The Dreaded Final, Part 2

Well, the finals that I talked about a couple of weeks ago have come and gone.

I had some plans, some hopes, and some fears, and think that, on balance, it went pretty well.

Using PollEverywhere, I surveyed the two sections, asking them to reflect on the final: what preparation did and didn't work, and how they think that it represented what they knew.

Preparation:

"The preparation that worked for me was to memorize the problems and use some of the problems in the back of the book. What didn't work for me were the harder problems by myself."

•  This seems telling to me.  I really feel like the first sentence (memorizing) implies the second (trouble with something that you didn't memorize).  I try to communicate this all the time, but it's difficult when memorization has worked so well for so long with so many of them.

"i wrote down all the equations i needed to know and key ideas that went with them. i asked questions before the test and did all my reassessments."

"I wrote down all the equations and reassessed before the exam. I did a few goalless problems on my own."

• Woo-hoo, SBG!  Reassessing isn't as much about the grade as it is about increasing your understanding.  Doing is more effective than reading, watching, etc.

"I wish I had worked a little bit more in the ratios area."

"having more practice problems would have been helpful for me"

•  Fair enough.  Though we've done lots of WCYDWT? problems, which also require students to construct their own questions, we'll practice goal-less problems more often in the future.

"so generally I felt that while I was doing the goalless problems at home I was never really sure if the questions I was asking were the "right" questions to ask or if there were any "right" questions to ask or if doing goalless problems was the right way to study. I attempted to read possible questions and mimic them with regards to the setups you provided but i'm not sure if it worked. It seemed like it worked better than just trying the goalless problems. I wish that I had done a few with you rather than try to figure it out on my own.  

"I think doing problems from the book helped me see different ways to solve the questions"

"The preparation I did was less about specific problems than about overall concepts . I made sure that i could do basic to middle range difficulty in all the standards before pushing to harder problems . This preparation worked great for me."

• Concepts... yeah!  I also like the differentiation between different difficulty levels with the same skills.  There are flavors of SBG that work that way explicitly.  Mine does it implicitly, but it's something to think about in the future.
  

Execution:

"I felt rushed to do this since I felt like I spent more time coming up with variables for the problems than solving them."
 
"I liked the test, it gave us a chance to do well on the test."

"I liked how it gave us a chance to show what we know than specifically asking us to find something."

"I also felt that after I left the exam there were all sorts of things I knew but didn't get the chance to work it into the exam, but overall I did feel that this format of test had the right concept and I just needed to find a different way to prepare for it." 


"This format , though i did well on it , is very stressful . Because of no limit , I did not stop writing until all my time was up. It was difficult for me to feel satisfied with not either filling everything in or doing everything I am capable of doing. Despite this, my grade reflected what I thought it should be in terms of what i knew so i can't really complain." 

• I'm pretty pleased with all of that.  Every format of test has its own quirks, but I'm going to stick with this one as a final format for a while.  I really think that I got to see a better picture of what they knew on this one, decoupled from their ability to decode the questions or picture the scenarios that I ask about.

Upgrades for Next Time:

• We'll do more explicit goal-less problems throughout the course, so that there shouldn't be any "newness" factor.
• I need to account for the large number of standards vs. short time issue.  We did all of the mechanics that we learned in 90 minutes.  I gave everyone a 4% lift to account for the fact that it's not unreasonable for someone to miss a concept or two with those constraints.  I don't want to just select some of the concepts, because the goal is to see everything that they know.   The time is 2 hours for the spring final, but there'll be E and M concepts added as well.  Hmmm...  Comments and suggestions welcome!
• I'll print out paper for them to use, with a big box for scenario number in the upper right corner.  Numbers in the upper left + staple in the upper left = hard to read.

Yo-yos with Yo-yos

The intrepid AP Physics class had some fun with yo-yos this week, figuring out why it rolls one way when you pull on the string one direction and the other way when you pull the string in another direction, and the angle at which it'll just slide.  Even cooler: it doesn't depend on the coefficient of friction of the surface!

We're grateful to Rhett over at Dot Physics for this video.

They also figured out from what height that they could drop a yo-yo (while holding the string vertically) and have it hit the ground at the same time as a falling ball.  They did this for two idealized shapes of yo-yos (which wouldn't make good toys): a hoop and a uniform cylinder.  Their predictions were calculated as a fraction of the height of the ball, and they drew the locations on the board, set up their objects aligned with the drawings, and dropped!

The predictions were awesome; Kyle's timing was less so! :)  Video linked to the picture!

Coke v. Sprite?

Inspired by Dan Meyer's super-cool WCYDWT problem Coke vs. Sprite, students in physics and honors physics set out yesterday to determine if the Coke glass or the Sprite glass had more of its original drink at the end.  I have the results here and a few observations and extensions (intended for my students, but hey, who's counting?).

In the honors class, there were four predictions of Sprite, three of Coke, and three that they'd be the same.  As they pursued the problem, some opinions changed when confronted with the icy-cold refreshment of the math.

