I Built a Crappy Digital Activity…Here’s How I Fixed It.

In the past 3 years, I have used Desmos Activity Builder in a number of different ways in my classroom: to introduce new ideas, as a formative assessment tool, and to allow students to “play” with mathematical ideas through Polygraph and Marbleslides. An activity I developed last year and re-built this year reminded me of two ideas I need to keep on my radar at all time. First, building an effective classroom activity is really, really hard.  Second, don’t be stubborn in evaluating an activity – it pays to be brutally honest.

races.JPGFor my 9th grade class last year, I wanted an activity which would cause students to think about variability in data distributions, and introduce standard deviation as a useful measure of variability. You can preview the activity here.  Take a few minutes, test drive it, and see if you can suss out the problems.

So, what went wrong.  Well, a number of things – but here are the two primary suspects.

  1. It’s too damn long! It takes way too long to get to a working definition of standard deviation, and by screen 14 students are all over the place.  Using student pacing could help remedy some of this, but I found much of the class losing interest by the time we got there.
  2. I was stubborn! I was looking for a “cute” visual way for students to think of standard deviation as “typical distance from the mean”.  In my zeal to hammer this working definition home, I tried to build slick graphs which lost many students.

6 millionHow to fix it – last year, the Desmos teaching faculty developed the “Desmos Guide to Building Great Digital Activities“.  It’s worth a read (and a re-read) now and then to guide activity construction. In my variability activity, this bullet point from the guide resonated with me: Keep expository screens short, focused, and connected to existing student thinking.  In many of the screens, I over-explained things.  Students don’t want to read when they are completing a digital activity, they want to investigate, create, and explore.  I robbed them of that chance.

citiesToday I tried my new, rebuilt variability activity with 2 classes (slimmed down to 12 screens from 19), and there was a vast improvement in class engagement. There were more opportunities for students to express their ideas regarding comparisons of distributions, and we had plenty of time to pause, recap, discuss and think about next steps.  A number of points from the Desmos Guide drove my thinking:

Ask for informal analysis before formal analysis.  While I kept in the “typical distance” definition of standard deviation, it was only in a small way – we’ll move on to a more formal definition next. Students were able to conceptualize standard deviation as a useful measure, and now can move on to a formal definition.  My old activity felt too “sledge-hammer-ish” and I knew it.

Incorporate a variety of verbs and nouns. I provided a number of ways for students to think about variability and distribution comparisons in the early screens, and strove to build different-looking screens.  This kept the ideas fresh, and students talked with their partners to assess these differences in different ways.

Create activities that are easy to start and difficult to finish.  In the last 3 screens, I ask students to extend their thinking, be brave, and apply new ideas.  For those students who got this far – most did, these screens elicited the loudest debates.  We ran out of time at the end, but we have some good stuff to build off of tomorrow morning.

I’ve learned that it’s important to be honest about an activity.  It’s easy to blame the students when something goes wrong, especially which class heads away from learning and towards frustration.  But performing an activity autopsy, focusing on clear goals, and keeping the design principles in mind is helpful to move an activity forward.

 

EdCamp and My Amazing Principals

alg-ad-snickers-betty-white-jpgThe first week of district PD – lots of meetings, scads of “sit and get” messages, and every administrator making sure their voice is heard.  I suspect what I am describing is not unique to my area. A great opportunity to energize is lost, and the “grind” begins. And I haven’t been too shy about expressing my displeasure through tweets when I am frustrated – I can be kind of a jerk (think of those Snickers ads…better?…better…).

This week my school admin team got it right. And I feel fortunate to work with them. 

For about a year, my school’s admin team had kicked around the concept of a school-wide EdCamp. To be honest, I never thought it would see the light of day…there are just too many other things loaded into the calendar.  So an invitation to work with a team of teachers to organize a high school-wide EdCamp was a true surprise…then the work began.

We planned 3 morning sessions, followed by lunch and prizes.  But beyond the structure of the day, we had a lot of talking-up to do.  Would our teachers, many of whom had never been to an EdCamp, understand the concept?  Would people propose sessions? Could we engage the curmudgeons in our teaching ranks? At our opening faculty meeting, we showed a brief video to help teachers understand the EdCamp concept, then talked it up over the next 2 days.

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The morning of the conference many teachers suggested ideas, asked questions and thought about what they’s like to learn. In the end, we had a nice variety of topics and it felt like there was something for everyone!

