Telling students not to procrastinate solves the wrong problem.

In seeing my students working to prepare for semester exams over the last week, I have spent some time thinking about the advice I give students about how to manage the stress associated with this time of year. The reality for them (and for me, for that matter) is that there is a lot going on right now. A quick rundown of my obligations: exams have to be written, assessments marked, comments graded, recommendations written, assignments double-checked for accuracy in the grade-book...this doesn't even mention the non-school related tasks on my plate. Some tasks I spread out over a few days usually in order to avoid the non-linear way that unpleasantness increases as a deadline approaches. Some tasks have to be done last minute, and there's no way around them.

When I see students cramming and working feverishly to get things done, part of me wants to channel the oft repeated (and nonsense) advice that 'if you had started earlier, you wouldn't have this problem.' And then I stop. Grand scheme of things, this is not really helpful. You don't tell someone that just cut off his finger that doing so was a dumb idea. The important part is managing the situation in a way that balances all of the relevant costs and benefits to maximize the overall outcome. The biggest problems my students have is not (only) that they put things off. It's that they think they can effectively manage the stress that comes with it by following some common, but misdirected principles. Here are my categories of guiding principles:

Ways students foolhardily trick themselves into doing what they do:

  • Principle of Work-Equivalence: As long as I am working on something I need to be working on, I am using my time effectively. After all, it all needs to get done, so why not just pick something and work on it?
  • Principle of Longevity: I've been doing this school thing for long enough - I know this has worked for me in the past, so I'm going to keep doing it. This comes from a major trend that I see with my students at the moment. Even more frightening is that the older they are, the better they think they are at managing things during stressful times. The way I see it, the opposite is true.
  • Principle of Education through Suffering: If I am not suffering as I get things done, I am not working hard enough. Carrying around stacks of papers, losing sleep, having unproductive (but fun) study parties seems to be par for the course. It certainly isn't something that disappears after high school graduation.
  • Principle of Poor Prioritization: I know what I really should be spending my time doing, but this other mindless task seems like a much better use of my time. This is not about online distractions, though that is a big factor for all of us. This is when a student decides to white out all of the mistakes in his/her notebook from throughout the semester because he or she thinks this will make studying easier. Rewriting notes can be a useful exercise if it involves some sort of processing/summarizing/grouping of ideas. Simply copying them over is a passive activity that feels like it should help, but probably is less productive than other tasks.
  • Principle of Confidence: I'm going to work on the things I am already good at doing to boost my confidence. This will better make me able to tackle the things I don't understand. I've had conversations with students that do know what they need to work on, but avoid those things like the plague because learning new things is difficult. Revisiting strengths is occasionally a good idea, but again, it is not truly productive.

Figuring out how to shake students of following these guidelines is really what we need to work on. We need to not just just lecture them about getting organized, planning out stressful times, taking effective breaks, and being deliberate about all of these processes, but model how to do these things. My question is one of practicality though - what are the best ways to do this? Is the best way integrated as part of existing courses? (My gut says yes.) Is it about going back to pencil and paper planners? Is it about using technology to help with reminders, calendars, etc?

The thing that I find most difficult about discussing this is that it always turns into a conversation about avoiding procrastination. I agree that this would help...if our students weren't already told this hundreds of times per year. The design problem that needs to be solved is: given that our students are stressed, how do we help them work through it? Furthermore, how do we make the most of our own experience as adults working through stress, but deliver that experience in a way that doesn't start by telling students what they believe is wrong?

A tale of two gradebooks - my SBG journey continues

I realized this morning that I could look back at the assignments from my PowerSchool gradebook from a year ago and see the distribution of assignments I had by the end of the semester:
Screen Shot 2012-12-12 at 8.32.14 AM

My grades were category based - 5% class-work, 10% homework completion, 10% portfolio, 60% unit tests, and 15% quizzes. This comprised 80% of the semester grade, and was the grade that students saw for the majority of the semester. A semester exam at the end made up the remaining 20%.

While I did enter some information about the homework assignments, my grade was just a reflection of how they completed it relative to the effort I expected them to make while working on it. No penalty for being wrong on problems, but a cumulative penalty developed over time for students tending not to turn it in. This, however, was essentially a behavior grade, and not an indication of what they were actually learning. The homework was the most frequent way for students to get feedback, and it did help students improve in what they were learning, but the completion grade was definitely not a measure of what they were learning at all. There were six quizzes that fit into my reassessment system. Not important enough to matter, I realize now with 20/20 hindsight.

The entire Standards-based-grading community shoots me a look saying 'we told you so', but only momentarily and without even a hint of snark. They know I am on their side now.

