## Making Groups - A Genetic Algorithm Experiment

I've wanted to experiment with genetic algorithms for a long time, but never quite found the time to make it happen. I guess part of it was that I never believed the algorithm would work and find what I wanted.  I decided recently to pick this project back up after a long time (with some prodding from good people) and actually make it work. I think the major push came when I realized that I wanted the ability to make mixed groups, or homogeneous groups, and balance gender, and prevent certain students from being together. Was I over-constraining? Was the possibility that I was over-constraining keeping me from even trying to do this in the first place?

Thus, I decided to actually make this happen. I also decided I wanted to make it look much nicer than the Python version I've been using now for over four years.

You can see the code directly here at CodePen, or play with it below.

See the Pen GroupMaker by Evan Weinberg (@emwdx) on CodePen.0

The basic algorithm is this:

• Fill in a list of students with names, genders, skill levels, and an optional list of names with whom a given student should not be grouped. Line 2
• Generate a bunch of random groups of students with these properties. For each group, calculate a series of metrics that the fitness of a given group. Lines 45-156
• Calculate the score of a grouping, which consists of a full set of groups that contain all of the students of the class. Line 200
• Generate a bunch of groupings, sort them according to score. Take the top 10 groups, and make swaps of students between groups to make a long list of groups. (This is lines 214-224.) This is the mutation step of the genetic algorithm. Sort them again according to score.
• Repeat for a few generations, then take the top group.

It's pretty fascinating to watch it work. I made the scoring step uniform for gender by tweaking the coefficients in Line 200. You could also make this score value gender balance, a range of abilities, or anything else.

This is screaming for a nicer UI, which I have in the works. For now, it's out there in its fairly un-commented state. If you want to hack this to use with your own students, you'll want to tweak the student list in Line 2, the numbers of groups of each size (groups of 1, groups of 2, groups of 3, and so on) in Line 242, and possibly the values I use in the score generation line in line 200.

## An Experiment: Swapping Numerical Grades for Skill-Levels and Emoji

I decided to try something different for my pre-Calculus class for the past three weeks. There was a mix of factors that led me to do this when I did:

• The quarter ended one week, with spring break beginning at the end of the next. Not a great time to start a full unit.
• I knew I wanted to include some conic sections content in the course since it appears on the SAT II, and since the graphs appear in IB and AP questions. Some familiarity might be useful. In addition, conic sections also appear as plus standards within CCSS.
• The topic provides a really interesting opportunity to connect the worlds of geometry and algebra. Much of this connection, historically, is wrapped up in algebraic derivations. I wanted to use technology to do much of the heavy lifting here.
• Students were exhibiting pretty high levels of stress around school in general, and I wanted to provide a bit of a break from that.
• We are not in a hurry in this class.

Before I share the details of what I did, I have to share the other side to this. A long time ago, I was intrigued by the conversation started around the Twitter hashtag #emojigrading, a conversational fire stoked by Jon Smith, among many others. I like the idea of using emoji to communicate, particularly given my frustrations over the past year on how communication of grades as numbers distort their meaning and imply precision that doesn't exist. Emoji can be used communicate quickly, but can't be averaged.

I was also very pleased to find out that PowerSchool comments can contain emoji, and will display them correctly based on the operating system being used.

So here's the idea I pitched to students:

• Unit 7 standards on conic sections would not be assessed with numerical grades, ever. As a result, these grades would not affect their numerical average.
• We would still have standards quizzes and a unit exam, but instead of grades of 6, 8, and 10, there would be some other designation that students could help select. I would grade the quizzes and give feedback during the class, as with the rest of the units this year.
• Questions related to Unit 7 would still appear on the final exam for the semester, where scores will be point based.

I also let students submit some examples of an appropriate scale. Here's what I settled on based on their recommendations:

I also asked them for their feedback before this all began. Here's what they said:

• Positive Feedback:
• Fourteen students made some mention of a reduction in stress or pressure. Some also mentioned the benefits of the grade being less specific being a good thing.
• Three students talked about being able to focus more on learning as a result. Note that since I already use a standards based grading system, my students are pretty aware of how much I value learning being reflected in the grade book.
• Constructive Feedback:
• Students were concerned about their own motivation about studying or reassessing knowing that the grades would not be part of the numerical average.
• Some students were concerned about not having knowledge about where they are relative to the boundaries of the grades. Note: I don't see this by itself as a bad thing, but perhaps as the start of a different conversation. Instead of how to raise my grade, it becomes how I develop the skills needed to reach a higher level.
• There were also mentions of 'objectivity' and how I would measure their performance relative to standards. I explained during class that I would probably do what I always do: calculate scores on individual standards, and use those scores to inform my decisions on standards levels. I was careful to explain that I wasn't going to change how I generate the standards scores (which students have previously agreed are fair) but how I communicate them.

I asked an additional question about what their parents would think about the change. My plan was to send out an email to all parents informing them of the specifics of the change, and I wanted students to think proactively about how their parents would respond. Their response in general: "They won't care much." This was surprising to me.

