or punch it into a TI-89) and plug in the x and y to get z. It's a lot more challenging to understand what x, y, and z are, and why we use that formula and not another one.
Whether students know an equation or not is rarely relevant. Equations can always be looked up. What's more important is that students are able to logically analyze a situation (without any math as part of a problem), and explain why a certain approach should or shouldn't be used.
This forces students to not only analyze the problem itself, but also to justify their approach from a logical perspective. Logic, in the world of statistics, can only come about from a deep knowledge of fundamental concepts applied over and over again to different real world scenarios. Only then does the answer become "logical" as opposed to "difficult."
Students should eventually reach a point where instead of struggling with every problem, they react with, "Duh! Obviously!" and quickly move on. This is a sign that they've learned and internalized the logic behind the problems. Or that they're cheating.
That's why it's not enough to just say, "Duh! Obviously!" and scribble down an answer. Students should be able to explain why their answer is not only correct, but logical as well.
Some examples for classroom exercises and learning approaches include:
- Critiquing decision-making process before, during, and after an event's occurrence based on simple probability concepts. This can include decisions in sports, research, and so on.
- A class-wide discussion on a particularly difficult approach to analyzing a situation (such as a science article). Look into how they accounted for confounding factors, what the confounding factors could have done to the probabilities involved, and so on. Do the results actually provide any insight into the supposed population? Was the sample correctly identified and gathered? How would this influence results and probabilities?
- A critique of an article with a poll in it. Find out the source and methodologies of the poll to understand why it may have been incorrectly conceived and how the results may not actually represent the journalist's supposed population involved.