Reasonable Numbers, Unreasonable Nutrition

I just went to a McDonald's to eat and use the wi-fi to get some work done. Here's how it went down:

• Ordered 20 pc meal (stop with your judging eyes) 
• Cashier kid heard 10 pc. I didn't notice until after I had paid. 
• He called over manager. She decided to see what the price of the 20 pc meal was ($7.50), look at the receipt ($6.19), and charge the difference. 
• She asked the kid what the difference was. He was pretty satisfied with his answer of $1.20. She found an item for $1.15 and charged me. 
• Everyone involved was very nice and helpful, and works too hard for too little money.

There are a lot of failure modes for mental arithmetic, but there are some simple checks that you should go through. Here, anything that doesn't end with 1 is impossible. It's easy to come to $1.41 or maybe $1.21, but $1.20 shouldn't pass the smell test. 

We've been doing some curriculum work at school, and the math and science departments across all four divisions are convinced that this sort of answer-checking is something that kids have to have. They're right. It's a habit of mind for a scientist or mathematician, and it's something that we have to spend time with our kids on if we want them to learn it. 

$1.30 as an approximate answer's pretty good, and that's something else that we should work with kids on - coming to first approximations before solving a problem, so that we have some idea about what we're supposed to get, not falling prey to the "writing down whatever the calculator spits out" syndrome. These approximations can be about rounding numbers or about using a first-order Taylor series or squaring off a curve or whatever, but this is a skill that's even less frequently explicitly taught in schools than checking answers for reasonableness. Dan Meyer's "Give me a number that's too high, give me a number that's too low, give me a guess" is a great way to start.

There's certainly a lot of content to get through, but these mathematical practices are arguably at least as important, not least because they'll often survive after the content is forgotten. Don't we want to live in a world where people have these tools (even non-academic folk)? If the answer's yes, then put your class time and assessment questions where your mouth is this year - make time for work on reasonableness-checking and approximation.

Whiteboard Loudly

I came across "University Buys Bulletproof Whiteboards" today. It's about a move by UM-Eastern Shore to buy 200 18"x20" bulletproof whiteboards - at what seems like a cost of $300 a piece. The idea is that students and teachers can use these as shields in the event of a school shooting. Those logistics aside, two things:

1. This is a far cry from the $2 Interactive Whiteboard! Portable whiteboards are cheap and can instantly transform a classroom into a place of doing, rather than a place of hearing. While it's great that some of these whiteboards are going into UMES, I hope that they're also being used to change the environment of the classroom, rather than sitting next to desks waiting for bad news. For the price, they could buy/make a $2 whiteboard for every student at the school! The cost/benefit analysis here isn't really my point, but if these are worth $60,000, maybe it's also worth it to spend $5000 to outfit every room in the school with a set of student whiteboards, and worth the cost to train teachers to use them effectively to increase student engagement and learning.

2. I generally try to stay away from the bottom half of the internet, but the comments in the CNN article speak volumes. Almost everybody there cannot conceive of whiteboards that are not the exclusive domain of the teacher. (some disturbing images ahead, and, as usual, even more offensive stuff in other comments on the article, so follow those at your own risk)

• "Sure is a publicity stun[t]. Dumb one at that because it's pretty obvious that a shooter can figure out how to walk behind a white board."
• "How does a bullet-proof white board, which is mounted against a wall, protect anyone from bullets, which would be fired from somewhere inside the same room?"
• "The point derpmage is making is that all these whiteboards are mounted (i.e. screwed into the walls) typically in these classrooms. So, if something started, what is a teacher supposed to do? Are they supposed to somehow rip a bulletproof Kevlar Reinforced whiteboard off the wall somehow in order to use it to protect themselves and others? Not going to happen. A waste of taxpayer dollars."
• "There's a hook for easy hanging. Did you honestly think that you were the only one smart enough to realize that having it bolted to the wall would be problematic? It may be a waste, but they did have the foresight to consider the access issue."
• "Many whiteboards are used as standalones next to the blackboard... not hung on walls..."
• "Most schools got away from blackboards and use large whiteboards attached to the walls and use markers. This is really too small for classrooms. It wouldn't hold much information. Besides, the teacher may be safe but not the students. One University building has more then 200 rooms."
• "You take it off the wall and use it as a shield."
• "Is the professor supposed to hold the whiteboard -all the time- in preparation for the moment a gunman comes charging through the door? Otherwise they'll be dead before they get to it."
• "Also, I reckon these whiteboards may be more handy for a crazy gunman than the professor trying to hide behind it. Simply take out professor and ... BINGO, the gunman now has a shield against law enforcement to hold off their position! Super dumb in my opinion."

