Seeking in the MTBoS

A recent post by Greg Taylor got me thinking about what I'm actually looking for when I started to engage in the MTBoS (Math Twitter BlogoSphere).  Initially, I was just exploring the space to see who and what was even out there, hoping there would be somebody who would want to help me develop my new Statistics class (about 2 years ago).  Since then, I have just been content with finding stats teachers on Twitter and following their blogs.  My best discovery, Glenn Waddell's blog, has supplied me with all kinds of good ideas that I've put into practice.

TMC14 (Twitter Math Camp) was awesome last week.  For the first time, I feel like I was finally able to meet all of these people I saw online, along with a ton of other stats teachers who I had no idea existed (I have a feeling they didn't know I existed either).  More importantly, I started to get to know this group of awesome people and see the huge variety of personalities, types of schools, personal interests, etc that is just hard to see through a Twitter feed.  At the same time I met people in real life, I finally got some traction on understanding how to communicate with this group via Twitter, a skill that will serve me year-round.

Getting back to Greg's post, I had my first negative reaction to my awesome week after reading.  It triggered the realization that I didn't find what I was looking for deep down -- somebody who wanted to completely take apart and redesign high school stats.  Everyone seemed to have a basic mental framework for how stats worked and wanted to incorporate new activities, ways of explaining, and tech tools into that framework to improve their course.  I wanted to completely dismantle the course and build it back up with the core elements I value -- real-world application, fun and engagement, minimal homework, and lots of student autonomy.  Over the past couple of years, I've been doing this on my own since I've been fairly unplugged with the community (my class site, my rationale for my outline), but I want that to stop.

So my plea: is there anyone out there who just feels like stats class is fundamentally flawed, who is willing to break completely from a textbook, who wants to try full-on project based learning in stats?  More than sharing lesson concepts or activities, but a full-on commitment to design a new course that we co-teach during the year?  I hope the design process we engage in leads to the ability to reuse many of the videos, homework problems, projects, and assessments that we've used before, but if it doesn't and that reason matters, I want to build out whatever resources we need.

I'm so thankful one of my co-workers was open enough to teach my current version of stats with me this upcoming year so he can question and help me refine the course.  Maybe, once we get into the thick of the school year, I won't feel this isolation with stats anymore.  However, I still want a teammate in the thick of the design process (now) who is as bothered as I am by typical stats classes and thinks there is something to be found by creating an effective project-based curriculum.  I don't care how much or little you know about stats -- I was clueless two short years ago.  I just want somebody with the same mindset and goals.  Thank you.

TMC folks like to play

I'm was a first-timer at TMC (Twitter Math Camp, which is a real thing) this past week down in Jenks, OK.  If I had to describe it in a sentence, it is a gathering of passionate math teachers who actively blog, comment on each other's blogs, and tweet at each other year-round to improve their practice and be a community.  The TMC crew is incredibly open and responsive to newcomers.  As a group, I also noticed a surprisingly high level of emotional intelligence when interacting in person.  It was easy to listen in and be listened to.

Only after a couple days did I pick up on my biggest insight: TMC teachers love to tinker and play.  Justin L was sitting one night playing with ways to generalize a parabola without completing the square.  Edmond spent a few days playing with paper cutouts so he could let others build an awesome 3D soccer-ball-like shape.  I've been enjoying recent posts from Jonathan and Glenn as they talk about playing with different structures of the curriculum in Algebra 2.  Malke was busy every night in the lounge inventing new math dances.  Even when I look at the thing people found most interesting that I worked on - a simulation of Ultimate Frisbee that is used to replicate the Moneyball process - it was not the most time consuming thing I worked on to make my stats curriculum.  It was the most playful thing - something I made on a whim the weekend after I saw the movie Moneyball for the first time - because I thought it would be awesome to do.  Once I started to notice the playful attitudes most of the other TMC campers took, I noticed it everywhere in the group.  And I couldn't help but notice that teaching kids to play with math is something we, or at least I, almost never teach or even encourage in class.