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As I walked around during the sessions, I was thrilled to see rooms filled with discussions, and teachers from different departments with an opportunity to engage.  I know there is no possible way every to reach everyone, but I hope it was a day of professional learning for most.

On my end, I offered a session “Activity Builder for the Non-Math Crowd” which seemed to be of use to those assembled. Then later, a session where we just did math – problems from Open Middle, Nrich, Visual Patterns and others let math teacher talk, learn, and think about engaging problems for their classrooms. You can download the problems I shared with this link.

Thanks to the fantastic people I work with for letting me be part of this: Baker, Dennis, Kristina and Melissa.

And a big thanks to the HH admin team: Dennis, Ralph, Tracey and JZ.  I appreciate the opportunity, and promise not to complain again….until the next time…..

 

Baseball, Brain Cancer and Relative Risk

The 1993 Phillies were the most fun team I have ever followed.  I was nearing the end of my college years, and I vividly remember the insane night when me and 3 buddies celebrated a win at 4:30 in the morning, and the exact spot I was sitting when our hearts were broken with Joe Carter’s home run (I still look away when it comes up on highlight reels).

This week the catcher of that team, Darren Daulton, died after a battle with brain cancer.  Newspapers have shared memories of “Dutch” and among the articles is one which reminds us of the surprising number of former Phillies who have passed away due to brain cancer (Tug McGraw, John Vukovich, and Johnny Oates). A revised 2013 article from the Philadelphia Inquirer analyzes the the unusual number of Phillies who have developed brain cancer, and contains many appropriate entry points for Statistics courses.  Some highlights from the article:

  • A comparison of the observed effect to random chance – here a professor of epidemiology summarizes: “You can’t rule out the possibility that it’s random bad luck.”
  • A summary of plausible variables which could lead to elevated levels of exposure, such as artificial turf (which may have contained lead) or anabolic steroids.
  • An analysis of the increase rate of brain cancer among Phillies – here we are told that the Phillies’ rate is “about 3.1 times as high” as the national rate.  A confidence interval, along with an interpretation and associated cautions are also included.

Let’s explore that “3.1 times” statistic…time to break out the technology.


A few weeks back, I attended the BAPS (Beyond AP Statistics) workshop in Baltimore, as part of the Joint Statistics Meetings. Allan Rossman and Beth Chance shared ideas on using their applet collection to explore simulation (see my earlier post using the applets to Sample Stars) along with a “new” statistic we don’t often talk about in AP Stats – relative risk.

To start, I used the Analyzing 2-Way Tables applet and used the “sample data” feature.  Here I attempted to use the same numbers quoted in the article:

The national rate was 9.8 cases per 100,000 adult males per year, while the rate in the former Phillies was 30.1 cases per 100,000 – about 3.1 times as high.

There are two issues here: first, to perform a simulation we need counts, so numbers like 9.9 and 30.1 just don’t play nice.  I’ll use 10 and 30.  Also, I wasn’t surprised that this site was not real happy with my using a population of 100,000 for simulation.  Here, I am going with 1,000 for convenience and to make the computer processor gods happy – we can debate the appropriateness of this down the road.

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The applet will then simulate the random assignment of the 2,000 subjects here to the two treatment groups (group A: being a Phillie, group B: not being a Phillie). How likely is it that we will observe 30 or more “successes” (which here represent those who develop brain cancer) in one of the two groups?  In the applet, we can see how the “successes” have been randomly assigned from their original spots in the 2-way table to new groupings.

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AT BAPS, Allan Rossman then explained how we can summarize these two groups using Relative Risk, which is listed under the “Statistic” menu on the applet. In general, relative risk is the proportion of success in one group divided by the proportion of success in a second group.  If we have proportions in two groups which are equal, then the relative risk would be 1.  We can then link to the newspaper article which claims a 3.1 “relative risk”, simulate many times with the applet (below we see the results of 10,001 simulations), and compare to the reported statistic.

risk.JPG

According to the simulation, we should only expect to see a relative risk of 3 or above about 0.08% of the time – clearly an “unusual” result.

But the article does not claim a significant difference, and cautioned against doing so as a number of assumptions were made which could alter conditions.  This would be an opportunity to discuss some of these design assumptions and how they could change the outcome.

Rest in Peace Dutch!