Jury Selection: A Stats Lesson Opportunity

I started writing this blog post last November, and then never finished it. Now that I’m getting ready to teach a statistics class this coming year, it seemed a good time to revisit this experience I had, and how math really does show up in real life justice questions.

One week in early November, I was summoned for jury duty. For the first time in my life, I actually had to go in. I had the option to defer up to 90 days, but really, there was no time that would be better – Thanksgiving Break, Holiday Break, and semester final exams are all things I don’t want to miss out on, so I took my chances. Besides, I’d always wanted the opportunity to serve on a jury, which I thought would be a fascinating learning experience. I wasn’t expecting the lesson I got.

Santa Clara Hall of Justice

Monday morning, I rushed to the Santa Clara Hall of Justice, 2nd floor, and registered as a juror, and waited. I sat next to an older African American man who was reading a book on John Carlos, while I tried to grade some papers that I hadn’t gotten around to over the weekend. I found out we were in the same group when our group number was called over the loudspeaker. We joined a sea of prospective jurors and made our way into the courtroom where we filled up all the available seats. I’d estimate that there were well over 100 jurors. The judge came in, and explained the basics of the case, as well as the reasons that jurors could immediately be let go (health issues, family or financial hardship, etc.).¬† The same black man sitting next to me indicated that he had some health issues, and sure enough, he wasn’t back in the afternoon after the judge spoke with all the hardship claims. And that’s when I noticed something strange. At least, I naively thought it was strange, but it turns out to be a common and well researched problem.¬† The defendant was a young black man, and after the potential juror that had been sitting next to me was dismissed, there were no potential jurors that were black. In a county that is quite diverse, the summoned jurors included mostly white people, some people who appeared to have an East Asian background, a few who appeared to be Latinx, a small number of Pacific Islanders perhaps, but the only black person in the courtroom each day was the defendant.

The judge did bring up implicit bias, which initially impressed me, but he barely touched on it, and neither the D.A. nor the defense attorney made much of the fact that there is a significant racial element and a likely bias that is not adequately addressed by merely mentioning that it exists. I’ve been working towards a goal of equity for a long time, I’ve read about bias, attended lectures and workshops on bias, and try to educate myself regularly, and am sure that bias is still a big part of my initial decision making. I am more aware of it, and there are things I can do to address it, but I also think that I’m in the minority in the white population in terms of my awareness of how bias works. It makes me that much more concerned about how the general non-black populations’ biases will affect their ability to be fair and impartial when determining the guilt or innocence of a black man.

As juror after juror got excused, and new jurors had their numbers come up to be up in the selection pool, I wondered what I would want should I get to that point and have my background questioned. On one hand, if I voiced my concerns around the systemic racism inherent in the justice system as evidenced by the lack of peers in the potential jury pool, and if I voiced my concerns about the ability of witnesses to accurately identify a person, and if I voiced my concerns about the potential for a guilty verdict to lead to a sentencing that would be counterproductive and punitive and not rehabilitative or restorative, then I would be excused, could go back to my classroom, and not have to spend the next month writing sub plans. On the other hand, if I minimized those thoughts, maybe I could be on the jury and make a difference and be fair and impartial because of my background, and even help to ensure that the rest of the jury takes their own biases into account.

I admit to breathing a sigh of relief when the D.A. and defense attorney agreed on a set of twelve jurors and two alternates, and I was one of the 13 people still left in the audience, our numbers not called. Even so, I am so curious about the reasons that, in such a diverse county as Santa Clara county, where 2.8% of the population is African American (a percentage lower than I thought), so little was made of the fact that the 14 jurors selected were all white and Asian. But, like I noted before, this is frighteningly common, and there are many, many reasons behind it. Seems like a good set of problems to explore and model with some probability and statistics.

Walk-Up Songs in Class

My old friend from my high school/hacking days, T.J. Connelly, has one of the best jobs in the world. He is the D.J. for the Boston Red Sox, New England Patriots, and (as of this year) the Boston Bruins. He chooses the soundtrack for each game, playing just the right song or song excerpt for that double play, that fumble, that hat trick. ar-170529350He chooses everything – except for a few givens (Sweet Caroline and Dirty Water come to mind), and the walk-on music for each of the Red Sox batters. I even got to go and catch up with him last summer on a trip to Boston, where we got to see where he watches the game, does magic with his laptop, and coordinates with Josh Kantor, the organist, to provide the soundtrack for a night in Fenway Park.

Here I am with my family, in T.J.’s office overlooking home plate after the Red Sox game.

It was after that visit, and after reading some tweets and blog posts and having some conversations with Matt Vaudrey and Ed Campos, Jr. that I decided to incorporate walk-up songs in my classroom. (Plus, it meant I could justify paying for a streaming music account. I happen to use Spotify, but if you use another streaming service (Pandora, iTunes/Apple Music, etc.), any of them should work.) This small change ended up being one of the simplest best ways I’ve found to connect with and engage with almost every student.

