We spent the last four days in beautiful San Antonio learning from many great stats educators (thanks Doug, Josh, and others) and eating tacos. Luke and Lindsey also facilitated a session titled: Statistics and the Redesigned SAT. Here are the highlights:

 

Simulation Based Inferential Thinking and Reasoning

Doug Tyson took us through the “Can you smell Parkinson’s?” activity, in which participants used simulation to model a chance process, made a dotplot of results, and then used the dotplot to try and answer a question.

Josh Tabor took us through the “Does caffeine increase pulse rates?” activity, in which participants used simulation to model a chance process, made a dotplot of results, and then used the dotplot to try and answer a question.


The Stats Medics went through the “Does Beyonce write her own lyrics?” activity, in which participants used simulation to model a chance process, made a dotplot of results, and then used the dotplot to try and answer a question.

Are you sensing a theme here? It became clear this weekend the power of simulations (and dotplots) to get students thinking inferentially. All of these activities are extremely accessible (no prior knowledge required) and allow us to get students to think and reason about significance testing and P-values without all of the formal language and calculations.

Inferential thinking and reasoning exists at many levels and must be grown throughout the school year. Here is a possible progression of questions that take students from the experience of the activity to the formality of significance testing:

 

Questions for Inferential Thinking 

  • Is this result surprising?
  • How far is this result from what is expected?
  • Does the result provide some evidence for a claim?
  • How likely is it we would get this result, purely by chance?
  • Assuming some claim is true, what is the probability of getting this result (or more extreme) purely by chance?
  • Does this result provide convincing evidence for some claim?

These questions should not all happen in one lesson. In fact, it is probably best that there is time in between each of these questions. Students accumulate new knowledge throughout the year, which unlocks their ability to handle the next level of questioning (or to think about that question deeper). Think of the original activity and simulation as planting the seeds. We will then water the plant throughout the year until it blossoms when we get to formal significance testing.

One of the keys to this success is the teacher’s knowledge of the end goal and the thinking skills that students will need to reach this goal. I most certainly didn’t know this in my first years of teaching statistics (in my first year, I didn’t know what a P-value was until I got to that chapter!). But once I became familiar with the content, I realized that the whole course is designed to build up to the end goal: success in inference. And this success doesn’t happen purely by chance. We need to be intentional in growing ideas throughout the year, to build the story of inference.

NCTM Annual Conference 2017: Build the Story of Inference