Here is a screen shot of the assignments in my grade-book as of this morning:
Screen Shot 2012-12-12 at 8.35.40 AM

There is a clear indication of what my students have been working on here. With the exception of the portfolio, a student can look at this (and the descriptions I've included for each standard) and have a pretty good idea of what they did and didn't understand over the course of the semester. They know what they should be working on before the semester exam next week. The parents can get a pretty good idea of what they are looking at as well. I knew making the change to standards based grading (SBG) made sense, but there have been so many additional reasons I am happy to have made the change that I really don't want to go back to the old system.

I'll do more of a post-game analysis of my SBG implementation in PowerSchool soon. I will be making changes and enhancing parts that I like about what I have done so far. I have to first make it through the busy time ahead of marking exams, submitting comments, and getting my life ready for the extended winter break that is peeking its beautiful head over the piles of reassessments on my desk. It is really satisfying to see that my students have weathered the transition to SBG beautifully. Their grades really do emphasize the positive aspects of learning that a pure assignments & points system blurs without thinking twice.

Crowdsourcing a learning-to-teach framework

After a good conversation with a friend that is getting started with teaching, I was thinking a bit about the process of learning to teach. Things that I obsessed about as a first year teacher come much more naturally now, but if you asked me what I needed to learn in the beginning, I would have babbled on like an idiot. Knowing what to focus on when everything is so new, not to mention feeling you aren't good at any of it, you understand why it is so easy for students to shut down when we ask them to 'be responsible' without helping them understand what we mean. Our job as teachers is to provide students with a framework that will help them be successful in learning what we teach them.

You would hope that guidance in this would be an essential component of teacher preparation programs, but it often doesn't, particularly in cases where observation is a box to be checked, not a pathway to improvement. There are many frameworks for observation, but I haven't seen one that specifically gives guidance (or even a curriculum?) for what new teachers should be looking for when in a mentor teacher's classroom. Most of the observation forms I've seen are in evaluating teachers for teacher quality. When I go to watch a colleague, I'm thinking about how I'm going to use what I see to improve what I do, not how to make them a better teacher. I know what I am looking for because I've had the keys to my classroom for a little while.

C'mon internet, let's work together to create this and help our newbies. We were all new to this once, and there's a lot that we may not realize we are thinking about after pulling out our hair and having teaching nightmares for so long. (Do they ever stop?)

To be clear, the goal is to start conversations between new teachers and their mentors, not put new teachers in a position to evaluate those who are being observed. We want to make the most of this time that is probably the most valuable teacher preparation tool outside of standing in front of a class yourself.

I've put a document designed to compile these ideas here:

So you're a new teacher. What should you focus on this week?

Please add to the list and snarky-up the title. There may even be a better way to organize this so that it isn't a big list that again serves only to intimidate. Maybe along the lines of Emergency Compliments?

Cell phone tracking, Processing, and computational thinking

I gave a survey to my students recently. My lowest score on any of the questions was 'What I learn in this class will help me in real life.' I've given this question before, and am used to getting less than optimal responses. I even think I probably had a higher score on this question than I have received previously, but it still bothers me that we are having this discussion. Despite my efforts to include more problem solving, modeling, and focusing on conceptual understanding related tasks over boring algorithmic lessons, the fact that I am still getting lower scores on this question compared to others convinces me that I have a long way to go.

I came up with this activity in response. It combines some of the ideas I learned in my Udacity course on robotic cars with the fact that nearly all my students carry cell phones. While I know many cell phones have GPS, it is my understanding that phones have used cell towers for a while to help with the process of locating phones. It always amazes me, for example, how my cell service immediately switches to roaming immediately when driving across the US-Canada border, even when I had a non-GPS capable phone.

My students know how to find distance using the distance formula and sets of coordinates, but they were intrigued by the idea of going backwards - if you know your distance from known locations, can you figure out your own location? The idea of figuring this out isn't complicated. It can most easily be done by identifying intersections of circles as shown below:

One of my students recalled this method of solving the problem from what he saw in the movie Taken 2 , and was quickly able to solve the problem this way graphically in Geogebra. Most students didn't follow this method though - the general trend was to take a guess and adjust the guess to reduce the overall error until the distances were as close to the given distances as possible.

I got them to also look at other situations - if only two measurements to known locations are known, where could the cell phone be located? They played around to find that there were two locations in this case. I again pointed out that they were following an algorithm that could easily be taught to a computer.

I then showed them a Processing sketch that went through this process. It is not a true particle filter that goes through resampling to improve the guessed location over time, but it does use the idea of making a number of guesses and highlighting the ones with the lowest error. The idea of making 300,000 random guesses and choosing the ones that are closest to the set of distances is something that computers are clearly better at than humans are. There are analytical ways of solving this problem, but this is a good way of using the computational power of the computer to make a brute force calculation to get an approximate answer to the question.

