Yikes. Another couple months. And a lot has happened: I experienced senioritis firsthand, our house has been rendered uninhabitable by a kitchen remodel (so we’re living out of suitcases in friends’ spare rooms), and my first year of actually teaching stats has drawn to a close.

It is time to reflect.

My tendency is to flagellate myself about how badly I suck, so (as suggested by Karen E, my brilliant and now former assistant head of school, we’ll miss you, Karen!) let me take a deep breath and report first on what seemed to work. Plenty of time for self-flagellation later.

### Resampling, Randomization, Simulation, and Fathom

The big overarching idea I started with—to approach inferential statistics through resampling à la George Cobb—worked for me and for at least some students. It is not obvious that you can make an entire course for these students with randomization as the background. I mean, doing this is mapping an entirely new path through the material. Is it a *good* path? I’m not certain, but I still basically believe it is.

To be sure, few of my students got to the point where they automatically chose the right technique at every turn. But they did the right thing a lot, and most important for me, I never had to leave them in some kind of mathematical dust where they made some calculation. For example, (and I may be wrongly proud of this) we got through an entire year of statistics *without* introducing the Normal distribution. This may seem so heretical to other teachers, it deserves a post of its own. Later. The point here is that no student ever was in a position of calculating NormalCDF-of-something and not understanding what it really meant.

Did they perform randomization tasks and not really understand? Sure. But when they did, they did so “closer to their data,” so they had a better chance to fix that non-understanding. They didn’t rely (for example) on the Central Limit Theorem—which, let’s face it, is a black box—to give them their results.

### Fathom and Technology

Fathom was a huge suggess throughout. It was great to be able to get them all the software and assign homework in Fathom. They enjoyed it, and really became quite adept at using the tool.

One big question was whether they would be able to use the “measures” mechanisms for creating their own simulations. Basically, they can. It’s a big set of skills, so not all of them can do everything we covered, but in general, they understand how to use the software to implement randomization and simulation techniques. This goes hand in glove with actually understanding what these procedures accomplish.

We also became more and more paper-free as the year went on, setting and turning in more and more assignments as pdfs. The “assignment drop box” wasn’t perfect, but it worked well enough.

### Starting SBG

I decided to try standards-based grading, at least some local version of it, in this first year. On reflection, that was pretty gutsy, but why wait? And it worked pretty well. Most importantly, students overwhelmingly approved; the overall comment was basically, “I like knowing what’s expected.” Furthermore—and this may be a function of who the kids were more than anything else, bit I’ll take it—there was hardly any point-grubbing.

It is also satisfying to look over my list of 30-ish standards and see that

- They largely (but not completely) span what I care about.
- They set standards for different types of mastery, ranging from understanding concepts to using the technology to putting together coherent projects.

They need editing, and I need to reflect more about how they interact, but they are a really good start.

### Flipping and Video

At the semester break, I decided to take a stab at “Flipping the Classroom.” This was a big win, at least where I used it most—in giving students exposition about probability.

There is a lot that can go wrong with videos as instruction (the Khan brouhaha is a good example; see this Frank Noschese post for a good summary of one view) and I want to explore this more. But the basic idea really works, and the students recognized it: if it’s something you would lecture about, putting it on the video has two big plusses:

- They can stop and rewind if they don’t get it
- You can do it over til you get it the way you want. No more going back and saying, “when I said
*x*it wasn’t quite right…”

My big worry is that if I assign videos as homework, hoping to clarify and move on in class, that the lazy student may *watch*, but will blow off *thinking*, assuming that they can get me to cover it again. I need to figure out a non-punitive way around that problem; or maybe it’s not so bad simply to be able to use class time for the first repetition…

### Some Cool Ideas

Besides these esssentially structural things, I had some frankly terrific ideas during the year. Some I have mentioned before, but let me list just four, just as snippets to remind me what they were; later if I get to it I’ll elaborate:

- Using sand timers and stopwatches to explore variability.
- Going to the nearby freeway overpass to sample cars.
- Using the school’s library catalog to do random sampling.
- Going to the shop to make dice that were not cubes.

There were other curricular successes such as using old material from *Data in Depth*—particularly the Sonatas—for work during the first semester.

### Wonderful Kids

I can’t say enough about how much I appreciate the students. Again, I could do better at helping create a really positive class culture, but they did pretty damned well on their own. They got along well, took care of each other, exchanged good-natured barbs, were good group members and contributors.

Even the most checked-out seniors, already accepted into college and having reached escape velocity: they may not have worked very hard outside of class, and assignments may have slipped, but in class they were engaged and still learning. And some juniors did strong, strong work that will make writing college recs easy next year.

And I got a couple of those letters—teachers, you know the ones I mean—that make it worth the effort.

So all in all, a good year. Much to improve, yes. But it’s worth savoring what went right.

So exciting to read what worked for you this year! I would love to hear more about how you did SBG though. I did it this year in Alg2 but still working my way through how to do it in AP Stat.

Thanks so much!

I enjoyed reading these entries, even when I didn’t understand half of what you talked about. I enjoyed your presentation at Asilomar, and maybe one day, if I have to take a statistics class, it will all make more sense.

For now, I appreciate you as a teacher passionate about teaching well and doing right by his students!

I’m also very interested in how you did SBG in AP Stats.

As a newer AP Stats teacher, I’ve borrowed many of your ideas for my classroom and I can say that my students are better off this year than my students last year. Thanks for the great blogging!

Thanks! In answer to your first paragraph, note that my class is

notan AP class. My experiences may still be relevant, however, and I’ll be reflecting on that soon and posting my (drafty, mutable) standards for everyone to tear down to the studs, move a couple walls, change the plumbing, fix the dryrot—ack! I’ve got our remodeling project on the brain….Hi Tim,

Just returned from a beautiful and relaxing vacation and found your post. I started my own blog (confidentlylimited.wordpress.com) in which I plan to work through SBG for my AP Stats class (as well as for Algebra 2). I also plan to introduce randomization techniques in teaching AP Stats, but since the AP curriculum is pretty much set in stone (for now) it will be a challenge to meld the standard curriculum with randomization. It will be interesting to see if we can draw some common conclusions from all the stats teachers who are trying SBG and/or randomization. Look forward to more exchanges of views.

One resource you may be unaware of is a new AP-worthy text by Lock, Lock, Lock, Lock, and Lock. (I am not making this up). One of them is Robin Lock, of Rossman, Chance, and Lock,

Workshop Statsiticswith Fathom. They apparently introduce everything with randomization. It may be a good resource; check out their current web page.Thank you for your reference. This would be the third textbook that I know of which emphasizes teaching statistics through randomization. The first is the Tabor/Franklin text ” Statistical Reasoning in Sports”. It is extremely well written as one would expect from these two and even though it is geared to applications in sports, it encompasses everything in a first-year stats course, not only inference. The second (in preparation) is “An Active Approach to Statistical Inference” by Tillman et al (Hope College). This does both randomization and the algorithmic approach. Looks like George Cobb’s vision is beginning to take textual shape.

It remains to be seen how students respond to this approach.