Sunday, April 22, 2018

Tuesday, April 17, 2018

How to teach a class you've never taught before

Short answer: work hard.

Oh you wanted specifics? Keep reading.

One of the intricacies of education is that we can do the same thing year after year but nothing is the same or we can teach a completely different class and everything is still the same. Here are two examples:

I taught Physics every year for ten years. In that time period there have been new national and state standards implemented, two major bell schedule adjustments changing the number of minutes per day and week, furlough days have come and gone, new rallies and school traditions take instructional time, I have changed rooms four times, decided to forgo homework and gotten a new textbook twice. While I have taught "Physics" for ten years the class I would teach now is not the same as when I started.

I have also taught Conceptual Physics seven times in ten years. Several times there was a year in between in which I did not teach it. The population changed from freshmen only to freshmen and English Language Learners to open to all students to freshmen and special education only. The book has not changed but I have also had the same schedule and calendar changes I experienced for Physics. Because the class was meant to sere students that need additional support many of the pedagogical approaches and project based learning remains the same.

It can be hard to teach a course you have taught before with textbook or schedule or population or calendar changes. And then you may have to teach something completely different. Physics teachers often have to teach non-Physics courses because of traditionally lower enrollment in Physics classes compared to say Chemistry. In some schools they are the only Physics teacher and thus teach multiple levels. We tend to have more preps (different classes to teach) and change them up more often than other science disciplines. In your career you will probably at least once have to teach a brand-new-to-you course that makes you feel like a new teacher all over again. That's what happened to me this year with AP Physics C.

While I would love to say I met the challenge gracefully with my years of experience that was not always the case. Sometimes the workload crushed me. It definitely left my family neglected, our house in disorder and our lives chaotic. But as the end of the year approached I found that it got easier, not because the curriculum did but because I had developed a process. I found, through absolute trial and error, what helped me and what did not. I realized I went through the same steps in the same order at the start of each unit and it started to get (incrementally) easier.

And thus I decided to share, not because it is innovative or particularly amazing but because it could be helpful. I know someone out there, experienced or not, will be told in the coming weeks that they will be teaching (gulp) some class brand-new to them. It is daunting, makes you question whatever skills you thought you had and the workload downright sucks. So if some of this process helps you, great. If not, hopefully it helps lead you to your own.

Start with what you are given:
If you are inheriting the course from someone else you may find that you have also inherited a few filing cabinets worth of material. Or binders. Or shelves and shelves of "teacher resources." It is time consuming but worth it to go through this materials and do a first sort of what is and is not useful. Ditch the floppy disc versions of your textbook's teacher materials; ditch multiple copies of supplemental materials (unless there is more than one teacher). Check with your district about district copies of these resources, they may wish to consolidate extras in their warehouse for potential future use. You don't have to read every piece of paper left for you in a file cabinet now, you don't have to decide to adopt everything they left for you but you may want to keep it to give yourself the option.

As I moved into my new room this year there were eight total file cabinet drawers left for me for Physics and AP Physics. In my first sort I kept one copy of everything. I wanted to be able to read the labs he wrote but figured even if I decided to do the same ones I would probably be retyping it. I wanted to be able to see what his tests looked like, but knew I didn't need a class set. I kept a copy of his handwritten lecture notes so I could see how he implemented material, even though I planned to make powerpoints. I kept the manila folders, overheads and single sided paper to reuse as scrap paper. In the end, I filled four full size recycling bins with the paper I discarded, that was just the double-sided stuff. What I kept fit in two 4" binders in page protectors. I separated the stuff by unit, or at least by what I thought was by unit at the time. I was left with no digital files, except for uneditable pdfs I was able to download from  his website before the district took it down.

As the year has progressed I started every unit going through what I was left. I looked over and digitized the lecture notes (you can copy it into a tablet or just scan it) to see how the material was presented before. If there was a worksheet that I wanted to use I would retype it as it was at first. I then did the worksheet myself and edited it how I wanted to for my own kids. Basically I took a look at what was done before as a guide, not to follow exactly but just for comparison. It provided a place to start, so I didn't have to start from scratch. There were plenty of worksheets, labs, etc. that I took this second look to and tossed aside. If you are lucky enough to start a new-to-you course that someone else teaches, start with everything they have. You can change things but it is invaluable to see how someone else teaches it, for better or worse.

Textbook resources:
While you may or may not use your textbook, electronic or print, your district has probably adopted one. Looking through it can be helpful if you have to learn or relearn material. I would read and take notes on each chapter, so that I could experience how the material was introduced just like my kids would. Most publishers have digital teacher resources now, either for download or on their website. My publisher has answer keys, lecture powerpoints, test banks, image galleries, simulations and more. So as to not re-invent the wheel, for each unit I started my lecture powerpoints using the textbook ones as a base. As the  year progressed less and less of the original remained but it saved me time when I had so little. While using pre-made resources is not ideal, you should personalize your curriculum for yourself and your students, it is not the worst starting place. In later years of teaching the course you will probably use your own materials more and more.

Find reliable resources:
No class should be taught by textbook alone. Finding a few trusted and reliable resources for your class is important. This may be a professional networking site or another teacher's website or even social media. I found helpful materials on a wiki page, PrettyGoodPhysics, that will sadly need to relocate. There were a few YouTube Channels that provided consistently good tutorials by subject for myself and my students. Sometimes it would be for a different course (AP Physics 1, 2 or Honors Physics) but good video lessons are good video lessons regardless. I recommend Flipping Physics, Dan Fullerton's APlusPhysics, Mrs. Twu's video tutorials and  AKLectures Physics series. If I needed to review a topic, or more importantly to learn what to emphasize for my students, it was very helpful watching other teachers teach it.

Social media turned out to be one of my greatest resources this year. I was able to find other physics teachers I did not know on Twitter and could follow or use hashtags like #APphysicsC to find resources by course. I was able to share data that didn't make sense and tag the equipment manufacturer who would often very quickly respond with suggestions. I once tagged @VernierST in the middle of a class period about weird looking data and got a response before my students left that period. They would continue to work with me for days as I tried to troubleshoot. Other teachers could jump on the thread and make suggestions or share sample data in the worst case scenario that nothing worked. I could share pictures of student work that made me scratch my head, asking more experienced teachers how I could prevent such incorrect problem solving in the future. As other teachers shared pictures of labs or demos they were doing I could save the picture for future use. I've even reached out to individuals to ask for their lab write-ups, ask follow-up questions or for advice. And they respond! Teachers usually like to help other teachers and many have been amazingly generous, sending me full curriculum guides, sample lecture notes, etc.