At the beginning of the year, while I had students writing their mathographies, I had students fill out a form in which they submitted their walk-up song request. It had to be school appropriate, and I needed to be able to find it on Spotify. Once they chose their songs, I created a class playlist for each period. Then, any time I wanted students to share what they had been working on, I would randomize the playlist and play whatever song came next. When a student hears their song, that’s their cue to go up to the board and start contributing with their solution, thoughts, or whatever they chose to add. There have been a few observations I’ve made. Students get noticeably excited when their song plays – it’s a little contribution, by them, to the whole class, that has nothing to do with math. Some students will start dancing their way up, or singing their way to the board. They are more likely to take a chance and put something up to show their thinking, and even more likely to show more work (because they get to hear more of their song). Sometimes, with longer problems or situations, one student’s song will end, and the next one begins, and there’s an exchange, a natural and organic collaboration, taking place. A few times during the year, I’ll allow students to change their song (or add a song, which doubles their chances of going to the board). I even had one of my Pre-Calculus students last year try to add 5 songs so he could dominate the class. I did have to deny that request, but loved the enthusiasm.

It’s true that some students will not want to choose a song, which gives me free reign to pick a song for them – usually by my favorite band. But the students who do choose songs are telling me, and the rest of the class, a little bit about themselves. I got quite a range: BTS, ELO, Macklemore, Billie Eilish, Van Halen, ABBA, the Kinks, Beethoven, Newsies, and more. There was an incredible variety of genres, and I heard some new music that I had to check out. In fact, one of my students’ love of BTS gave me a way to connect with the incredible Rafranz Davis, an amazing educator and passionate fan. She loves BTS as much as I love Marillion, if you can believe it.

If you’d like to get a glimpse into my students’ taste in music, check out these Spotify playlists!

Period 1 Geometry

Period 2 Algebra 1

Period 4 Algebra 1

Period 5 Geometry

Period 6 Geometry

Period 7 Pre-Calculus

Finding a way to incorporate music can be an incredible way to bond with your students and create a class culture that is meaningful, welcoming, and comforting for all. Oh, and fun. Did I mention it’s fun?

A few other side notes:

  • Random playlists may be truly random, or they may be pseudo-random. Truly random could (and likely will) have some repeats, and will not have a completely even distribution. This can be a nice mathematical discussion to have with students. Apple addressed this long ago in iTunes.
  • Sometimes, when a student or student group has something really interesting on paper, I’ll purposefully play a song from that student/group. Sometimes I tell them, sometimes I don’t. I’ve also been know to play Bohemian Rhapsody a second time from the beginning, since it’s so epic.
  • There are times when a student is just having an off day. If their song plays, I’ll often check in with them, and sometimes will skip the song if they just aren’t up for it. Just because this is intended to be fun doesn’t mean it necessarily will be fun for everyone. I created these playlists to build connection and community, so doing things that damage connections and community is counterproductive, and not worth the stress. Following up later can sometimes help, too.
  • Marillion is playing Royal Albert Hall in London for two nights in November.

    “We’re melting our guns as a show of strength”

    Who wants to buy me tickets to go? (Monday the 18th is already sold out, but there are still tickets for Tuesday the 19th. I may also need airfare, a hotel, and a sub.)

  • The featured image is from an ABC News feature on the history of walk-up music in baseball. I couldn’t find the artist name to attribute it, but would gladly do so if someone knows.

Student Generated Assessment Rubrics

On Twitter, I was asked about the rubrics that I created with my classes, but it was while I was away from my laptop, and so I said I’d write a long-overdue blog post to show some examples. I worked with students a couple of years ago at the beginning of the year on how we could develop good, general rubrics that would be used for our assessments throughout the year. I already had some ideas based on what others have done, and what CPM suggested, but it was nice to work with students on what would make sense to them. We discussed as a large group in each of my classes what qualities showed mastery of a standard skill, and how we could demonstrate that on an assessment, and then how we could describe it in our own language. I used a fake assessment with a variety of fake student responses, and we debated how to sort them into different scores. With some discussion, there was unanimity about how many points (out of 4) each assessment should receive.

That led to three rubrics, one for each of my subject areas (Algebra 1, Geometry, and Pre-Calculus) that I was able to use throughout the year for each assessment. My assessments are designed to measure a student ability on one particular standard or skill. Since I do teach in a private school, I have a fair amount of flexibility on what I am teaching, and am not required to stick to Common Core standards. In any unit, I will have between 3-8 assessments, and each of those assessments is between 2-5 questions. These replace the larger unit tests, and they are in many ways similar to quizzes, except that students are able to retake assessments for any skill, as many times as they choose (until the end of a semester) to demonstrate their growth and mastery of each skill. I’ve seen a number of different excellent variations on this (which I may link to at a later time when/if I get around to a general post on Standards Based Grading). This post is specifically about the rubrics, though.

And speaking of rubrics, here they are.

Algebra 1:


Alg1 Rubric


Geom Rubric.JPG

Pre-Calculus: (Note: Pre-Calculus is a little different, because it uses a 6 point rubric. This is because I have an opt-in honors component. All students who are not electing to take on the Honors component of the class are scored on a 4 point scale (although scores of 5 and 6 will count as slight extra credit, and if a student is always getting scores of 5 or 6, I will keep encouraging them to take on the Honors assignments.) Students who are taking the class as an Honors class are graded on the 6 point scale, and have an in-depth assignment for each unit that explores some additional depth or breadth of a unit.)

Pre-Calc Rubric

I hope this helps – it’s just a quick overview, but it’s a great activity that helps students really understand how they are being evaluated, and I love that I’m no longer taking away a point here and a point there for every little thing that doesn’t actually say anything about how well a student has mastered a particular concept.