Belated goodness of the calculus variety

I've been out of the habit of blogging for some time now, mostly because I'm teaching new courses this year. One is AP Calculus, and while it's way more fun than I imagined it would be, the workload is onerous.

I've been trying to integrate as many real-world experiences as possible into class. Curiously, some students really resent this: they believe that math courses are for doing dry problem sets, not analyzing phenomena from the wild. It's an interesting mindset, and breaking the I-we-you routine (see third paragraph) that they expect has proven difficult. We've found a compromise that seems to be working reasonably well, and we've been doing some neat things.

Yesterday we found a way to do the classic sliding ladder problem experimentally. It took a while to get the setup right, but in the end it worked like a charm.

The camera was a little bit too high to see the constant velocity buggy, but I was able to track its motion using the top of the bulls-eye I drew on a piece of paper and attached. The vertical bulls-eye worked like a charm- Tracker's autotracker function is sweet.

Using the x, y, and dx/dt values at t=1.4s predicted a dy/dy of -0.255 m/s Experimentally we got -0.2146 m/s. Not bad for the first go-around.

Stuff I've found useful lately:
Keeping me full of good ideas: Think Thank Thunk
Notes and Organization: OneNote
Graphing: FluidMath (still working on using this more- wish it worked inside OneNote or that OneNote had better math recognition)
Good read: Dan Kennedy
I'll do my best to post more regularly. Hope all is well!

Summer Reflections

I've been meaning to write this for some time, and I finally got the chance during a trip I took recently. I wanted to reflect a bit about the year and start thinking about next year.

Regents: The course went pretty well. I've been giving a lot of thought to how I teach- part of me wants to abandon my lab program (which I love) to spend more time on whiteboard debriefing. However, our 38 minute periods don't lend themselves to this mode. I was pushing for adjacent labs with the same roster as the class, but it doesn't look like it's going to be possible. I love the idea of physics soulmates that Kelly uses!

AP: I erred on my timing. I was pushing to be able to assess each target 3 times on in-class assessments  With ~40 standards and two on each weekly assessment, this simply wasn't possible. I backed off this after the first semester in an effort to make up for lost time, but the damage was done. We also ditched the independent lab program, which I wasn't happy with anyway- it seemed like the students weren't interested and didn't have the time or motivation to finish things that needed a little bit more oomph outside of class. We spent a lot of time on an awesome projectile motion project with tennis balls, but we probably didn't have that much time to spare. I realized it once we were partway through, but didn't want to do it half-assed.

Toward the end of the year the pace was too fast- we were able to cover the material, but it didn't truly sink in. In addition, there was a lot of backlash against SBG. About half the class was dissatisfied with it, others wanted to see it modified in one way or another. They also blamed it for the slow pace of the course, which wasn't the root problem- it was how I implemented it. Some of the students lost faith and were very upset with their experience, saying on their final reflection of the year that they would not recommend the course to future students.

I was disappointed by this, but I understand where they were coming from. As a school/system we're so fixated on the HW/quiz/test system of getting a good grade that something different seems to throw students for a loop. For the majority of them, despite their best intentions, when push came to shove they didn't do the recommended conditioning since it wasn't required. They left it all until the end of the marking period and tried to cram it in, but since they weren't practicing as they went their skills in these areas suffered, and then the new topics that built on these skills were shaky.

My advisor in graduate school always told me that you are what you grade. I have always tried to follow this mantra in determining how I want to assess my students. The last time I taught AP Physics using a traditional grading system I used the following breakdown::

30% Homework
30% Tests
15% Labs
5% Quizzes
20% Class Participation

This year I gave 70% to core standards, 20% to advanced standards, and 10% to experiments and class participation.

Here is what I'm thinking about for next year: go back to a traditional grading system, but with a SBG twist and modified percentages to encourage the behavior I want to see.

15% Homework
40% Tests/Quizzes (in class work)
25% Experiments
30% Class participation

I want to make sure they do homework/practice, but not doing it perfectly shouldn't kill their overall average. So I want to base the bulk of their grade on what they do in class. I really liked the weekly assessments and frequent feedback, so I might try to keep that trend going with bi-weekly test/quizzes and then bigger assessments for each marking period- sort of like the prelim system used at Cornell.