And perhaps most importantly, they don't judge much. On Twitter and on the College Board AP Physics C list serve I have posted problems that I cannot solve, or conceptual issues I still have that are preventing me from teaching it to my students. More experienced teachers have been able to respond with suggestions, solutions or alternate ways of approaching the problem. Everyone was patient as I usually started out my requests with "Since it's my first year teaching #APphysicsC..." And since I was putting that question out to anyone who could answer, people that could would and I would crowdsource some great solutions.

I also collected textbooks. Luckily we just adopted new AP textbooks so we had a textbooks from all the big publishers who had sent materials during the adoption process. I currently have six textbooks on my table, and I would often flip through all of them. For each chapter I would look through them to see if the example problems were different, how the material was grouped or arranged and to see what was emphasized. If my adopted textbook emphasized a type of problem that didn't appear in the other textbooks it helped confirm what was outside of the scope of the class.

Ask for help:
You know you should but it may still be difficult to admit that you don't know everything (yet) about your new course and you need help. Sometimes it was about the scope of the course, as my textbook includes a lot more than what is included on the AP Physics C exams. Sometimes the problem I tried to do out of the back of the chapter or on a worksheet I found was coming out wrong or I didn't have the answer to check it. Whatever it was I found that there were a few people I could ask for help. Most I knew personally through NCNAAPT but some I had met through my AP summer training or interactions online. I tried to spread out my questions, rotating through my "will help me" rolodex so that I did not take advantage of those willing to help me. I tried to figure it out by myself and not have to ask unless I was really stuck. My friends seemed to know this and did everything they could to help me when I asked.

Get trained:
I am a firm believer in proper science teaching professional development. Not all PD is good, don't get me wrong, but there are some consistently helpful training opportunities I always enjoy. For new teachers PTSOS and the Exploratorium's New teacher Institute of course. The national AAPT Summer and Winter meetings and your local AAPT meetings are full of the best-of-the-best resources shared among physics teachers. I find that the down-time in between workshops with other teachers can spark the best conversations and lead to lots of good shared ideas.

If the new-to-you course is an College Board Advanced Placement one you can also take a sanctioned AP training. They can be pricey but are often offered throughout the year. I had a hard time finding summer training for AP Physics C last year and had to travel to Texas to attend one. While it was helpful, I did not feel that one was enough to be comfortable teaching the course. I asked my district to send me to another one this summer and I'm crossing my fingers that there is more to learn.

Practice Practice Practice:
I found that, much like my students, I benefited from lots of practice. While I wouldn't do every problem in my textbook, I would probably work through twice as many as my students. I tried to do every conceptual question and did the ones that another AP Physics teacher using my book assigned. I figured that this more experienced teacher had probably already weeded out the problems that were too hard or awkward and these problems would be good for my students. Sometimes these still tripped me up and I decided early on that if I couldn't do the problem, I would not assign it to my students. By doing more problems I was able to see patterns in how the questions were asked or what they were asking for as well as improve my own problem solving technique. This also meant when it came to assessments I had more problems that I could solve then I had given to students to use.

One particularly helpful resource was an online workbook of released AP multiple choice and free response problems arranged by subject. This meant that I could look through the simple harmonic motion section and see all the problems ever asked on the AP exam about SHM. I could pick and choose the problems I wanted, combined with the textbook's test bank, to make my own tests. Sometimes working through all these extra problems seemed time consuming, especially if I wasn't going to assign them all, but overall it really helped my understanding.

Get organized:
This is easier for some than others, and I am not saying that everyone has to be a super clean desk all the time, but, if you are collecting new resources for a new class that doesn't do you any good if you can't find the cool thing your saved when the time comes. The easiest method is to create a folder for each unit and throw it all in there. At the start of the year I made a folder for each section of the AP Physics C objectives so that when I found a few resource I could sort it appropriately. This meant that prior to the start of the unit I would have maybe half a dozen to a dozen files before I really started to build the unit. As the unit progressed I would sort what I was using from the extra resources I wanted to keep from the assessments I would give. Since I tended to save everything I could get my hands on I would end up with a lot of files. For example, I started my magnetic field and forces unit with 5 digital files and two weeks later, before I've even written their test, I have 150.

Take care of you:
At the risk of sounding like a spa commercial, you need to take time out for yourself. Even though I was part time, developing new curriculum this year became my life. It was not unusual for me to work 12 hours a day, as in actual sitting down work, not just being awake for that long. I neglected my hobbies, cleaning, my health, because the work "had to get done." It will be the most work you've done outside of your first year to develop a new curriculum. Apologize to your family up front. However, do not lose yourself to it. Prior to this year I was trying to work on life-work balance and I failed miserably this year. I wish I had taken more breaks, spent more time with my kids, etc. but I didn't know how to get all my work done and do everything else. It got better as I developed this process and that's why I'm sharing. Hopefully having a game plan will help you develop your new-to-you course without drowning in your work. A burnt out teacher is not a helpful teacher.

To summarize:
1. Start with what you are given.
2. Try textbook resources.
3. Find reliable resources
4. Ask for help
5. Get trained
6. Practice Practice Practice
7. Get organized
8. Take care of you.

That's it, just 8 easy steps! (Totally sarcastic by the way)

It will be tough but by trying to focus on what I knew worked for me, I've almost gotten through it. As I can almost see the bright light on the other side believe me when I say you will too. Good luck!

Saturday, April 14, 2018

Resources ... In Color!

You have to have lived many summers to remember when "In Color" was appended to television show titles to distinguish them from humdrum black and white programs. Leslie Neilson spoofed the practice, along with everything relating to 1960s police dramas his Police Squad!.

I added color to my curriculum a few years ago. It began with writing a lab around PhET's "Color Vision" simulation coupled with pocket microscopes. The lab is called "Pixel Peeping" and it's a big eye-opener (!), especially when they look at the phosphors lighting up in yellow.

