Monthly Archives: September 2014

Revising My Thinking: Repetition

Traveling with students has always been one of the most rewarding parts of the teaching job. Seeing students out of their normal classroom setting draws out their character much more than content alone can. One particular experience on a trip last week forced me to rethink aspects of my classroom as I never could have predicted it would.

On our second day of the trip, students experienced the lives of Chinese farmers. For breakfast, we paced a series of stalls cookies of sizzling noodles, Chinese pancakes, and tea eggs - students could spend no more than ten Yuan on their breakfast. After leaving the market and driving for an hour, we arrived at a village surrounded by tea hills. Here, the farmer experience began. The students were divided into three groups and set out to compete for first, second, and third place in a series of tasks; their place determined how much the group would be paid in order to purchase dinner that night.

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Students tilled the ground with hand tools to plant vegetables, with a seasoned farmer showing them what to do, and then judging them on their efforts. The farmer's wife gave a dumpling making lesson, and then had students make their lunch of dumplings according to her example. The third task involved collecting corn from a nearby field and putting it into a woven sack. Teams were judged by both quantity and quality. Many students tossed out corn that had shriveled kernels and silk from beetle larvae around the stalks. Students at this point guarded their yellow post-it notes (where the guide recorded their earnings) carefully, chasing them down when they flew away in the wind.

In the final task, students were to earn money by assembling plastic pens. For every one hundred pens put together, the group would earn 1 Yuan, or about 16 cents. Our guide said we would work on this for three hours. I prepared her for the likelihood that the students might not last that long. Such a simple task would surely result in disinterest, especially in a group that was already distressed by our insistence that their mobile devices stay put away for the majority of the day. To myself, I questioned whether an investment of three hours into the task was really necessary to get students to appreciate the meaning of a day of hard work or to understand the required input of human energy to create a cheap plastic item. They were already exhibiting signs of fatigue before this, and a repetitive task like this couldn't make things any better, right?

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The first pattern I noticed was that students quickly saw the need for cooperation. Each student felt the inefficiency of building one complete pen, one at a time. Without any input from adults, the students organized themselves into an assembly line. They helped each other with the tricks they discovered to shave off seconds of the process. They defined their own vocabulary for the different parts and stages of assembly. Out of the tedium, they saw a need for innovation, and then proceeded to find better ways on their own. While they worked, they sang songs, told jokes, and made the most of the fact that they could socialize while they worked.

The students were brutally honest with our guide about the value of the work they were doing. They expressed disbelief that they couldn't be paid more for their time. The guide responded by reminding the students of the real costs of things: 17 Yuan for a chicken, 2 Yuan for bottles of clean water at dinner. The students responded by asking for the price of the pens at the market ("0.8 yuan each" said our guide) and said that without the people working, the pens wouldn't be made. By the end, students had assembled 3,880 pens, and had smiles on their faces even at that point.

The other outcome of this activity was that each student was permitted to keep one pen as a keepsake of the day. For a group of students that routinely leaves things everywhere, these pens were guarded and treasured as closely as their mobile devices. A couple of them were so attached that they insisted on bringing their pens with them for pre-dinner free time at the creek.

There were so many lessons that came out of the repetitive nature of this task. As I said, I underestimated the level to which students would be engaged by this activity. They took pride in their work. They tested their pens carefully before counting and bundling them together with a rubber band. They took time to understand what they were doing in order to find better ways.

I routinely look for students to have similar discoveries in my class. There is repetition. There is a need for careful reflection on the quality of an answer or clarity of explanation.

I do, however, try to hasten this process because I underestimate the value of repetition during my class period. I've argued before that class time should be spent making the most of the social aspect of the classroom for learning. Repetitive drills don't tend to make the cut by that standard. This is, after all,one of the points I frequently make about the role of computers and computational thinking. I do introduce students to tedious processes, but usually cut out the middle part of students feeling that tedium themselves, because I figure they get it without needing to actually experience it. I do this to save time, but I now think I might be spoiling the punchline of every lesson in which I take this approach.

After seeing the students themselves invent and create on their own and as a group (and with no adult intervention), I now feel the need to rethink this. Perhaps I'm undervaluing the social aspect of repetitive tasks and their potential for building student buy-in. Maybe class time with meaningful repetition is valuable if it results in the community seeking what I have to share from my mathematical bag of tricks. Maybe the students don't fully believe that my methods are worth their time because I tell them what they should feel instead of let them feel it themselves.

Perhaps I'm also reading too much into what I observed on the trip. I am , however, quite surprised how off the mark I was in predicting the level of engagement and enjoyment the students would have in spending three hours assembling pens. I'm willing to admit my intuition could also be off on the rest.

Sensors First - A Changed Approach

I presented to some FIRST LEGO League teachers on the programming software for the LEGO Mindstorms EV3 last week. My goal was to present the basics of programming in the system so that these teachers could coach their students through the process of building a program.

The majority of programs that students create are the end product of a lot of iteration. Students generally go through this process to build a program to do a given task:

  1. Make an estimate (or measurement) of how far the motors must rotate in order to move the robot to a given location.
  2. Program the motors to run for this distance.
  3. Run the program to see how close the robot gets to the desired location.
  4. Adjust the number in Step 1. Repeat until the robot ends up in the right location.