You can look at the activity we did in class here:
Using Cell Phones to Track Location

Who’s gone overboard modeling w/ Python? Part II - Gravitation

I was working on orbits and gravitation with my AP Physics B students, and as has always been the case (including with me in high school), they were having trouble visualizing exactly what it meant for something to be in orbit. They did well calculating orbital speeds and periods as I asked them to do for solving problems, but they weren't able to understand exactly what it meant for something to be in orbit. What happens when it speeds up from the speed they calculated? Slowed down? How would it actually get into orbit in the first place?

Last year I made a Geogebra simulation that used Euler's method  to generate the trajectory of a projectile using Newton's Law of Gravitation. While they were working on these problems, I was having trouble opening the simulation, and I realized it would be a simple task to write the simulation again using the Python knowledge I had developed since. I also used this to-scale diagram of the Earth-Moon system in Geogebra to help visualize the trajectory.

I quickly showed them what the trajectory looked like close to the surface of the Earth and then increased the launch velocity to show what would happen. I also showed them the line in the program that represented Newton's 2nd law - no big deal from their reaction, though my use of the directional cosines did take a bit of explanation as to why they needed to be there.

I offered to let students show their proficiency on my orbital characteristics standard by using the program to generate an orbit with a period or altitude of my choice. I insist that they derive the formulae for orbital velocity or period from Newton's 2nd law every time, but I really like how adding the simulation as an option turns this into an exercise requiring a much higher level of understanding. That said, no students gave it a shot until this afternoon. A student had correctly calculated the orbital speed for a circular orbit, but was having trouble configuring the initial components of velocity and position to make this happen. The student realized that the speed he calculated through Newton's 2nd had to be vertical if the initial position was to the right of Earth, or horizontal if it was above it. Otherwise, the projectile would go in a straight line, reach a maximum position, and then crash right back into Earth.

The other part of why this numerical model served an interesting purpose in my class was as inspired by Shawn Cornally's post about misconceptions surrounding gravitational potential and our friend mgh. I had also just watched an NBC Time Capsule episode about the moon landing and was wondering about the specifics of launching a rocket to the moon. I asked students how they thought it was done, and they really had no idea. They were working on another assignment during class, but while floating around looking at their work, I was also adjusting the initial conditions of my program to try to get an object that starts close to Earth to arrive in a lunar orbit.

Thinking about Shawn's post, I knew that getting an object out of Earth's orbit would require the object reaching escape velocity, and that this would certainly be too fast to work for a circular orbit around the moon. Getting the students to see this theoretically was not going to happen, particularly since we hadn't discussed gravitational potential energy among the regular physics students, not to mention they had no intuition about things moving in orbit anyway.

I showed them the closest I could get without crashing:

One student immediately noticed that this did seem to be a case of moving too quickly. So we reduced the initial velocity in the x-direction by a bit. This resulted in this:

We talked about what this showed - the object was now moving too slowly and was falling back to Earth. After getting the object to dance just between the point of making it all the way to the moon (and then falling right past it) and slowing down before it ever got there, a student asked a key question:

Could you get it really close to the moon and then slow it down?

Bingo. I didn't get to adjust the model during the class period to do this, but by the next class, I had implemented a simple orbital insertion burn opposite to the object's velocity. You can see and try the code here at Github. The result? My first Earth - lunar orbit design. My mom was so proud.

The real power here is how quickly students developed intuition for some orbital mechanics concepts by seeing me play with this. Even better, they could play with the simulation themselves. They also saw that I was experimenting myself with this model and enjoying what I was figuring out along the way.

I think the idea that a program I design myself could result in surprising or unexpected output is a bit of a foreign concept to those that do not program. I think this helps establish for students that computation is a tool for modeling. It is a means to reaching a better understanding of our observations or ideas. It still requires a great amount of thought to interpret the results and to construct the model, and does not eliminate the need for theoretical work. I could guess and check my way to a circular orbit around Earth. With some insight on how gravity and circular motion function though, I can get the orbit right on the first try. Computation does not take away the opportunity for deep thinking. It is not about doing all the work for you. It instead broadens the possibilities for what we can do and explore in the comfort of our homes and classrooms.

Who's gone overboard modeling in Physics? This guy, part I.


Fatal error: Cannot declare class VideoPress_Video, because the name is already in use in /home/weinbergmath/webapps/blog/wp-content/plugins/jetpack/modules/videopress/class.videopress-video.php on line 7