Next, I wrote an add-on activity called "Fun with Colors!" An interesting exploration of color mixing.

Then I saw this groovy video, and showed it in conjunction with the color activities. Biological pixels!

Science Friday: Where's the Octopus?

Then I saw this wee gem from Steve Mould, and thought to add it, too. How does your brain average red and blue when your green cone is silent?

The Royal Institution: Colour Mixing: The Mystery of Magenta

But I bristle at the notion of just showing a video or asking students to watch a video without having questions attached to ensure mental engagement. Otherwise, it's just watching TV. If it can't be done in class, it makes for great "YouTube homework."

So I put together some questions that could be answered while watching these brief clips.

Chromatophores and Trichromats

I had been using an iOS app to mix colors on my iPhone and iPad. But the app ecosystem is lively and active, so old apps die and new apps arise. An app developer named Insight currently offers an iOS app called Color Mixing. It has your standard color addition of primary colors (RGB) as well as color subtraction (CMY). It seems groovy, though I haven't tinkered with it much yet. I'm reluctant to develop an activity around such an app, since it may be gone tomorrow.

If you've got some groovy color stuff that works for you, post about it in the comments.

Sunday, April 08, 2018

Fluorescent Puffin Bills and Tetrachromacy

Serendipity. What a great thing among the scientifically curious.

Ornithologist Jamie Dunning’s serendipity compelled him to shine ultraviolet light on the already decorative bill of a puffin. And he saw something apparently not previously documented in the learned journals.

Birds, those opulent tetrachromats, are apparently up to their colorful shenanigans once again. We humans, humble trichromats that we are, just miss things sometimes. (It’s clearly not just the ability to fly that makes Naomi Hamilton Jealous of the Birds! But I digress.)

Read the story, behold the images, and mention it when you teach about colors and color mixing.

Puffin beaks are fluorescent and we had no idea.

Monday, April 02, 2018

Mechanical Universe High School Video Questions

Some of us are old enough to remember physics lectures. I may have even dabbled in that art during the first five years of my career. But its appeal faded as I placed increasing emphasis on more active learning techniques. The closest I get to lecture is guided discussion into a topic. 

We spend more time in laboratory, demonstration, and experimental activities these days.

But I do not banish all exposition as an enemy of learning. I outsource that task to the likes of Paul Hewitt (via Conceptual Physics Alive!) and The Mechanical Universe, especially the High School Adaptation

The High School Adaptation was originally released in oddly-grouped quads. For my purposes, I rearranged the episodes into sets that made more sense to me.

I couldn't show episodes of either series until I had question sets to accompany them. Active engagement in an otherwise passive activity, I suppose. The question sets I wrote for Conceptual Physics Alive! are distributed by Arbor Scientific. (You can get seven sets for free at the link.)

The sets of questions I developed to accompany The Mechanical Universe High School Adaptation episodes is now distributed at Teachers Pay Teachers: The Lessons of Phyz.

When I create a set of video questions for in-class viewing, I try to produce two different worksheets to diminish any wandering eyes tendencies of side-by-side table partners. I use a heavy font to increase legibility in low light since videos are often shown in diminished classroom illumination. The questions are to be answered while the video is playing.

The questions are also varied in type: fill in the blank, multiple choice, matching, and short answer. There are often illustrations involved in the questions. Importantly, these are low-level questions. They are not deep; they do not involve synthesis. They are not prompts for paragraph-length reflections. Their purpose is to keep students connected to the lesson in real time.

Too many video question sets I see strike me as impractical for real-time responses. They shoot for the upper reaches of the Bloom's Taxonomy mountain. I love high-level questions and use them as much as I can. But not during video play. Other question sets are wire-to-wire fill-in-the-blanks from the text of the narration. That's a bit extreme at the other end. I prefer to mix it up a bit while keeping it simple.

In any case, here are the sets of The Mechanical Universe High School Adaptation questions I've posted to TpT.

The Law of Falling Bodies · The Law of Inertia · Newton's Laws · Moving in Circles

Kepler's Laws · The Apple and the Moon · Navigating in Space · Curved Space and Black Holes

Conservation of Energy · Conservation of Momentum · Angular Momentum

Temperature and the Gas Laws · Harmonic Motion · Introduction to Waves

Electric Fields and Forces · Equipotentials and Fields · Potential and Capacitance · The Millikan Experiment

Simple DC Circuits · Magnetic Fields · Electromagnetic Induction · Alternating Current

Wave Nature of Light · Models of the Atom · Wave-Particle Duality

And now the bad news: If you don't already have the High School Adaptation edits of The Mechanical Universe, you can't really get them anymore. Intelecom had the distribution rights once upon a time, but it appears they have since dropped it from their offerings. If you're a card-carrying member of a library that subscribes to the Hoopla media service, you're in luck.

So much for my schemes of early retirement...

Monday, March 26, 2018


You know it's a bad situation when the hashtag basically writes itself.

This first year of teaching AP Physics C: Mechanics and Electricity & Magnetism has had lots of lessons, one of which I was not expecting. I assumed (and you know the old saying about assuming anything) that students in AP Calculus or Multi-Variable Calculus could graph data. And I was wrong.

Well to clarify, they can graph but they often choose not to. Be it innate teenage laziness, prioritizing their overwhelming workload, or even just forgetfulness, my students don't spend the time on their lab graphs that I would expect. My expectations were laid out at the beginning of the year, as they were in regular Physics and I'm sure every science class they have ever taken. They are summarized below:

1. All plotted graphs (not sketches) should be at least a half a page in size and made on graph paper.
2. Axis and best fit lines should be made with a ruler.
3. Each axis should be labeled with the quantity and units. Each axis should have a uniform scale but it need not be the same from one axis to the other.
4. The graph should have a descriptive title (i.e. not "Graph #3").
5. If multiple data sets are plotted use different colors and/or different data point symbols. Include a legend.
6. Add a best fit line or curve to your data that gets as close as possible to all of your data points. Do not "connect the dots." If the best fit relationship is linear include a slope triangle to calculate the slope of the line.

