A Tool for Organized Planning

There are only two types of people who truly understand the volume of papers that teachers must manage: teachers and the family members of teachers. As the son of a teacher, I swore to myself that I would not have the piles upon piles of paper invade my home the way my dad’s papers used to invade ours growing up.

I wish I were writing a post with a silver bullet to keep papers and grading perfectly organized. I’m not. (But please do leave any suggestions in the comments!)

While I still struggle with paper organization, I have created a nice tool to keep my lesson planning organized: a custom-made googledoc spreadsheet that I use as a calendar.

This is my master planning tool. It’s color-coded by month, and I’ve pre-populated it with important holidays and dates in the DCPS calendar. It’s an easy-to-edit, big-picture view of my year that I can share with colleagues and co-teachers.

When I’m teaching a course for a second time, I often keep the old course map open to look at how I approached different topics. I also make notes to myself in the spaces to the right of the calendar with lessons learned along the way, such as the following note from the polynomials unit of my pre-calc class last year:

Screen Shot 2016-08-17 at 3.12.45 PM.png

Each year I start with a new blank slate and use the calendar to map out my units.

Please feel free to copy this calendar into a new googledoc to use for your own organizing.

What other things do you do to stay organized?

Update 8/21/16: Some people have been unable to copy the calendar from the view-only setting I created for the public link. Let me know if that’s the case, and I can give you temporary editing privileges.

Visibly Random Groupings: Why an Initially Terrifying Prospect Turns Out to be My Favorite Way to Promote Equity

Summer is often a time of reflection and change. We teachers make our New Year’s resolutions in August, not January. So as you think about the coming school year, and what small steps (or giant leaps) you’d like to take to do things differently, let me make an easy suggestion that changed my life this past school year: group students randomly.

Wait! Don’t go! Before you stop reading because, “that’s just crazy!” or “that’ll never work in my classroom” or “what about these ten problems with implementing random groupings that I immediately thought of?!”, allow me the time to argue that random groupings (1) are good for students, and (2) make your life easier. And yes, I promise to address your concerns about why this is the craziest thing you’ve ever heard of.

Good for Students: How Random Groupings Send Subtle Yet Important Messages that Promote Equity

In my opinion, the single most important reason to group students randomly is the fact that when we don’t, students will try to read into the groups we assign and the roles they should fill within those groups.

If we group homogeneously, they might think, “Yep, I’m in the dumb kids’ group. No surprises there. I’ll just pray I can make it through this class without looking like an idiot,” or alternatively, “I’m in the smart kids’ group! That means my ideas matter the most when we discuss things as a class.”

If we group heterogeneously, they might think, “I’m the smart one in this group; these other kids are not going to be able to keep up with my genius or help me solve this problem,” or alternatively, “I’m clearly the dumb one here. I’ll just copy down whatever the smart kid says.”

Even if students aren’t conscientiously narrating these thoughts to themselves, they are certainly internalizing the subtext of the group they have been placed in and their “role” with that group.

Furthermore, these unproductive thoughts are often filtered through the lens of race and gender and any other way that students can feel marginalized in a math class. Whether we like it or not, students carry the baggage of cultural norms and biases, social expectations, and status into the classroom.

Random groupings therefore send a powerful message: everyone is equal, everyone’s ideas are valid and deserve to be heard.

Before learning about random groupings, I used to make groups by trying to “spread out” the strong and weak students, i.e. I’d make sure that my strong students weren’t too clustered, and that the weaker students always had someone who could support them. While I did this with the best of intentions, this approach is problematic:

  • I was assigning “strong” and “weak” classifications to students based on prior achievement. Despite the cumulative nature of much of mathematics, a quality math task will invite innovative and creative ideas that can come from anyone, even a student who struggles with some basic skills.
  • There are many ways to be “smart” in math class. Most people tend to assume that being “good at math” means being able to do basic arithmetic computations quickly and accurately. While that’s a great skill to have, most mathematicians (myself included!) will readily admit to struggling with that particular skill. When we assign groups based on prior achievement, we’re only validating a narrow definition of what constitutes being “good at math”.

By grouping students randomly, we send the message that there are multiple ways to be smart at math (seeing patterns and connections, drawing a graph or diagram to visualize a problem, communicating ideas clearly, etc.).

Obviously your students won’t fully internalize the idea that there are lots of ways to be smart at math simply from random groupings alone; this message needs to be explicitly reinforced many times over. But random groupings are a powerful way to put your money where your mouth is. This can start to chip away at the status barriers preventing full participation and engagement.

If we truly believe that all students can be successful in mathematics (and if you don’t, why on earth are you teaching?), then visibly random groupings are the only way to organize the classroom.

For more about why random groupings are essential, listen to this tumblr post from Ilana Horn, check out her blog Teaching Math Culture, or read her book, Strength in Numbers: Collaborative Learning in Secondary Mathematics.

But What About…? Calming Your Fears

I will be honest: even after reading enough to be convinced that visibly random groupings are a good idea in theory, I was terrified of actually implementing them. What if the random groups create nightmarish social dynamics? What if all the weak kids get put into one group and completely flounder?

To that second concern, I’ll note that if a bunch of “low” students end up in one group together, oftentimes they will realize that there are no “strong” students to hide behind, and they will rise to the challenge. And if they don’t, then at least they’ll be concentrated and you can spend extra time with their group!

But back to the broader concern that randomization can create bad social dynamics. This is obviously true, and you don’t have to live with those bad dynamics. Supporting randomized groupings doesn’t mean you have to blindly accept a group that you know won’t work together well. The key is that you change groups based on social, not academic considerations. For example, you could say, “I know you two always get chatty together, so I’m going to switch you to another group.” Or, as was the case in one of my classes last year, if two students have associations with rival gangs, they should definitely not be seated together!

