Stats is hard sometimes
We spent the first three weeks working with one-variable statistics: measures of central tendency and spread and understanding normal distributions and standard deviations. I pulled a lot of activities and problems from the Interactive Math Program, a really great high school textbook series for integrated Math. This unit was so rich in applications and connected well to the probability theory students studied last year.
The first project that brought things together for students had them analyzing the massive international data sets available at gapminder.org/data. Students picked a particular set of data that was interesting to them (anything ranging from infant mortality to literacy rates to square kilometers of forest) and analyzed it for the world over a period of several years using statistical measures, as well as for the United States and another country (I asked them to use a country in which the foreign language they're studying is spoken so that they could report on their findings in their language class). Full directions for the project here. Great way to get students to be excited about means and z-scores! I was blown away by their projects - lots of students researched to learn more background about their question and to explain the differences in the world data vs. what was happening in the U.S. and the other country they analyzed. The presentations took an insane amount of time though, what with students going way over the recommended time frame, technology malfunctioning, and two fire alarms that happened on consecutive class days. Teachers who have students present their projects in class, any suggestions on structuring this better? Classmates were attentive and asked good questions (I had them give feedback to each other that was shared so that helped with engagement, I think), but it took a loooooong time. Given how little time I have this year to teach so much content, I was hyperventilating a bit at giving away a full week for presentations.
Counting up observed values of M&Ms
Our final unit project is for students to design and conduct a research experiment on a question of interest to them and analyze their results using hypothesis testing. These are due next week and I'm very curious to see what results they generate.
The one complaint that students have had, and one that I really want to resolve, is that they feel like they don't conceptually understand all of the formulas. I did try to derive with them as many as we could, but some (like the formulas for sampling error) require more math than we currently have. This is something I've struggled with before... should we only be using and working with formulas/theorems that students are capable of deriving or at least being able to recreate the derivation of? I hate waving a magic wand and pulling formulas out of thin air (or at best, giving promises that one day, if they take more advanced statistics and probability theory, they too will be able to see behind the smoke and mirrors). Bleah. I love that students are dissatisfied with simply receiving formulas from on-high, and I want them to continue expecting rigor and proof in what we're doing. How do others make peace with this?