I don't feel that any of these requirements are too extreme, strict or beyond what they are being taught in math class. Yet as the year has progressed I have seen the graph quality decrease. The occasional student "forgets" to do it on graph paper; I may let it slide. Once in awhile someone makes the graph too small and I'll draw an unhappy face on it in red pen. The mistakes were becoming more common but due to drowning in curriculum development I kept ignoring the growing problem.

But then it became too big. Last week I collected student lab notebooks with two labs in it. One required several graph sketches (just a variable labeled axis and a general shape, no plotting) with two plotted graphs and the other only required two plotted graphs. Students had begged for additional time for lab notebooks and after agreeing I joked that I was expecting perfection.

I did not get it.

It started with one unbelievable graph. Bad enough that I snapped a picture and posted it on my Twitter feed. Then there was another. And another. I collected enough of the "worst" that I decided that I had to have a little "talk" with my classes about quality of work. I assembled them into a powerpoint and planned the reckoning.

The big day was today and I had it all set up to make the big points in an amusing way, but letting them know I was serious. I started each class with, "I graded your lab notebooks. We need to have a bit of a chat. What math level are you in again?"
Students warily reply "Calculus..." because they know they're getting set up.
"Oh that's right," I reply, "So you should be able to make a graph right?"
They nod.
"Well, I thought so too, but we need to talk about that."
In one class a student said, "Oh man, she made it into a powerpoint, that can't be good."
I assured students that these contributions were anonymous, and that if their graph was included I still care for them and I know that they can do well in Physics. They just had a big "oops" with this graph. 

We proceeded to flip through the examples, with a mixture of roaring laughter (to the point of tears for some) and absolute disbelief.
They had questions:
"Someone turned that in?"
"Is that a hole in that paper?"
"What is that line even supposed to be doing?"
"Were these all from that one assignment?"

One student at the end said, "Wow, and we had extra time so you wanted them to be perfect." Yeah kid, I was shocked too.

In the end it was a funny way of reminding them of my expectation, and now I have a collection of some of the worst graphs I've ever seen. Of course I would rather not have had the situation at all but at least we can all benefit. The collection is available as a pdf and individually below. Feel free to use in your classroom for the same purpose, hopefully they help you avoid your own #GraphFails.

Only one data point really? No ruler used for the axis, not made on graph paper, no slope triangle and the best fit line doesn't even go through the single data point!

One of my students said that this apparent best fit line (that completely missed every data point) might be a Z-axis. I don't know if that makes it better. And no, seeing the grid through the back side of a blank piece of graph paper doesn't count. 

Not on graph paper, not made using a ruler and made a thicker line (potentially to hide poor data). Actually I don't even know if these data points are even properly plotted. We decided this was more of an artistic representation of someone else's graph than a graph itself.

Students often ask to use Excel, and they can, as long as they can use it right. This is not right. I have no idea how that best fit line worked with that data. 

These are supposed to be sketches, not plots, with a variable on each axis. That pen tip is for scale. Yes they are that small.

If you're asked to make a slope triangle on your graph it will probably be linear. When in doubt, the student apparently thought drawing a slope triangle would help anyway. 

When I said a "uniform scale on each axis" I didn't think I need to be specific and say you need more than one number to establish a scale.

Of course having no scale is worse. 

The large data points on this were annoying but not terrible. It was the sneaky breaking of the graph that they tried to slip past me.

When your data doesn't seem to have a trend, I guess plugging it into a calculator is one way of finding a best fit line. 

Then again, even if the best fit line seems obvious maybe you should use your calculator to double check. 


Thursday, March 15, 2018

Why California's musical road sounds terrible

When Honda produced a musical road in Lancaster, California a few years ago, I linked to their commercial and developed a lesson that included it. A Blog of Phyz post was duly posted.

The off-key result (and a bit of auto-tuning) bothered me. And I certainly didn't keep that a secret. I assumed it was an implementation error of some sort, and tried to invoke the notion that, "It's not that the dog sings well, it's that the dog sings at all!"

Creative science YouTube content creator, Tom Scott, did the legwork, er, wheel work to get to the bottom of this grooviness gone awry. It boils down to "centers" vs. "gaps". Take a look.

If you spend time distinguishing between random and systematic error, you'll want to add this to your curriculum there.

Why California's Musical Road Sounds Terrible

Scott refers to his source: Caltech's David Simmons-Duffin. Here's the well-crafted and thorough article posted at way back in 2008. It really is well done, and he calls out Honda for auto-tuning the last two notes of the road, as did I. Spend some time and enjoy this post:

Honda Needs a Tune Up

Wednesday, February 28, 2018

A place for everything

Physics teachers hope to inherit or acquire useful lab apparatus. When I arrived at Rio Americano in 1986, the physics program had suffered through a year of long-term subs and mis-assigned teachers. Prior to that, the physics teacher was someone who was handy with tools and a fan of PSSC. We didn't have much, and what we had was dedicated kits aligned to the PSSC lab manual, conceived and produced in the post-Sputnik, pre-Apollo era.

I have had the good fortune of securing funds for considerable capital outlays for quality physics demonstration and laboratory equipment over the years. Rio's School Improvement, Gifted And Talented Education, Parent Teacher Association, and Science Boosters programs have funded a variety of my requests. It's been a patient siege, but in due time, the classroom was well-stocked for my needs.

When I did my student teaching at Ann Arbor Huron High, there was a physics equipment storage room the size of a regular classroom with rows of shelves: it was essentially an apparatus library. When I was a student in a physics class at Grand Rapids Central High, there was a classroom and a lab room. At Rio I have my classroom and share a tiny storage room with a neighbor. So what I get has to fit in a small, fixed amount of space.

Here are a couple of storage solutions I've adopted and continue to appreciate. Now that I teach four different physics courses, I often need to haul out or store materials in the wee breaks between classes. Half-gallon milk cartons, small utility tubs, and removable drawer storage are leveraged throughout the classroom.

The analog current and voltmeters stack nicely into the tubs and the tubs fit nicely into the drawers.


Brass masses and mass hangers store nicely into strategically cut milk carts, and the milk cartons fit into the tubs. As do sets of disparate clamps.


Flip a couple of the milk cartons for convenient tub stacking. There is no tubthumping.


When the classroom was "modernized" in 2000, two storage cabinets were added. And promptly filled.



I'm an unapologetic fan of removable drawer storage racks of all sizes.