Frank posted a short SBG reflection. I'm not sure how I'll assess by concept- if I use the standards I utilized this year I'll have to pare them down and redesign them- some weren't great. What really caught my attention was the first link in his #2. What I love about this method is how you have tests, but the scores aren't set in stone. You can try that section again on the final exam, and if you do better it erases your previous grade. But if you did well on the original test, you don't have to complete that section on the final exam. I'm trying to figure out how to do this- it's complicated by the need to submit marking period grades that are set in stone every 10 weeks. Hence the leaning toward a quarterly exam with more frequent quizzes on individual topics/concepts. The trick is going to be organizing it from the outset.

Doing this should also help me with my pacing. This has always been something that I struggle with- I am loath to move on until the majority of students have mastered a concept because I know that shaky foundations make for a weak overall structure. Always something to improve, that's for certain!

favorite things

My AP students did a project with tennis balls and projectile motion a while back. It took longer than I wanted, but the results were awesome.

I also wanted to share one of my favorite lab experiments in recent history. Not because of its results (slightly shaky), but rather because of its ingenuity and playfulness. And who wouldn't want to have a pogostick in the classroom?

Actually, it gets old after a bit. Both the squeakiness and the constant "no, that's someone's lab, you can't bounce on it all day long.

Model trains? Yeah, we can do that.

 Ballistic pendulum with a stomp rocket? Sure. The group decided to attach neodymium magnets to the end of the rocket and the back of the bucket to make absolutely sure that the collision was inelastic.

Next week I'm going to be sharing my Fulbright experiences with the Global Physics Department. Can't wait!

the white hole

I gave a test to my Regents Physics students this week. After the test as he left the classroom, a pupil of mine said he thought it was a good test. At first I was struck by this- a student telling me I wrote a good test? Awesome! Maybe it was a good test... Then I started thinking about it. Why did he think it was a good test? Because it was easy? Because he thought it was appropriate? Because it played to his strengths?

I wasn't sure. The student in question is bright, but not the most focused. He also has trouble with details- writing down starting equations, units, etc. The other day we were practicing and I mentioned that he had neglected some units. He asked me why they're needed, I explained, and then he decided it wasn't worth his time, even if the Regents exam will penalize him heavily for their omission. The test opened with difficult multiple choice, a short essay, and then some problems to solve. Nothing terrible, but many students made it harder than it needed to be. To illustrate this, let's consider two problems. First:

They said that the horizontal throw of the rock wouldn't make any sort of difference. Most mentioned a demo I had done in class with two pennies and a ruler, and the majority got full credit. I was pleased- it seemed like they understood.

Later in the test, the following problem appeared: 

The results were much worse than I had expected. 60% of the students used the horizontal velocity as the initial velocity in the vertical direction, and then got bogged down solving the resulting quadratic. It was painful to see. Was it a bad question? I don't know- what do you think? I thought it was good until the results came back.

On a bigger scale, this got me wondering it the test I administered was a good one. Is any test good? Would a more conceptual test be better? Would such a test prepare them for the state exam at the end of the year?

I've been using Standards-Based Grading with my AP students, but not with my Regents Physics class. Testing the waters, so to speak. I love SBG, but the workload is tremendous. Would it be better? Undoubtedly. Would it do me in? Perhaps. I hope to redesign my Regents class for next year from the ground up, and I'd love to incorporate SBG. We'll see how that plays out- lots of it depends on the school administration.

By the way, the student who complimented me on the test passed with a 70. I see three possibilities:

1) he thought it was a fair test but didn't know the material as well as he should have and complimented the test despite this
2) he was over-confident and thought he'd done better than he actually did
3) he was just messing with me.

I don't think it was the third one. I'm a reasonable judge of character and he was being sincere.

On a final note, in class yesterday we were talking about energy, and a student asked about black holes and what would happen when you fell through one. We talked about how it would rip you apart, and then he said "but when you come out on the other side through the white hole, it would put you back together again, right? It basically made my day, I laughed so hard I was almost crying. Apparently there is a vein in my forehead that starts to pulse when I'm either laughing or angry, and the kids all noticed it today. Sweet- there goes my poker game, and now I've just told the world about my tell!

back in the saddle

It's been a while since I've posted. Mostly because I've been super busy, but perhaps I was also putting too much effort into my posts to make them perfect. No time for that now, so you'll be getting the raw versions.