Even folks that notice the small sizes of the boards go through contortions to imagine them on the wall, in the professor's hand, etc. I haven't seen a single comment understand the idea that the whiteboards are for the students. If you're whiteboarding, don't keep it a secret! It's pretty infectious, so let some teachers see students working actively with whiteboards, figuring things out, collaborating, being skeptical... ; it got me hooked!

A few links about whiteboarding:

• Colleen Megowan's Dissertation, from the ASU Modeling site
• Mistake Game (O'Shea)
• Whiteboarding and Socratic Dialogue (Wenning)
• Math Whiteboarding (Dickson)
• Whiteboarding (MacIsaac)
• Using Interactive Whiteboarding to Support Student Learning (Blanton)
• Making Thinking Visible (Abud)
• Intro to Whiteboarding (Rowen)
• Whiteboarding posts (PoL)

LaTeX Code for Standards

If you're interested in displaying coarser standards with core skills and proficiency indicators (or whatever you want to call them) in nice LaTeX boxes, here's some code for you!

There are two main templates that I work with - one with a subtitle for the standard and one without. The centering on the vertical text doesn't (in my experience) work, so I just have to play with the size of the parbox to make that work, but everything else renders pretty easily.

Edit: Thanks to Aaron Titus for pointing out two necessary inclusions:
\usepackage{multirow}
\usepackage{graphicx}

No subtitle:

{\footnotesize \begin{tabular}{| p{.7 cm} | p{1.7 cm} | p{13 cm} | }
\hline
\multirow{8}{*}
 {\rotatebox[origin=c]{90}{\parbox{22 mm}{{\large{\bf Friction }}}}}  
&Core Skills & Identify situations in which friction forces are present and understand the microscopic model of friction forces\\ \cline{3-3}
& & Differentiate between static and kinetic friction \\ \cline{2-3}
& \multirow{2}{*}{\parbox{1.7cm}{Proficiency Indicators}} & Determine the direction of the friction force \\ \cline{3-3}
& & Use an appropriate expression for the magnitude of the friction force \\ \cline{3-3}
& & Understand the relationships among normal force, friction force and friction coefficients \\ \cline{3-3}
& & Solve problems using friction \\ \cline{2-3}
& \multirow{1}{*}{\parbox{1.7cm}{Adv. Ind.}} & Solve complex friction problems, including banked curves (not at design speed) \\ \cline{2-3}
\hline
\end{tabular} }
\vspace{2 mm}

Subtitle:

{\footnotesize \begin{tabular}{| p{.15 cm}  p{.15 cm} | p{1.7 cm} | p{13 cm} | }
\hline
\multirow{8}{*}
{\rotatebox[origin=c]{90}{\parbox{32 mm}{{\large{\bf UFPM }}}}}  
&\multirow{8}{*}
{\rotatebox[origin=c]{90}{{\parbox{50 mm}{\scriptsize \centering Unbalanced Force Particle Model}}}} &Core Skills & Recognize when the forces on an object or system are not balanced from observation, graphs, equations, or descriptions of the motion  \\ \cline{4-4}
& & & Identify the presence and directions of normal, tension, and weight forces  \\ \cline{4-4}
& & & Draw a force diagram (FBD) accurately showing directions and types of forces acting on an object or system  \\ \cline{4-4}
& & & Write net force equations describing an object or system; they should indicate that the forces are not balanced in the appropriate dimension(s)  \\ \cline{3-4}
& & \multirow{2}{*}{\parbox{1.7cm}{Proficiency Indicators}} & Draw FBD correctly indicating that forces are not balanced; recognize same \\ \cline{4-4}
& & & Choose and consistently apply workable direction(s) of positive \\ \cline{4-4}
& & & Correctly apply Newton's 3rd law \\ \cline{4-4}
& & & Choose appropriate axes for force analysis \\ \cline{4-4}
& & & Solve problems using net force equations and/or FBD \\ \cline{3-4} 
 \hline
\end{tabular} }
\vspace{2 mm}