Here are photos of lab sets of correlated items:

Dynamics carts


After students have used the materials and it's time for clean-up, it helps to have a photograph of how the drawer should look when restored to its low-entropy status. Lay it on top when storing the drawer. I printed this latest edition (with the new Smart Carts) on heavy card stock.


Circuits (batteries, bulbs, wires, switches, power resistors, capacitors, magnetic battery connectors)


Magnetism (bar magnets, compasses, wires, lead-free solder, ignitor battery, rod clamp, collar hooks, wood dowel, Ampere's Law apparatus, Genecon)


Wave Optics (CD, whiteboard markers, binder clamps, diffraction gratings, laser tripod)


Clickers (each group is assigned four: e.g., Group E: E1, E2, E3, E4)


The plastic removable drawers are also nice for storing class sets of a particular item, like force sensors.


On the off chance that I've left you with the sense that I'm a fastidious neat-nick, I assure you that the rest of my classroom (and much of my humble abode) are ongoing celebrations of disorder.

Saturday, February 10, 2018

Gaussian Surfaces for the win

I worked all last weekend learning how to integrate the Electric Field near an infinite line of charge, finite line of charge, charged ring and charged disc. It was brutal. The only thing worse was working my AP Physics C students through it. Students are "supposed" to learn it, it's right there in the College Board Objectives for the course:

4. Fields and potentials of other charge distributions
a) Students should be able to use the principle of superposition to calculate by integration:
1)      The electric field of a straight, uniformly charged wire.
2)      The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge.
3)      The electric potential on the axis of a uniformly charged disk.

Yet the concept is infrequently seen on the AP exam so some teachers hope for the best and don't teach it. I decided I would do a one day lecture along the lines of "Just follow me through the math kids!" I figured it was the best of both worlds, they technically saw it and some might remember it and I wasn't wasting much time. They did dutifully follow the notes but based on the pained expression they didn't "get it." I didn't like that every video tutorial I found said "And now you just check your integral table ...." because my students wouldn't have one on their exam. I told students the emphasis was on the relationships, what did and did not affect the strength of the field. I told students not to memorize the equations. If the problem did appear on the exam it would probably be for a partial charged ring, also known as an arc, which was done slightly differently and seemed much easier. Combine the not fun math and my inexperience with it and I was not a happy teacher for a few days.

So what do unhappy teachers do? Go back to good teaching strategies. My kids (and I) were getting confused so I made a reference table with a (1) a description of the situation with variables, (2) a picture that matched and (3) the final equation they got from the integration. Its available here as a pdf.

When I passed out the chart I asked them, "And what are we not doing with these equations?" and students answered "Memorize them!" So they tucked them away and may never have looked at them again.

A few days later as I was reviewing Gaussian surfaces I watched Dan Fullerton's APlusPhysics video about them. He pointed out that using Gaussian surfaces around an infinite line of charge you derive the same equation as in my chart above. My mind was blown. [cue explosion noises] When I lead students through Gaussian surfaces we worked through the derivation for the Electric Field around an infinitely long charged rod using a Gaussian cylinder. I had them take out their charts and pointed out the equation was the same as what we had found a few days ago. Then I asked them to look at the disk of charge equation and asked what it would look like as it became an infinite plane as R goes to infinity. There were audible gasps. "Wait, this is so much easier than that integration." Physics works kids. Gaussian surfaces for the win.

Friday, February 02, 2018

Induction .... Nailed it!

Induction is one of those things that make students go "Whhaaaatttt???"
You have probably seen and demonstrated a moving wooden meterstick like this:
Usually when I do that demo in regular Physics my students call me a witch. I don't exactly correct them. I wanted an equally "wow!" demo but didn't want to repeat myself in AP Physics C. While searching for something completely different I stumbled upon this small image of an induction experiment.

At first I wasn't sure if I could do it but after some experimenting I found a set up that worked. I set a nail on a styrofoam cup (made some grooves in it so that it would stop the nail from rolling) instead of a metal rod. I couldn't find any metal rods that weren't gross and rusty. I used a rubber rod and wool but any friction kit combination should work.

First I charged the pith ball through induction with the rod. Then I moved the nail point close but not touching the pith ball. I would recharge the rod and bring it close but not touching the nail. The pith ball on the other end would repel. My students were amazed. They watched me do it but they still had to think about which item was charged vs neutral. It led to lots of additional questions, some we were able to answer experimentally, some would probably require some more charge:

1. What happens if you touch the nail with the rod? The nail would then have the same charge as the rod and pith ball. I presume the nail would continue to repel the pith ball even when the rod were removed. We tried this but could not confirm with the small amount of charge we had. 

2. If the pith ball is charged won't it be attracted to the neutral nail without the rod inducing a separation of charge? Yes! You'll notice in the video below that I move the nail in after the pith ball is charged. Otherwise I found that the pith ball would pull towards the nail immediately.

3. Would it work with an insulator? I presume so but didn't get a chance to try it. 

Below is the video of the demonstration for absent students:

Depending on the strength of your charge source you could set up a wide variety of things like this as discrepant events for your students to puzzle over.

Saturday, January 27, 2018

Pendulum "Oops!" to "Opportunity"

It's my first year teaching AP Physics C (Mechanics and Electricity & Magnetism) and I am wrapping up our last Mechanics unit on Simple Harmonic Motion and Universal Gravitation. I had my students work through a simple simple pendulum lab to investigate whether the initial position, length or mass affected the period. I also wanted them to investigate physical pendulum lab and started to research them. Most labs I found used meter sticks with holes drilled in them. While I love using my industrial drill press I did not like the idea of damaging meter sticks I just got with a grant. I found 8-10" pieces of steel bar in my cabinets with two holes in each but that number of holes limited the data my students could take. I realized that hardware stores sell lengths of steel or aluminum bar with pre-punched holes so decided to investigate that.

I was able to find  1/16" thick pre-punched steel bar that was cheap. As  I tried to gather enough pieces for eight lab groups I found several bars that were bent. Remembering the destructive force that is off task high school students I worried that these bars weren't strong enough to last. There was 1" square pre-punched steel tube that was much sturdier so I set up an experiment right there in the aisle. Luckily the nuts and bolts are in the aisle so I found the right size 4" bolt (5/16") and nuts to match. After several iterations (and much waving off of employees) I found that a washer and nut on either side of the tube let the long bolt work as a pretty good axle and held the tube in place. The tubes were more expensive but hardy and I could get two 18" pieces from each one. I also bought a thinner solid bar I would drill just a few holes in for a larger all class demo.

