This past semester has been an emotionally grueling one. After my initial foray into this topic in my first blog post (exploring the balance of skilled practice with true mathematical inquiry, pursuing authenticity of the discipline), I began to see just what I was up against. Not only because I ambitiously decided to “gut renovate” most of the semester’s content, but also because I have never seen students explore this concept of “normal” in such an up-close and personal way. After two projects exploring how to apply statistical representations, central tendency, and normal distributions, students are certainly eager for all of this messy world of statistics to finally click into place. As a collective, my students are grappling with more complex questions about statistical relationships, correlation, causation, and want to be able to make the ambitious claims that explain the world’s patterns around them.
And that’s where I precisely slow them down.
I’ve learned that there have been complex layers of “skills,” particularly when we explore how to use and apply statistics. In addition to all of the vocabulary, graphing skills. numeracy, and computational skills involved with using data representations, students have gone through many iterations of developing questions.
In Project 2: Class Competition, students investigated which of my 3 classes was the “best,” in a manner of speaking. On simple large sheets of brightly colored paper, students crafted their own variables and metrics for evaluating which class was the “best.” After many, many rounds of feedback, trial and error, and persistent frustrations with Googlespreadsheets, where students able to make deeper connections about the many layered factors that one considers in a “great” class—beyond simply student grades. This translated to an eye-opening seminar in which many students ultimately made the conclusion that despite the arbitrary “wins” we could identify through this graphic organizer, there was no concrete way to highlight a class as a “good class” or a “bad class”—seemingly simple, yet complex lessons in classroom culture to have over, and over, and over again.
In project 3, we had a few more complex ideas to explore. In this guinea pig year of Statistics, I personally grappled with the types of direct instruction/practice students would need to apply some of these heavy terms.
From whiteboard practice (and fun posing) to college-style lecture, students were certainly talking about these concepts in theory.
When it came to our last and final project, which would ultimately become the PBAT, students seemingly had an arsenal of resources to explore “What is normal at ESA?” and to further explore differences between sub-populations at our school. The social implications of breaking up our school community have been plenty—deciding the metrics of responding to questions about “gender,” being highly sensitive to the many ways in which this Census could potentially invade into our students lives—this has all felt like a weighty responsibility. I feel eager to push my students’ understandings in the world of normal distributions, beyond the image of a bell curve. I am pleased when a confident scholar will bout that being “normal” is “vastly overrated,” and even more pleased when students name the role of standard deviation in deciding a “normal range.” But I wish we could have done more—grappled with the diversity of this country, the damning way in which we cram college grades into such a distribution. The fact that “normal” in all respects has changed for the United States drastically in the last 200 years.
The social and authentic implications are almost so varied, I am overwhelmed.
I am eager to explore the concept of “normal” when exploring incomes of NYC residents, especially when we consider the distribution representing the cost of 1 bedroom apartments in this wonderfully frustrating money-pit of an island. The potential to investigate seem limitless. The narrow bridge to empower students–rather than drown them in despondent numbers and graphs–seems like a lofty journey to make. Stay tuned for post-panel meltdowns and realizations.
WOW! Sarah, it is definitely no small feat to completely rewrite your curriculum and you have done so in a way that is so personally authentic to our students. I agree that your essential question has incredible societal implications, and your unit brings real depth to the meaning of using math and education for empowerment. Will you continue this work next semester? How can they build on the work they did next semester to consider what is normal in the city, in the country?