Updates:

Regents Physics: moving forward, but slower than I would like. Still working on projectile motion. Some neat experiments in progress (does adding flavoring to water affect how it freezes... Build your own air-zooka... piezo-electric film canister poppers, etc.). I did something different with Unit 4 this year. Started with the 3rd law. I liked it, but made a mess of the introduction itself. I made a new worksheet and added it to the mix. Decided to set it in space to put off dealing with Fg for a while. I decided to use two rockets, but that was a bad idea, because the students had to consider thrust. I'll use the same sequence if I teach the course this way next year (see note below), but rather than rockets and engines I'll use something like two objects that an astronaut is batting around. Ball in a cup game perhaps? Not sure why you would take that into space, but hopefully you get the idea.

AP Physics is going well. Again, slower than I would like, but I'm ok with it. Our foundation is rock-solid, now the pace will increase. I am confident that we'll get through all the topics, but we'll have to keep the pressure on. Still doing SBG and the weekly assessments. Two minor changes: they can apply for re-assessments using a paper form now (in addition to the google docs form), and no guarantee of seeing each target 3x on in-class assessments. I found that this was taking too long, and also made the students reluctant to apply for re-assessments because they knew they'd see the material again. Right now we're doing a museum-style installation of tennis ball arcs in the room (a la Helaina/Shawn). I'm psyched with how it's going. Lots of trial and error with the actual hanging methods (who knew that a fishing line wouldn't hold a clove-hitch without a keeper knot?), but the kids are troubleshooting really well. We'll have lots of arcs, some bouncing, etc. Probably some inverted gravity as well to keep things close to the ceiling and out of our way.

Writing all my AP units in LaTex because I promised myself never to use Word for anything bigger than a unit test. It's good, but slow. I'm getting better, much better, but it still takes a while. Hopefully this will be the only time I have to do it and the future years will just make tweaks.

Next year:
I'd really like to teach AP Physics again. The year-on, year-off cycle isn't much fun- I feel like there are all of these things that I want to do and then forget about. One of the best things about having Regents Physics every year is that I get the chance to consistently tweak things.

Next year I'm hoping to have lab and class back-to-back for my Regents students with the same rosters. Maybe even labs 3x every 6-day cycle rather than the current 2. I might abandon my current Modeling materials in class and independent labs in small groups during lab method and do bigger stuff with smaller independent experiments mixed in. SBG? Maybe. I spend a lot of time on it and I'm only using it with my AP class right now. We'll see if the change comes to fruition. It would be a great change, but lots of work.

New things:
I stumbled across desmos (courtesy of mathalicious) and love it. I would tweak a few things (like why can't theta be  variable?), but overall it's really powerful. My AP kids are using it a lot for their arcs.

Hope to write more soon and make this updating thing a more regular occurrence.

25 percent

The end of the 1st quarter of the school year is upon us. My AP students are feeling it most acutely- some have several targets they haven't achieved proficiency on yet. They're signing up for re-assessments, and it looks like it's going to be a very busy week. The limit is one re-assessment a day, which can contain up to two targets. They have to submit their requests via my google docs form at least 24 hours in advance, which makes this whole she-bang reasonable. One particularly organized student submitted 3 different requests for next week, which was stunning at first, but at least I had the weekend to prepare.

People keep asking what I learned while I was in Argentina. They want to know what techniques I learned or what tricks the teachers shared with me. I feel like it's a let-down to say this, but when I think back about it, what I learned had more to do with how my actions can affect the class. I realize now that I'd become complacent, not in my methods or what I did, but in my expectations of students. In Argentina I saw students that were on a similar level as my own who were being pushed harder and challenged to go beyond what my own students were tackling. I realized that the limiting factor in my teaching wasn't my students' capabilities or work ethics, but rather my own ideas of what they could do.

