Monthly Archives: May 2015

Reaction Time & Web Data Collection

If you put out an open call through email to complete a task for nothing in return, it might make sense not to expect much. I tried to make it as simple as possible to gather some reaction time data for my IB Mathematics SL class to analyze. My goal for each class has been to get an interesting data set each time and see what students can make out of it. After several hours of having this open, I had a really nice set of data to give the class.

I know my social networks are connections between some phenomenal people. That said, I didn't know that the interest in trying this out would be so substantial, and in several cases, get people to try multiple times to get their own best time. In less than a week, I've collected more than 1,000 responses to my request to click a button:
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I coded this pretty quickly and left out the error correction I would have included given the number of people that did this. I've been told that between phones, tablets, desktops, laptops, and even SmartBoards, there have been many different use cases for times ranging from hundredths of a second to more than five minutes - clearly an indication that this badly needs to be tweaked and fixed. That said, I am eager to share the results with the community that helped me out, along with the rest of the world. A histogram:

There's nothing surprising here to report on a first look. It is clear that my lazy use of jQuery to handle the click event made for a prominent second peak at around 0.75 seconds for those tapping on a screen rather than clicking. Some anecdotal reporting from Facebook confirmed this might have been the explanation. The rest of the random data outside of the reasonable range is nothing more than poorly coding the user experience on my part. Sorry, folks.

This isn't the first time I've done a data collection task involving clicking a button - far from it. It's amazing what can be collected with a simple task and little entry cost, even when it's a mathematical one. One of the things I wonder about these days is which tools are needed to make it easy for anyone (including students) to build a collection system like this and investigate something of personal importance. This has become much easier with tools such as Google Docs, but it isn't easy to get a clean interface that strips away the surrounding material to make the content the focus. For all I know, there may already be a solution out there. I'd love to hear about it if you know.

Maintaining Sanity, Reviewing Priorities

I've had a really busy year. I've always said at the start of the school year that I'm going to say 'no' more frequently in as politely a way as possible. I've said I'd be more honest about priorities. Instead of spending time writing code for something that might be really cool as part of a lesson next week, I need to get tests graded today. I've had more preps this year than ever before. I have big scale planning to do relative to my IB classes and their two year sequence of lessons, labs, and assessments. In a small school like ours, it's difficult to avoid being on multiple committees that all want to meet on the same day.

Probably the hardest part has been figuring out what my true classroom priorities are. I'd love to look at every student's homework, but I don't have time. I'd love to make videos of all of my direct instruction, but I don't have time. I'd love to curate a full collection of existing resources for every learning standard in my courses, but despite designing my own system to do this, I haven't had time.

Over the course of the year, however, I've found that the set of goals I have for every class can be boiled down to three big ones:

Give short SBG assessments as frequently as possible.

These need to be looked at and given back in the course of a class period, or they lose their effectiveness for students and for my own course correction when needed.

Provide more time for students to work during class. Use the remaining time to give direct instruction only as needed, and only to those that really need it.

Time I spend talking is unnecessary for the students who get concepts, and doesn't help the students that do not. If I'm going to spend time doing this, it needs to be worth it. This also means that I may not know what we need to review until during the class, so forget having full detailed lesson plans created a week at a time. I think I've accepted that I'm better at correcting errors along the way than I am at creating a solid, clear presentation of material from start to finish, at least given time constraints.

It has been more efficient for me to give students a set of problems and see how they approach them than tell them what to do from the start. There are all sorts of reasons why this is also educationally better for everyone involved.

Focus planning time on creating or finding interesting mathematical tasks, not on presentation.

I've always thought this, but a tweet from Michael Pershan made it really clear:

What I teach comes from the learning standards that I either create or am given. Maximizing opportunities for students to do the heavy cognitive lifting also maximizes the time these ideas spend simmering in their heads. This rarely occurs as a result of a solid presentation of material. It doesn't necessarily (or even usually) happen by watching a perfect video crafted by an expert. When you have a variety of mental situations in which to place your students and see how they react, you understand their needs and can provide support only when necessary. Anything can be turned into a puzzle. Finding the way to do that pays significant dividends over spending an extra ten minutes perfecting a video.