I felt pretty pleased with myself on my way home. Students would be able to adjust the distance from the center of mass of their physical pendulum to the pivot point and conduct multiple trials. The tubes were strong, I have a mounting system that wouldn't let them slide off and fall so I was feeling pretty good.

Then I realized why everyone used bars and meter sticks: they had negligible thickness compared to the length. After asking some other physics teachers it was decided that the effect was probably small:

"For a "flat" piece, thickness along the dimension in the same direction as the axis of rotation won't matter. The "other thickness" will, the moment of inertia about the center of mass should be 1/12M(l^2 +w^2), where w is the dimension perpendicular to the length and axis of rotation. That's going to be dominated by the length term in this case. If you rotate about the end, then you need to add in a (Ml^2)/4 term from the parallel-axis theorem. Since these are rectangular cross sections rather than "flat," the analysis should be more complicated, but hey, we're ignoring all of the holes in the metal, so I'm not sure how far down the rabbit hole we want to go in the first place.

-David Marasco, Foothill College"

Whew! Crisis averted! I sawed the 3' pieces in half (use a fine-toothed blade on a saws-all and a friend), filed the edges and put a bolt on each one. It felt like an easy lab set-up, I could hand one to each group and confidently ask them to vary the distance and find the rotational inertia of the physical pendulum using the slope of a graph.

Fast forward a week and some students let me know that they would be absent for this lab so I needed to make an alternate. I decided to collect stock data, that I would tweak a bit before giving it to them to analyze. When I started plotting the periods I measured for different distances from the center of mass of the pendulum I started to panic. I wasn't getting a line they could take the slope of! Then I called myself an idiot.

Using the equation for the period of a physical pendulum, one gets the impression that the rotational inertia, I, is a constant you can solve for using the slope. But I had forgotten that the rotational inertia would change as the pivot position changed due to the Parallel Axle Theorem:

I thought my students might make the same initial mistake and decided to go with it. For the alternate version students were given hypothetical period and distance measurements for a bar physical pendulum. They were asked to graph it and describe why it wasn't the linear graph they were expecting. Then they would use one position to calculate the rotational inertia of the bar and compare that to the theoretical one using the equation.

I liked the way they would go into the experiment expecting one thing, realize their mistake and still do a few calculations. So I applied it to my whole class activity as well. Timing meant that students wouldn't be able to collect a lot of data and I thought combining group data would help add to their initial confusion. (Because sometimes I'm mean challenging like that.) I explained to students that they had a physical pendulum with holes that they could mount it from and we discussed why they couldn't use the hole (almost) at the center of mass of the tube. Each group was to collect 3-4 data points of their choice and then submit their data to me. We put all data points into a spreadsheet I had made ahead of time. It was nice having multiple groups time the same pivot position to help flush out the shape. Students were concerned immediately about patterns in their data and as the graph filled in more data points in real time there was a furrowed brow on all.

Then, there was the spark, a little "Oh! Wait it shouldn't be straight!" would erupt from some student and they would start to realize their mistake. I showed them this graph I found that matched their own data and they felt relieved. They hadn't broken physics. The rotational inertia changed every time they moved the pivot.

I asked students to choose any one data point from their trials to calculate the rotational inertia at that location. Then we surveyed the groups and found the highest values were at the pivots closest to the end of the tube and the smallest were closest to the center of mass. Students recognized that trend form our initial work with rotational inertia; moving the pivot farther and farther from the center of mass makes it harder and harder to rotate as quantified by an increase in the rotational inertia.

I asked students if there was a way to get the rotational inertia of the pendulum as if it was pivoting at the center of mass and after some discussion they realized that they could subtract the Parallel Axis Theorem value from each of their values. They ended up getting fairly close answers despite different groups taking the data and choosing different pivot points. Win!

With the unintended complexity of the tube vs the bar I'm quite pleased how it turned out. Students were able to confirm facts they knew and learn some new ones while getting hands on. And now they know some fundamentals about physical pendulums way better than reading about it.

Monday, January 22, 2018

How to cheat on your next eye test

Next time your at the Department of Motor Vehicles renewing your driver's license, don't be surprised if you see people in the lobby staring into spinning spirals just before they take their eye test.

Why? It turns out an old favorite illusion, referred to as the "expanding motion effect," can induce increased visual acuity. This illusion is demonstrated in the Exploratorium's "Depth Spinner" Science Snack. It's a perennial favorite among visitors to our ExploratoRio Open House event.

In any case, researchers at the Universities of Glasgow and York incorporated use of the illusion with eye chart tests.
The team discovered that visual acuity—the ability to see fine detail—can be enhanced by an illusion known as the ‘expanding motion aftereffect’. While under its spell, viewers can read letters that are too small for them to read normally.
When participants stare at the center of a spinning pattern that spirals inward for about 30 seconds, shifting their view to a stationary object will induce the illusion that the static object is expanding.
Participants who started with normal visual acuity and saw [inward spinning] spirals ... showed improved visual acuity.
It's as it they were looking through a camera and zooming in on the smallest letters in the eye chart.

It is important that the spiral is spinning inward. Staring at an outward spinning spiral induces a shrinking effect.
Those who saw [outward spinning] spirals ... actually performed worse after exposure to the spirals.
Anyone who's enjoyed this illusion knows the effect is temporary.
But don’t throw out your eyeglasses just yet: the researchers note that the overall boost to visual acuity is small and fleeting.
I would not have expected this outcome. Hat tip to Richard Wiseman's appearance on Skeptics' Guide to the Universe. The Sun ran an article with the obligatory animated spinner.

Sunday, January 21, 2018

Kids these days

When I was a new teacher, I was wary of veteran teachers who complained about "kids these days". The gist was that students of a long ago yesteryear were capable of hunkering down and rising to the challenge of rigorous academic coursework, while today's students simply cannot hack it. I didn't see it. My students were rising to the challenges I set before them. What was the problem? I never wanted to age into that seemingly inevitable "get off my lawn" stage.