So I proceeded with the unit. I used a mix of direct instruction, some Trello style lists of tasks from textbooks, websites, and Desmos, and lots of circulating and helping students individually where they needed it. I tried to keep the only major change to this unit to be the communication of the scores through the grade book using the emoji and verbal designation of beginner, intermediate, expert. As I also said earlier, I gave skills quizzes throughout.

The unit exam was a series of medium level questions that I wanted to use to gauge where students were when everything was together. As with my other units, I gave a review class after the spring break where students could work on their own and in groups, asking questions where they needed it. Anecdotally, the class was as focused and productive as for any other unit this year.

I was able to ask one group some questions about this after their unit test, and here's how they responded:

The fact that the stress level was the same, if not less, was good to see. The effort level did drop in the case of a couple of students here, but for the most part, there isn't any major change. This class as a whole values working independently, so I'm not surprised that none reported working harder during this unit.

I also asked them to give me general feedback about the no-numerical-grades policy. Some of them deleted their responses before I could take a look, but here's some of what they shared:

• Three students confirmed a lower stress level. One student explained that since there was no numerical grade, she "...couldn't force/motivate [her]self to study."
• Five students said the change made little to no difference to them. One student summed it up nicely: "It wasn't much different than the numerical grades, but it definitely wasn't worse."
• One student said this: "The emojis seemed abstract so I wasn't as sure of where I was within the unit compared to numbers." This is one of a couple of the students that had concerns about knowing how to move from one level to the next, so the unit didn't change this particular student's mind.

• This was a really thought-provoking exercise. A move away from numerical grades is a compelling proposition, but a frequent argument against it is that grades motivate students. By no means have I disproven this fact in the results of my small case study. If a move like this can have a minimal effect on motivation, and students get the feedback they need to improve, it offers an opportunity for considering similar experiments in my other classes.

There are a couple questions I still have on this. Will students choose to reassess on the learning standards from unit 7, given that they won't change the numerical average when we return to numerical grades for unit 8? The second involves the longer term retention of this material. How will students do on these questions when they appear on the final exam?

## Trello for Class Organization

Our school hosted the Vietnam Technology Conference this past February.

(Yes, I'm just getting around to talking about it. Don't judge.)

One of the sessions I attended was about agile development in education, specifically as a way to organize the classroom into a room of independently functioning teams that are all trying to reach the goal of learning content. The full details on the philosophy can be found at http://eduscrum.com. I most certainly am not following the full implementation described there.

My interest was piqued by the possibility of using a Trello board to organize tasks for my classroom. I always make a digital handout for each class that consists of a series of tasks, links, problems, and chunks of information. Within the class block, I weave these together in a mix of direct instruction, group tasks, PearDeck activities, Desmos explorations, and so on. I advise students not to just do every problem on my handouts from start to finish because there is an order to my madness. I have a plan for students to go through the different activities, but I don't always clearly indicate that plan on these handouts.

This is where Trello came in. For my past two units in PreCalculus, I broke up the tasks on my digital handout into tasks on a Trello board. This consists of a list of tasks, and then three columns labeled 'to-do', 'in progress', and 'completed'.

I put students in groups, and then shared this Trello board here with them. Their group needed to make a Trello board for their group, and then copy the day's tasks onto their group's board. I told students how long a 'sprint' (an agile development term) was going to be, and the group would decide which tasks they would collectively (or individually) do during that time. They moved these tasks into the appropriate column of the board. As I continued to use the system, I realized that I could color code tasks according to the learning standards, and identify them according to the day of class. This helped students to understand the context of individual tasks later on.

The thing I liked the most about this experiment was that it actually enabled students to take charge of what they were doing during the lesson. I sometimes said that I was going to go over a concept at a particular time during the class block, and that teams could pay attention or not depending on their needs. This could be replaced by videos of this direct instruction to allow for more asynchronous learning for the students that weren't ready at that time. There were some great conversations between students about what they did and didn't understand. I could circulate and interject when I saw the need.

This put me in the position of curating interesting and productive tasks related to the course content, which is a lot more fun than planning a lecture. The students also liked being able to talk to each other and work at their own pace. Here's some feedback from the students:

#### What they liked:

• "I think it was nice how I could do things by whatever pace I felt more comfortable with to an extent since we did things as a small group rather than as an entire class."
• "It kept me working and thinking the whole class. It also helped me work out problems independently which helped my understanding."
• "I liked the ability to keep track of all my work, as well as knowing all the problems beforehand. I also like being able to have more time to discuss with friends to understand how we each came up with various solutions."

#### What could be improved:

• "Maybe I rather stick with traditional teaching methods. This is borderline self-taught and it's not so much better with group of people that I don't know well."
• "I think it would be better to go through the theory and concepts of the standard first, meaning how to do a problem as a class before splitting into smaller groups for individual/team work."
• "For future classes, I would also like informative videos to be included so that we can learn new topics this way."

This feedback made it easy to adjust for the next classes, and I continued to tweak in the next unit. The students really like the act of moving tasks between the different columns on the Trello board too. I really like the ease with which students can copy tasks, move them around, and plan their time independently. There are some good habits here that I'll be thinking about expanding to other classes later this semester or for the next school year.