Going back to these three questions has helped me move forward when I am overwhelmed. How might I assess students working independently? What do I really need to show them how to do? What can I have my students think about today that will build a need for content, allow them to engage in mathematical practice, or be genuinely interesting for them to ponder?

What are your priorities?

Students Coding Tilman's Art with HTML5

I'm a big fan of the Geometry Daily Tumblr. Tilman's minimalist geometry images are beautiful in their simplicity. I've always wondered about reproducing art in code as a vehicle for learning to code, and have had it on my list to do this myself using Tilman's work.

In my web programming class, where we are currently playing around with the HTML5 canvas and its drawing capabilities, this concept was a perfect opportunity to let students play around with the art form. They quickly observed the beauty of what can be created using these tools, and the power of doing so by studying someone that is great at it.

Here are some of the results of their sketches. Some did precise imitations, others did their own interpretations. Click on the image to see their code posted on JSFiddle.

Dominick:

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Eason

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Steve

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Tanay>

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Jung-Woo

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Steven

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Circuits & Building Mental Models

I moved up my electric circuit unit this year for the senior physics class. Usually I put it after a full unit on waves, but after completing the waves unit with the IB students, I wasn't so pumped to go through it again from the beginning.

I began by having students try to generate the largest voltage they could from a set of batteries, motors, solar panels, lemons, and some other fun gadgets. That was a great way to spend a full 90 minute block. The next class, we played around with the PhET circuit simulator as I described in a previous post. The goal was to get them to have some intuition about circuits before we actually got down to analyzing it. Our conversation focused on batteries generally contributing energy to the circuit, and other circuit elements using that energy, leaving nothing behind at the negative terminal of the starting battery. Our working definitions for voltage, current, and resistance came out of the need for describing what was happening in the circuit.

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This started a pretty textbook version of the modeling process. I gave students some circuits, asked them to make a prediction for voltage/current, they made the predictions, and then tested them in the simulator. As needed, they made adjustments to their mental model to make it consistent across all examples.
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What interested me most about the results here was that the students put together a pretty solid mental model that centered on the voltage divider concept. This came out of their other assertion that current is the same for resistors in series.

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This led to the students tackling this problem on the second day of looking at circuits this way:
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In my AP Physics sequence, this is something I don't get to until Kirchoff's rules, so I was impressed with how nonchalantly they reported their answers after only a minute or so of thinking about the circuit.

On day 3, we went through an approximation of this lesson that I described in a previous post titled Starting at the end. We didn't get to the more complex circuits, but did get to the concept of parallel circuits.

On day 4, we spent a day getting our hands dirty building actual circuits, not with the simulator. The students had a good time piecing things together and seeing bulbs light up and make measurements with actual voltmeters and ammeters.

Today, on day 5, I was finally thinking I was going to teach them about equivalent resistance...but I hesitated. I was too scared that providing a formula would risk undermining all of the intuition they had developed.

The students worked through some Physics Bowl questions from a while back. Here's one:
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I noted down a student's explanation of why the answer was 36 volts, and another student's addition to explain why it had to be 42 volts:
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It then I threw this one at students:
Screen Shot 2015-05-13 at 9.57.47 AM I set the battery voltage to be 10 volts.

If my students had followed the sequence of physics lessons from the 2005 me, this would have been a piece of cake because they would have had the formula. Instead, they went through a nice sequence of stating what they knew and didn't know and making guesses. I suggested a spreadsheet as a way to keep track of those guesses and their reasoning in one place:

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We went through the spreadsheet cell by cell and decided on formulas to put in. In the end, they figured out that the final two currents had to be the same.

I did some guessing and checking following their monitoring of the values, and eventually ended up with the 100 ohm resistor having a voltage drop of 9.923 volts.

Only at this point (which was five minutes before the end of class) did I apply an equivalent resistance formula:
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It was a great moment to end on. My presentation of the equivalent resistance formula came out of a need, and for that reason, I was glad to provide it. I'm so happy I waited.