LaTeX Python Scripts

Here are the supporting materials from my final talk at AAPT's Summer Meeting 2013 in Portland, on LaTeX and Python in assessment creation.

There are two Python scripts and some LaTeX examples in the package. The scripts are:

• Assessment Maker Lite: takes problems from the problem database (well, really a folder of individual problem LaTeX files) and assembles a properly numbered and pretty assessment PDF
• Problemdb Lite: manages the problem database: it counts the problems, identifies the tags on each, and renders a PDF based on search criteria ("Vectors Drag" would search for problems containing both tags and "Vectors OR Drag" would get vector problems and drag problems) or gives a PDF of the whole set. Vertical space is removed, so the set will be compressed and will fit in a smaller number of pages, but it may cause awkward display at times.

There are some auxiliary documents, including a LaTeX example document and an Excel sheet to store assessment names and problem numbers for future reference (and easier entry into the Assessment Maker). 

You'll have to set some paths if you move things around, and definitely to reflect the location of your LaTeX engine and PDF viewer. There are comments in the code showing you where you might need to do that.

Any Python install should be fine: I'm using Python 2.7, if you're curious. You'll need a LaTeX install and the only custom style package needed is floatflt (available at CTAN and by Googling).

These can be expanded a great deal, including adding a GUI (I use Tkinter), polling Google docs (using GoogleCL) to create customized reassessments based on student signups, etc. These require more dependencies and directory-setting, so I didn't include them in the Lite versions.

I'm not a software engineer, so there's surely improvement to be made, features to be added, and errors to be checked (it'll just crash out if there's a compile issue, for example), but it should be fine for workaday use - it is for me! :)

Stick Figure Maker 1.0

Here's a VPython script that lets you click and drag to create stick figures in any position, so that you can take a screenshot and use them in test questions, etc. It's quick and dirty, but it should work for you, if you have VPython installed.

• Drag any of the red handles to reposition - the head's not independently movable yet
• Position the floor, if you need to
• Click the toggle switch to hide the handles
• Screenshot
• Done!

There's a short YouTube video of the process in action here.

Some examples:

Walking

Running

Ninja Attack!

I borrowed the kernel of the drag-and-drop code from Sherwood/Chabay. Let me know if you find it useful!

The source:

SBG Resources

I'm posting some resources from the SBG panel from today. Thanks to everyone that came! Here are some of the resources that we discussed:

• My Prezi (logistics)
• Stephen Collins's Presentation
• SuperFly (Andy Rundquist)'s Presentation
• My mindset materials: it's really important to talk a lot (that is, a little at a time, but over a long time) about learning, metacognition, grading, etc. 
• Lots of SBG links

SBG: Philosophy and Logistics

Teaching is always the best way to learn. Yesterday, Andy (SuperFly) Rundquist and I gave a workshop on standards-based grading at the AAPT summer national meeting in Portland. While preparing the workshop, I did several things. Watching all of Portlandia was valuable, but preparing the agenda and having conversations in the workshop were terrific.