Back then, a veteran teacher was anyone with ten or more years in the profession. But it was those with more than twenty years in the classroom who were most likely to shake a "kids these days" fist.

I now have more than thirty years of classroom teaching under my belt. And I now see why it happens. The struggle is real. And I don't have a ready solution.

In my own recollection, my Physics students of 1996-97 figured it out better than those of any year I've taught. (I'm referring to my Physics students in this post, not my AP1, AP2, APB, or CP students.) 

In 1996-97, I was entering my second decade of teaching and had settled on some pedagogy and policies that seemed to work for me and my students. A large majority of students in 1996-97 (N=116) essentially agreed to my terms and prospered as a result.

In contrast, my Physics students in 2018 (N=60) have largely opted out of my conditions and suffered predictably. Here's a side-side comparison of the grade distributions.

There were four sections of Physics in 1996-97; there are two sections in 2017-18. (There was one section of AP Physics B in 1996-97; there is one section each of AP Physics 1, AP Physics 2, and Conceptual Physics in 2017-18. These classes are not included in this analysis.) Seventy percent of Physics students earned an A or B in 1997; only 57% did so in 2018.

Why the dramatic difference? In my analysis, it is engagement. Engagement is difficult to quantify for purposes of comparison. My best method for quantifying engagement in 1997 relates to random homework checks. 

By that metric and its built-in tolerances, 29% of Physics students were very engaged in 1997, 45% were somewhat engaged, and 26% were disengaged. 

Since 2014, we have had a Test Correction Journal (TCJ) process by which students can earn back up to half the points they missed on each unit test. "Sweat equity" is required: students spend class time writing "journal" entries for each test item they missed. Completed journals grant students access to a ten-question quiz. A 10/10 gets you half your missed points back; 7/10 gets you 70% of half the points you missed, etc..

So I can now use TCJ performance as a measure of engagement. We have five unit tests in the first semester. Students who participated in all five are rated as "very engaged". Students who participated in four of the five are "somewhat engaged". Students who missed more than two TCJs are "disengaged". 

By that metric and its built-in tolerances, 28% of Physics students were very engaged in 2018, 27% were somewhat engaged, and 45% were disengaged. 

Here is how the Physics grades break down (2014-2018) when classified by levels of engagement. (N=382)

That infographic might take a moment to absorb. The green columns are grades earned by highly engaged students: mostly As, fewer Bs, fewer Cs, two Ds and no Fs. The yellow columns are grades earned by somewhat engaged students: some As, more Bs, some Cs, a few Ds, and two Fs. The red columns are grades earned by disengaged students: one A, more Bs, many Cs, dozens of Ds, and all but two of the Fs.

Excel is happy to make pie charts as well. Here are the grade distributions by engagement level.

Eighty percent of very engaged students earned an A or a B.

Somewhat engaged students were somewhat distributed across letter grades.

Half of disengaged students earned a D or F. One out of 382 earned an A.

My own assessment is that students who engage in the course will get a good grade. There is more to engagement than Test Correction Journals. Homework engagement is crucial. But I have no way to measure that, whatsoever.

Still though, you will most likely earn an A or a B if you are at least engaged in the TCJ process. You will most likely get a C, D, or F if you're disengaged.

Some might argue that in addition to preparing and maintaining quality physics pedagogy and policies, I have an obligation to compel or otherwise force students to engage in the course. I cannot bring myself to agree. 

At some point, students must have the option to engage or not engage. In my own highly biased assessment, I consider my course to be highly engaging as it is. And I believe there is a valuable lesson to be learned about the consequences of choices that we make when approaching an academic course. Physics is a college prep course; many students will be sitting in college courses in less than a year. 

I want my students to succeed. In my class and beyond. I know that no one will chase them down in college to make sure they are duly engaged in their coursework. If they know how to engage on their own, they will be set to succeed to the limits of their abilities.

Full engagement is not a guarantee of an A. An A represents a level of mastery that is demonstrated in various assessment instruments. Engagement puts an A, B, or C in play while virtually precluding a D or an F. Disengagement, on the other hand, operationally precludes a student from earning an A.

Choices and consequences.

Am I at the "kids these days" stage? I don't think so. Engaged students are doing very well in the course. Top grades are well within reach of anyone willing to engage. And AP students (unsurprisingly) remain highly engaged. I am bothered by the increasing number of students who choose to be disengaged in Physics.

One last graphic to convey my disappointment. This is this year's 1st period Physics class's test scores. This was the most disengaged class I've ever had. In the test scores field, red indicates a TCJ that the student missed. Yellow indicates a test that was made up during the make-up period following the administration of the test (usually about 10 school days). Blue represents a test that was missed and not made up in the make-up period. It was made up at the end of the semester. Black is a second test that was missed and not made up in time. It goes down as a zero. The letter grades are shown in the leftmost column. Green shading for very engaged students, yellow for somewhat engaged students, and red for disengaged.

Kids these days? No. Shaking my head? Yes.

Saturday, January 20, 2018

"Magnetic"—a song to add to your physics playlist

There comes an awkward moment in my AP Physics 2 course when we arrive at the topic of electromagnetism. Students enrolled in Physics last year studied magnetism in some depth, with a robust qualitative laboratory component. Students enrolled in AP Physics 1 did not hear the term "magnetic" in class at all: there is no magnetism in AP1.

So I segregate my AP2 charges by which course they had las year. The former AP1s move quickly through the Physics course material while the former Physics students get some enrichment by way of The Mechanical Universe, Conceptual Physics Alive, and Nova. Eventually we reunite and move into deeper issues of electromagnetism and induction, ending up at Faraday's Law.

The Nova episode is S31E07, "Magnetic Storm," concerning the changing nature of Earth's magnetic field. [Warning: do not make a drinking game out of each time a thunderbolt sound effect is deployed—you will not make it to the end.]

Nova - Magnetic Storm

In developing a video question set to accompany the episode, I noticed that a pop song was featured heavily throughout the episode. A bit unusual for Nova in my experience. The end credits included the name of the artist but not much else. It was enough to track down the... track.