So this year I've tried to push further. Not in a mean tortuous way, but in a hey-you-are-more-capable-than-you-think-and-I-know-you-can-do-this sort of way. One example was pretty minor, but it seems to be helping the students. When they write lab reports I've always had them include trend lines on their graphs. This year I've gone further- they need to modify the generic y=blabla*x + blerp equations to fit their own variables. For example, if they are changing air volume in a balloon and then measuring its airtime, the resulting equation should be something like time = (blabla seconds/pumps)*volume+blerp seconds. This seems to help reinforce that the equations are supposed to be modelling something physical; it's been easier to get them to make the connection between the equation of their equations and real world behavior at really big or really small values. This isn't anything new... I've expected my students to think about this type of stuff. It's just that few of them have. The relatively simple change in my expectations for their equations has produced the reflective behavior I wanted, though I didn't expect this to happen.

My students always choose their own lab topics and design their own experiments. This year we've seem some really neat stuff. One group chose to make a marshmallow gun, which is pretty neat. The cool thing is that they've gone down a different road than other groups who have tackled this topic in previous years. They've changed barrel length a little bit, but the big leap they made was to modify the scale of the gun. The original design was for mini-marshmallows, but they made new models to shoot regular-sized marshmallows and jumbo marshmallows. The air source they're using is still the same, so this led to an interesting discussion about scaling. Another neat thing was that the jumbo-sized marshmallows didn't fit perfectly in the barrel, so we had to wrap them in some wadding a la revolutionary war! Lots of layers to this one, but it's just one experiment out of roughly 20 that are running right now.

shopvac powered jumbo marshmallow gun

Another new wrinkle with my lab program is the reports themselves. I've used the same format for reports for the past 6 years with only minor changes. Each partner writes their own report, but they use different formats. One writes a technical report complete with abstract, and the other writes a popular report in a two-column format. I borrowed this technique from Larry Hiller in Buffalo, and I like it. Not just because it makes cheating much much harder, but also because it gets the students to think about their audiences. They can share graphs, tables, figures, etc., but the rest of the writing is their own. Ok, enough suspense (or rambling? hard to tell). The new wrinkle is that once students master the reports, they only have to submit a 1-page informal write-up that is graded on a sufficient/insufficient basis. The bar I set this year was a 90% on a formal report. I think I would make it >90% for future years, and maybe make them master both styles before they can switch to the informal reports. My students from last year who wrote ~8 formal reports in my course are slightly peeved, and rightfully so. I explained that I try to change things for the better each year, and that this is an experiment of sorts. I changed the AP C Physics course drastically this year, and I think it's way better than it used to be. But they don't have anything to compare it to, so they don't know how lucky they are. Speaking of which, this week they'll be completing a reflective activity about their performance thus far in my course. Anyone have any favorite questions they use to get kids thinking about their own work and efforts?

I have a few AP students who aren't nearly proficient on quite a few targets. I'm a little worried, but fingers are crossed that they'll pull it together before the end of the week. Nearly 25% of the year has passed, vacation season on the horizon... gotta make hay while the sun is shining!

Flaws, Solutions, and Ruminations

Wow, it has been way too long. I've been buried in work (mostly of my own creation), and this is the first time I've had a chance to come up for air. The other night I was leaving feedback for my students after their weekly assessment in class and I realized I was writing a lot. Mayhaps too much. Here is one entry:

Your graph of the backyard pool problem was pretty good. it put you in the right ballpark, but not quite close enough (the actual solution was 9 m). It was a reasonable graph, but you didn't show an algebraic solution to the problem, so I can't really tell how you're doing on this target. I get the sensation that the issue had to do with not having the equation you needed.... we need to be really comfortable with these equations. not just getting licensed to use them once, but knowing them well enough to be able to come up with them whenever we need them (or pull them out of our memories). If it was something else (like maybe the problem was intimidating), then I'd suggest some practice. Come see me sometime and we can chat about it.

The student who received this had an interesting issue- he had recently gotten a new iPhone and for some reason it was sending his texts and emails to his parents' computer rather than to his new phone (not sure how this happened). Well, mom got the updates from the BlueHarvest website saying that new comments were posted for him, and was astonished by the amount of text. I think that the word he used was actually "disturbed." Not sure if it's over the top or not, but it seems to have been a one-time thing, that particular night I had enough time to be able to geek out and write a ton, but that isn't normally the case.