As long as the groups are visibly randomized from an academic standpoint, with any conscientious tweaks occurring for purely social reasons, your classroom will still get the positive benefits outlined above.


So how can you actually implement this in your classroom? Ilana Horn shows an example of a chart you could hang in your room with different group roles. Simply shuffle cards with students’ names on them and place them randomly into the slots. Screen Shot 2016-07-06 at 11.00.15 PM

That’s way more sophisticated than what I did! At the beginning of this past school year, I was so nervous about random groupings that I decided to start out simple: I only did random groupings for a few specific, group-work tasks. I would visibly shuffle cards with students’ names, then put them down four at a time on desks to create the groups, saying the students’ names as I went.

Later in the year, I realized that random groupings are actually the greatest thing ever and I started using randomization to create my general seating chart. I would shuffle the cards, then have a student read them to me in order as I wrote students’ names on a blank seating chart. I would then allow students to silently raise their hands to request to move closer to the front if they had bad eyesight and had been placed too far back.

This whole process took about five minutes, and created a visibly randomized seating chart with student input. I found it was generally best to do this at the end of class and then have the new seating chart posted as students came in the next day.

Good for Teachers: How Random Groupings are Actually the Greatest Thing Ever from a Selfish Point of View

I hope that I’ve convinced you that random groupings are both good for your students and logistically feasible. But now for the selfish part: they will make your life as a teacher significantly easier.

Creating seating charts randomly has freed up soooooo much time! I cannot even begin to describe how much time I wasted two years ago trying in vain to balance the delicate Rubik’s Cube of student personalities and abilities, only to have each new seating chart seem even worse than the previous one. By making my seating charts randomly, I essentially gave myself hours of extra time to devote to lesson planning and grading.

Additionally, students used to feel personally insulted if I made a new seating chart that separated them from their friends, and they would lobby incessantly for specific seating arrangements. When students get a new seat that they don’t like but understand that it arose from a visibly randomized process, they complain less and for a shorter amount of time.

I also think that using randomization has made me a better teacher. It’s a great reminder to view all students as having the potential to make meaningful contributions, and it helps me avoid deficit thinking. When I began using random groupings this past school year, I found myself expecting more from the students who struggled the most, and as a result, they rose to higher challenges. (Mostly. Ish. Depending on the kid. This is education after all; silver bullets don’t exist!)

On the opposite end of the spectrum, random groupings are a good reminder that we can’t always tell who is going to struggle with a given task and who is going to need support. I had a student in my Geometry class this past year who demonstrated very early on that she was incredibly strong with the procedural skill of solving algebraic equations and was also quite adept at correctly setting up equations from geometric situations. I therefore thought of this student as one of my “stronger” students. When we started working on proofs, a lot of kids needed support and feedback, and I found myself being spread quite thin around the room. I ended up not checking in on this student (or the group she was working with) because I thought that she was one of my highest flyers and would be fine without me. It wasn’t until I read her proofs that I saw she was grasping at straws trying to form a coherent and logical argument.

I had let my preconceived notions of this student’s intelligence get in the way of recognizing that she needed more guidance and support to complete the task at hand. Random groupings can be a helpful reminder that we can’t necessarily judge future success from prior achievement in a subject as complicated, disparate, and interconnected as mathematics.

Concluding Thoughts

If you’re not already using random groupings, I hope you’ll consider this for next school year. It has the advantage of being good for students’ conceptions of themselves and others in math class, and also making your life easier. Furthermore, this is a fairly easy and straightforward new strategy to implement.

If you already use random groups, what have your experiences been? Do you have other ways that you put students into groups randomly? Please share!

Will random groupings magically solve all status issues in your classroom? Of course not. But it is one powerful piece of the puzzle that can help all students recognize that they have valuable ideas to contribute to the class.

Thoughts? Questions? Concerns? Please let me know!


A New Beginning or More of the Same?

There is a blind faith in data and numbers that pervades much of our society, particularly education reform circles. People who worship at the altar of this faith look at a school with low test scores and assume that the school (and by extension the teachers and principal) are “bad”. They often fail to ask some basic questions, such as:

  1. What is the quality of the test that the students took? Does it even measure what it purports to measure?
  2. Is the exam developmentally appropriate?
  3. How many of these students are emergent bilinguals? Were there any language accommodations given other than extended time and a dictionary?
  4. How many of these students experience violence or hunger or fear or insecurity on a daily basis? How does this affect their ability to concentrate?
  5. Did the students even try? Were they invested in the exam? Does it really represent the students’ best effort and understanding?

I could go on and on and on. This is just a small sampling of the many factors that make student standardized test data significantly less than reliable. Education reformers will tell you that there are big, complicated algorithms to account for things like student background and prior knowledge. As a mathematician, I am not intimidated into complacence by talk of a “complicated algorithm”. Rather, I note that the American Statistical Association has discredited the current obsession with test scores.

This brings me to the big news in DCPS this week: Kaya Henderson has announced that she will be leaving as chancellor. Will Mayor Bowser appoint someone who understands the vast limitations of standardized tests? Will she appoint someone who views PARCC results with serious skepticism? Someone who genuinely recognizes and trusts the professionalism of the district’s teachers (beyond the mere lip service that Kaya Henderson is so fond of)?

I’m not holding my breath for the kind of chancellor this district needs, but maybe I’ll be pleasantly surprised. New beginnings are new beginnings, and maybe DC will finally decide to listen to solid research instead of blindly chasing meaningless data points.

If you’re interested in more information about how and why standardized testing is ruining education, check out the article I wrote for the Washington Post last year. I like my original title better than the one they used: The Real Education Crisis.