Many of these teachers were on the cusp of their first year of SBG implementation, and itching for advice. One of the things that folks are always interested in is the logistics - grading scaling, calculating overall grades, mechanisms for reassessment, etc. The more important part, though, is the philosophy, and everything else is just implementation. If you're not sure what your purposes for assessment are, how that relates to feedback and what the students do next, then the potential benefits will be lost. This is an interesting contrast to traditional grading - because everyone's familiar with traditional grading, you don't actually need to consider why you're doing it, what you want out of it, exactly what the expectations are for the students, etc. That doesn't mean that any particular teacher doesn't, but think about it - do you really need to have a consistent philosophy of assessment to conduct your class and assessments that way? You really don't!

There are as many implementations of SBG as there are teachers, but there are, as I see it, two non-negotiable tenets of SBG:

1. To the best of your understanding, student understanding and the grade should be interchangeable, equivalent, homeomorphic, or whatever you want to call it.
2. Understanding changes over time (therefore... so should grades, by application of #1)

A corollary of #1 is that the grades have to be related to the content, rather than the assignments. That's where the standards-based part comes in. How you accomplish these, by grainy or coarse standards, student-initiated or teacher-initiated reassessments, with binary or other rubrics, etc. is highly dependent on your students (age, preparation, numbers), your school (time, culture, schedule), and you (personality, experience, class rapport). As long as you keep #1 and #2 in mind, communicate them to the students often, and everyone's clear that the students and teacher are a team working towards understanding, the implementation details aren't the main thing.

Basically, that's how you survive your first year of SBG. With that under your belt, start worrying about reducing paperwork, streamlining reassessment sign-up and administration, making reporting better, and all of that.

One big discussion that we had involved the inclusion of time as a variable in the grading. This is the default in traditional grading - there's not much reward for learning material after the test, so two students that both learn all of the material and score the same on the final could, because of the speed at which they learned it, get vastly different overall grades. The philosophy of SBG definitely tries to remove time as a variable, and I think that the improvement of grades to reflect improved understanding and the lowering of grades to reflect eroded understanding puts a very clear message out that enduring understanding is all that I care about, not how fast you learn or whether you can cram.

There was a little bit of pushback on that, and a good discussion followed. One idea thrown out was about employers - don't they want to know which person can learn the skill in a day instead of three? Probably they do, but I don't think that the traditional system actually communicates that clearly. Before I get to that, I don't think that it's appropriate to make that sort of thing an issue for novices; we're talking about kids in their first or second class here, not grad students ready to go into the workforce as physicists. 

The more important thing for me is the collateral damage that an attempt to include speed of acquisition by way of not allowing grades to change over time. The argument seems like it's about differentiating between these two kids:

...but in reality, it ends up being these two kids:

Without the incentive structure, support, and learning from assessments (when they're not final, they're easier to really take as indicators for improvement, rather than scarlet "D"s to be ashamed of and thrown away), a good number of those students simply fall of the the back of the pack, having a shaky foundation that they can't build upon. What I'm saying is that, with SBG, the
blue line" kid from the second graph can become the "blue line" kid from the first graph!

I've seen some criticism from others than SBG can allow higher grades than traditional grading. When applied correctly, that's a feature, not a bug.

My grade distribution is about the same as it was before, but each grade represents a higher level of understanding than before. When there's a mechanism to improve, the bar can be higher!

Interestingly, we heard from some local teachers that the state of Oregon is implementing SBG across the board in the near future. That seemed to have driven some of the high attendance in our workshop. I did a little searching, but couldn't find the details on the plan, so corrections/additions/clarifications are welcome in the comments. I'm certainly all for SBG, but it's really dangerous to make big top-down changes to these things. There must be a lot of teacher education and buy-in to make it work, or it'll be another passed ed fad, which would be a tragedy. Philosophy first, logistics second.

OK, tonight a little sushi to talk over the panel discussion on SBG that Aaron Titus, Stephen Collins, SuperFly, and I are leading tomorrow (8-10 in Broadway I/II) and then a day checking out Eugenia Etkina's new text at noon (Pavilion West) and the Demo/Lab (Galleria II) and Modeling instruction (Ballroom II/III) sessions from 4-6.