So I'm still using SBG with my AP class. Some get it, others do not. One student said she definitely needs to come in for extra credit because she hasn't mastered many standards. I gave her a funny look, and this led to a new round of discussion regarding how I will calculate their grade at the end of the marking period. She wondered if getting less than mastery still earned her points on a target (it doesn't by the way, but it shows progress in the right direction). For the record, this is a conversation we've had before, but it had new urgency since it's about 2.5 weeks away. We also had a long discussion about what it means to be proficient in a skill and what should happen if they have an off day and don't do well on an assessment. I had been removing their proficiency if they bombed a standard on a new assessment that they'd already mastered- the point if it is to have the skills mastered, which means all the time, right? They argued that sometimes problems can be intimidating and hard to start. We went back and forth, their argument being that a single bad day shouldn't be cause for a drop in proficiency- maybe it should take two poor showings to drop back below proficiency. I'm not sure about this, but if we went to the two strikes model then I think I should add a caveat that if they do drop, they have to re-assess post-haste.

The whole discussion came up because there was a problem on an assessment I wrote that went something like:
Gwen and her little sister Natalia are hanging out in the back yard. It’s a hot day and they decide to race to the pool. Gwen decides that since Natalia is younger, she deserves a head start of 5 meters. After they count down “3, 2, 1, go,” Natalia runs straight to the pool at a speed of 1 m/s. Gwen starts off running at 3 m/s, but after two seconds slows down to a more sedate 1.5 m/s. A graph of velocity vs. time is shown below with the motion of both girls plotted.

a. Create a quantitative graph of position vs. time that shows the girls’ motion using the axes below.
b. How far away would the pool have to be for the girls to arrive there simultaneously? 

The other interesting factor is that I didn't give my students any equations. They all have to get "licensed" before I will let them use an equation- basically they have to be able to show me how they derived it. I borrowed this from Kelly (aside: this will definitely be the case for the kinematics equations, not sure about the rest of the course). Some students either remember the equations or drew a quick graph of position vs. time and derived it again, while others struggled. So... all the kids graphed the situation correctly. Partway through the assessment one student asked me if he could solve the problem graphically. I repeated his question so the whole class could hear it and then answered that a graphical solution would be acceptable, but that it wouldn't prove to me that he was proficient in the problem-solving target. I encouraged the kids to give it a shot, and one said, "well, why would I? I'm already proficient on this target, so why would I risk dropping that?" Ah the fatal flaw in my plan. I think there needs to be a new score for intentionally evading a target--> -1. In all seriousness, I should have given him a zero, which I use as meaning that the target hasn't been assessed. So his proficiency would have been history anyway. I hadn't done this in the past because sometimes the assessments I wrote were too long for our 38 minute periods, and it didn't seem fair to penalize kids for my mistake. However, this was the first question, so that excuse doesn't fly. As I write this I realize I've just solved my own dilemma. Maybe this dialogue will be useful for someone else, but at least it helped me just to write it down.

I've also been giving some thought to what other people do. Frank's SBG never removes proficiency once it's attained. Someone else (who I can;t find or remember right now, mea culpa) takes the average of all the scores to assess their performance on a standard, but weights the most recent so that it's 80% of the score. I don't particularly like this- it kicks out the idea that learning something well erases past mistakes.

Not sure about this... the students also argued that I need to tell them what standards I'm going to assess in advance so they know where to study. I find this idea repulsive, it seems like it would undermine the entire process. Has anyone else encountered this request from students?

Today I stumbled across one of the best visual explanations of the differences between traditional grading systems and SBG on Bowman Dickson's Blog:

SBG

Angry Birds with traditional grading

I really like it and want to share it with my students. This week we also took on the Red Bull Stratos Jump a la iModel iBlog - constant v for Regents, full analysis for AP. It was neat, and I appreciate the efforts of those who tabulated the data. I was planning to, but didn't get around to it, and was thrilled to find it already done.

This post turned out to be way longer than I expected. I've mentioned a lot of stuff here. I'd love to hear what others think, so if you have any thoughts please chime in. I'll close with a quote from a parent who emailed me about her daughter's performance in my AP class and time spent studying (or lack thereof) outside of class. We exchanged several emails and this stuck with me: 

"... came home very disgruntled about today’s assessment. I was quick to ask if she had done any of the practice from the website. She stormed upstairs and said, “We should just have HOMEWORK!”  I think she’ll be availing herself of those practices now."