In the physics class, there were shifting predictions for a few minutes after viewing the video, but by the time we split into groups, everyone thought that Sprite was the winner. I put the big emphasis in this section on showing, explicitly, absolutely every step of the logic that got them from the beginning to the end.  I didn't have to tell them if they were right or wrong, though I did point out and wishy-washiness in their logic.  After all, only one conclusion can be logically argued from the video!

Some students (n-1, actually), picked a dropper size and manually calculated the sameness of the final original soda volumes:

     Solving a specific instance of a problem is a great first step toward building a general solution, but it really isn't the end.

If I prove that the Titanic can float (well...), that doesn't prove that everything metal or everything red and black or everything with one fake chimney (really!) will float.  A general argument is... general.  An example may be suggestive, but is just an example.  The plural of 'example' is not 'proof.'

A generalized algebraic argument may be made, but here's a super-elegant diagrammatic argument, made by an enterprising young lady in the physics class:

Another group had a similar idea, but used a dropper for the shape:

How about that? A diagram that helps solve the problem.  It seems to me that I might've said something before about diagrams being useful...

Here's another model of a related question that a group in the second honors class came up with.  It shows the amount of Coke/Sprite left in their original glasses as a function of dropper size.  The endpoints weren't too hard to find, though it was yet another clue for modeling:

     Always consider the special cases!

What would the final amount be if the drop had a size of zero?  ...of 12 ounces?  Those easy questions reveal the beginning, the end, and something about the shape.  It doesn't tell you everything, though: you need to know if the function's linear or... not.

It turns out that it isn't (it also turns out that I didn't get this picture taken until they'd erased their board and started to work on the next thing, so I recreated it - sorry!).  The group that made this graph used a calculator to find the original-glass percentage for 10 or 12 different dropper sizes (they did it all in a table, making it pretty easy).

Why isn't it linear?  Well, we can go all crazy with the algebra!  If we call the original volume V and the dropper volume n, then, after the first dropper is transferred:

Glass 1 - Sprite: V - n     Coke: 0

Glass 2 - Sprite: n     Coke: V - n

The second dropper's the trick.  The proportion of Sprite that's in the second glass is: (if you don't see the equation in your reader, click the post title to go to the original post - sorry!)

The proportion of Coke in the second glass is:

The amounts transferred are therefore:

Sprite:     Coke:

This leaves:

Glass 1 - Sprite:     Coke: 

Glass 2 - Sprite:     Coke:

These don't look equal at first glance, but they both reduce (after finding a common denominator) to:

Check the units: 

• Volume-squared over volume: units of volume - check!

Check the special cases: 

• If the whole glass is the transfer size, then the glasses should be half-and-half at the end, which the function predicts - check!
• If nothing is transferred, then the glasses should have all of their original soda - check!

The function correctly predicts the special cases, has good units, and all of the expected behaviors.  Now you know that you have a model worth working with!

Student Quotes

"...I can sacrifice my values for math."

The Great Rolling Derby

The AP students had a "Great Rolling Derby" at the end of the winter term.  The assignment was to build/find something that would roll to the end of the 6 ft long 8 degree incline that I made in my basement.

There was some creative thinking, elbow grease, engineering, and cookie eating, and we took a moment to remember inertia.

The winner is... Kyle!  

Here are the entries, ranked from top to bottom:

Actually, I entered my son Anders, too, but you can see how he placed:

We'll have to work on that.

The Reassessment Beast

I've had the end-of-term rush twice now with standards-based grading.

Observations:

• It's certainly more of a rush when reassessment's on the table.  Is this because I've totally changed the motivations of the kids, and they want to take every bit of opportunity to learn more physics?  Well, maybe a little?  Maybe not.   At the very least, this means that they're getting more exposure this way than they would have before.  
• I should be less flexible with the one reassessment per student per day rule at the end of the term, regardless of missing days of school, etc.  Really, most of this should've been done ages ago, and it would've done them more good for the remainder of the term, rather than just for the final.  I don't like the idea of setting some sort of expiration date for standards (say, within two weeks of the test), because the message is really that all of the material is important forever.
• I've been using review rubrics for one set of classes as the tickets to reassessment.  I think that they're generally doing a good job of making students engage the material in a meaningful way before reassessing.

Stats:

• Total (official) student remediations this term: 
• Physics (34 students): 129
• Honors Physics (25 students): 101
• AP Physics (5 students): 4
• Total student reassessments before the week before finals week:
• Physics: 30
• Honors Physics: 13
• AP Physics: 0
• Total student reassessments during the week before the final and finals week:
• Physics: 77
• Honors Physics: 66
• AP Physics: 4
• Number of students not reassessing anything all term:
• Physics: 7
• Honors Physics: 10
• AP Physics: 4

Questions that I'm happy to answer during a final

"Can you show me how to draw a lambda?  I'm sick of drawing it wrong."

Yes, yes, a thousand times yes.