Once the program gets the robot to the right location, this process is repeated for the next task that the robot must perform. I've also occasionally suggested a mathematical approach to calculate these distances, but the reality is that students would rather just try again and again until the robot program works. It's a great way to introduce students to the idea of programming as a sequence of instructions, as well as familiarity with the idea that getting a program right on the first try is a rarity. It's how I've instructed students for years - a low bar for entry given that this requires a simple program, and a high ceiling since the rest of programming instructions are extensions of this concept.

I now believe, however, that another common complaint that coaches (including me) have had about student programs is a direct consequence of this approach. Most programs (excluding those students with a lot of experience) require the robot to be aimed correctly at the beginning of the program. As a result, students spend substantial time aiming their robot, believing that this effort will result in a successful run. While repeatability is something that we emphasize with students (I have a five in a row success rule before calling a mission program completed) it's the method that is more at fault here.

The usual approach in this situation is to suggest that students use sensors in the program to help with repeatability. The reason they don't do so isn't that they don't know how to use sensors. It is that the aim and shoot method is, or seems, good enough. It is so much easier in the student's mind to continue the simpler approach than invest in a new method. It's like when I've asked my math students to add the numbers from 1 to 30, for example. Despite the fact that they have learned how to quickly calculate arithmetic series before, many of them pick up their calculators and enter the numbers into a sum, one at a time, and then hit enter. The human tendency is to stick to those patterns and ideas that are familiar until there is truly a need to expand beyond them. We stick with what works for us.

One of my main points to the teachers in my presentation was that I'm making a subtle change to how I coach my students through this process. I'm calling it 'sensors first'.

The tasks I give my students in the beginning to learn programming are going to require sensors in order to complete. Instead of telling students to program their robot to drive a given distance and stop, I'll ask them to drive their robot forward until a sensor on their robot sees a red line. I'll also require that I start the robot anywhere I want in the test of their program.

It's a subtle difference, and requires no difference in the programming. In the EV3 software, here's what it looks like in both cases, using wheels to control the distance, and a sensor:
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What am I hoping will be different?

  • Students will look to the challenges I give them with the design requirement built in that aim-and-shoot isn't an option that will result in success. If they start off thinking that way, they might always think how a sensor could be used to make the initial position of the robot irrelevant. FLL games always have a number of printed features on the mat that can be used to help with this sort of task.
  • When I do give tasks where the students can start the robot wherever they choose, students will (hopefully) think first whether or not the starting position should matter or not. In cases where it doesn't, then they might decide to still use a sensor to guide them (hopefully for a reason), or drop down to a distance based approach when it makes sense to do so. This means students will be routinely thinking what tool will best do the job, rather than trying to use one tool to do everything.
  • This philosophy might even prompt a more general need for ways to reduce the uncertainty and compound error effect associated with an aim and shoot approach. Using the side of the table as a way to guide straight line driving is a common and simple approach.

These sorts of problem solving approaches are exactly the way successful engineering design cycle works. Solutions should be found that maximize the effectiveness of a design while minimizing costs. I'm hoping this small change to the way I teach my students this year gets them spending more time using the tools built into the robot well, rather than trying to make a robot with high variability (caster wheels, anyone?) do the same thing two times in a row.

Ultrasonic Sensors & Graph Matching: Play, then learn

In my physics class this morning, the plan was to have students work through a packet of descriptions of constant velocity motion. Each description was either a position vs. time graph, a velocity vs. time graph, or a motion map. Students would then sketch the corresponding velocity/position graphs, and then actually act out these scenarios in front of an ultrasonic detector. With a live graph showing them what their position vs. time graphs were as they moved, mayhem invariably would result.

I had a last minute change to my plan this morning. Following the ideal set out by one of my favorite books as a kid and my favorite museum (the Exploratorium), I asked 'how can we play with this?'

I had the sensor ready to go at the start of class. I told a student to walk back and forth in front of it while data was collected. I didn't have to give any other instruction - they saw how their movement resulted in a graph.

I then put two post-it notes on the screen and told another student to make the graph hit them both:

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This was probably the first time since the first day of school that the class was all smiles.

After they had this figured out, I gave them another task: hit the post-it notes, but also make the graph go along a string taped to the wall:

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This took a bit more time for developing intuition, but they got this down.

It was only at this point when I introduced the packet of scenarios. They went right to work and sped their way through, helping each other when differences arose.

My usual assessment activity for this has always been that I could call each student up to generate a specific graph. Since they don't know who I'm going to call until the last minute, they ideally would work to understand how to generate each graph in front of the detector so that they were ready in case I called them up.

A student this morning said point blank that this plan did not sound fun at all. When I thought about it a bit more, I realized it was a fear based activity. The student instead suggested that I call each of them up, and give a number for a graph that needed to be generated, and the rest of the class could guess which one it was.

Clearly a superior idea. We proceeded to run the activity this way, and it was a blast.

I'm not sure why I haven't done this activity this way in the past. It's obviously superior to almost anything else for a number of reasons.

  • The activity starts with no numbers, just intuition and feedback. It's fun seeing your own movement be simultaneously measured and displayed in front of you. The need to communicate about the process is where the vocabulary and numerical measurement comes in - that's a perfect place for a teacher to step in once students are digging the activity.
  • The idea of setting an origin and detailing the meaning for increasing or decreasing position values isn't necessary here. Students figure out quickly how these relate to their own movement without any intervention on my part.
  • Any activity that gets teenagers out of their seats and moving around during the first block of the day (and does so in a way that also directly serves the learning goals of a lesson) is going to be vastly superior to pretty much everything.

A great way to open a rainy Wednesday in Hangzhou, by any measure.