How I organize statistics

A few discussions at #TMC14 and a recent Twitter conversation with @pamjwilson reminded me how differently I organize the topics in my statistics class.  Instead of trying to explain the what and why of this in 140 characters or less, I made this.

The AP Stats standard syllabus, the golden standard for even non-AP high school statistics classes, organizes the course into four major themes: exploring data (summary stats and graphs), collecting data (sampling and experimental design), anticipating patterns (probability), and inference (confidence intervals and tests).  The groupings make a lot of sense once you have a good idea of how stats works.  They also make a lot of sense if you are efficiently covering procedures through the textbook.  However, I don't think to do a good job introducing the new student into how this collection of procedures can be put to use.

When I completely pulled apart my class and abandoned textbooks, I started with a set of interesting projects first, and then worked backwards to attach relevant topics from the syllabus to the projects.  This took a couple of semesters to iterate, but eventually I noticed a beautiful thing - you could go through a complete flow of collecting, describing, and performing inference on data with every project.  In addition, a natural break between one-variable techniques and two-variable techniques emerged.

Starting with one-variable stats, for the purposes of AP Stats, you can have either quantitative data (numbers) or categorical data (multiple choice options):

• One-variable data describes a population, so you can either perform a census or take a representative sample (SRS or equivalent).
• Once data is collected, it can be summarized (quantitative with center, shape, and spread, and categorical with proportion).
• It can also be graphed (quantitative with histograms, dot plots, and box plots, and categorical with pie graphs and bar graphs).
• If you collected a representative sample and want to know how precisely your data predicts the actual population, you can simulate a sampling distribution and create a confidence interval.
• You can also check that your data provides sufficient evidence to prove a prior hypothesis incorrect by calculating a p-value.
• Finally, I end the cycle by asking students to communicate what they did and what they now know by writing or presenting their process and conclusions.

Now that students have a conceptual overview of collecting, describing, analyzing, and presenting data, we repeat the full cycle with two-variable data.  The first cycle I do is analyzing two quantitative variables:

• Difference in purpose of two-variable analysis (not to describe a population, but to identify relationships between two characteristics/variables within a single population).
• Introduce observational studies.
• Create scatter plots, discuss correlation vs. causation.
• Perform regression and create a model to predict one variable given the other.
• Use a confidence interval or test of the slope to better understand the variability in the model.

I repeat the full cycle one final time with a categorical explanatory variable (group A vs. group B) and either quantitative or categorical response variables.

• Teach experimental design as a way to create two groups that are identical in every way except one key characteristic.
• Compare two sample data graphically (quantitative response with stacked box plots, categorical response with adjacent bar graphs).
• Compare two sample data with confidence intervals and tests to establish that the groups are statistically different (or not).
• End the cycle again with students presenting their conclusions in context.  A statistically significant difference between groups means that the explanatory variable affected the outcome.

If you think that looping this process so many times would require far too much content in the first cycle to effectively teach inference, you are right, unless you teach only the concept and skip the calculation.  I use StatKey, a free, iPad-compatible online simulation calculator, to perform all initial inference calculations with students.  This prevents me from formally having to introduce the normal curve and its probability calculations, lets me skip most of the Central Limit Theorem, and lets me completely ignore the nit-picky assumptions of most intervals and tests.  By the time students get through all of these cycles, they have such a better conceptual foundation for everything we're doing that it is far easier to go back at the end and properly teach probability.  It is simply giving a new technique to calculating numbers they already understand via simulation, but now can understand via the magic of the normal curve and Central Limit Theorem / Binomial Theorem.

If you want a living example of how this organization works, check out my class website.  This fall, I am further modifying it to better use projects to motivate each cycle without having to frontload the content first.  Please comment if you have questions or can push me to think differently about how this is setup.