It's Judith Edelman's "Magnetic" from the 2009 Thirty One Tigers release, Clear Glass Jar, available on iTunes, Amazon, and wherever fine music is sold. Someone commented that Edelman's "Magnetic" is to electromagnetism what Don McLean's "Vincent" was to the art of van Gogh. You be the judge!

Judith Edelman - "Magnetic"

A comment for the video included the lyrics.

It's the buzz when I'm full
Of your sweet magnetic pull
It's the tug that I crave
It's how opposites behave

Is electricity all there is to you and me?

In the fields, in the fields
Where the static is revealed
If the north isn't true
Will I lose my way to you?

Is electricity all there is to you and me?

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

In the deep molten heart
Where these strange attractions start
If we are passionate
Will this rock remember it?

Is electricity all there is to you and me?

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

It's the buzz when I'm full
Of your sweet magnetic pull

Tuesday, January 16, 2018

Egg Toss video because—why not?

The final batch of clips from Grass Omelette XVII at Rio Americano. A nice catch and two spectacular splashes! With no sun, we were able to line up with the geometry of the field. Seems we should have taken a bit of Sharpie to the eggs to increase their contrast with the sky.

Large impact time to reduce impact force

Impact force too large #1

Impact force too large #2

Previous Grass Omelette XVII coverage can be found here:
Splash and Catch: Grass Omelette XVII

More robust coverage of this activity can be found here:
Egg Toss 2013

Saturday, January 13, 2018

Be Direct With Me

I am a huge fan of a CBC podcast called "Under the Influence with Terry O'Reilly". Tales of drunk Canadians engaged in Molson-fueled shenanigans? No. Each half-hour episode tells a carefully woven story connecting some element of advertising or marketing to the world where you live. You will learn things you didn't know about things that you do know with each episode. And each episode is the product of 20-30 hours of research. Subscribe to the podcast right now while you're thinking about it.

In an episode called "When Madison Avenue Met Broadway: The World of Industrial Musicals," O'Reilly played a few seconds of "Be Direct With Me". Just a few-second bite with not much to identify it. But I was transfixed. I deployed my hard-earned blue belt in google-fu and sourced the track. I then saw it was available on iTunes and paid for it immediately (I'm old and from the midwest).

I quickly set the track to a Keynote preso and roughed out a nice delivery. Then I spent several days refining and improving. I simply had to show this gem to my colleagues at the High School Share-a-Thon attached to the American Association of Physics Teachers Winter Meeting 2018 in San Diego.

High School Share-a-Thons can be lively affairs, typically held in the evening on Day 2 of the conference: between the workshops and the invited/contributed talks. For reasons nobody ever explained to me (and I asked), this year's Share-a-Thon was scheduled for 8:30am on Day 2, conflicting with many workshops. And... in the morning!

A few dozen intrepid instructors braved the San Diego rains and made it to the event. Sadly, the session presider did not. A few years ago (I want to say it was the Omaha Summer Meeting), the Share-a-Thon was left without a presider and I stepped up to awkwardly host.

Someone in the room in San Diego remembered that, and promptly ratted me out. So I was once again drafted into service. When the session began, only two of the several dozen attendees signed up to share. We had the room from 8:30am until 10:00am. I made the executive decision to dispense with the five-minute time limit and encouraged my colleagues to not be bashful—we're all friends here!

I showed a couple of things (videos of those things, anyway, as has become the trend among traveling physics sharers). Then I hit them with the video below. I truly didn't want to be up first for this event, but it was what it was.

In any case, the presentation. You will want to be sitting down for this.

I had a few more slides of humor and fun for my live preso; I intend to show it again at the NCNAAPT Spring Meeting.

Eventually more folks came up to share. Questions were asked and answers were given. We ended the session at 9:59:50am.

But industrial musicals? I had no idea. And they were huge in terms of budget, scale, and talent.

UPDATE: GE's Go Fly a Kite—the industrial musical from which this song comes—was written by the composer/lyricist team of Kander and Ebb, who also wrote Cabaret and Chicago. The double-album original soundtrack (souvenir recording) can be had via eBay for $99.99 as of this update. But it has also been posted to YouTube. I found "Be Direct With Me" as the opener for Side 3. The video shows the liner notes and dress rehearsal stills that correlate to the currently-playing track. While Valerie Harper was arguably the biggest enduring star in the cast, she did not sing "Be Direct With Me". Who did? Carole Woodruff. The only other credit I was able to find for her was a musical called Pleasures and Palaces, written by Frank Loesser and choreographed by Bob Fosse. It ran for a month in Detroit and was not reviewed kindly. Woodruff is the last singer listed in the credits. I have found no other relevant information on her.

Thursday, January 11, 2018

You spin me right round, baby, right round ...

Well, my accelerometer anyway.

I'm in the middle of my first year teaching AP Physics C and we ended last semester with rotation. Therefore, I'm looking at any spinning or round thing in a different light. I was at the RAFT San Jose store and saw giant wooden circles with rough edges for cheap. And this is RAFT cheap so I think it was <$4 for 8 of them. I snagged them unsure of what I would do with them and took them home to be inspired.

I ended up sanding down the rough edges to find they were very sturdy and furniture grade plywood. Since they were leftover from some manufacturing process they were perfect circles. I decided to make them into giant tops/ turn tables. I envisioned students playing with them at the onset of this unit to observe changes in rotational quantities, maybe use some slow mo video or accelerometers. Or perhaps we could use them for conservation of angular momentum. The possibilities are endless!

I reviewed some geometry and found how to find the center of the circle. I measured equivalent length chords around the circle and marked halfway across each chord. From this halfway point I drew a line perpendicular to the chord towards the center of the circle. Doing this a few times gave me a point, or at least a small area of the "center" of the circle. Since I was drilling a big hole in the middle I figured close was going to be ok.

We have a drill press in our mini-shop in the Physics prep room. I used a 7/8" drill bit to drill a hole in each disk. This allowed me to fit a 1/2" PVC pipe through the hole with a bit of wiggle room. Going down to a 1/2" bit was too small of a hole for the PVC to fit so the hole had to be a bit bigger. But "wiggle room" meant that if I turned the PVC axle the disk wouldn't rotate at the same speed. Hmm...

I used smooth 1/2" PVC endcaps on the bottom of about a foot of 1/2" PVC for my axle. The endcaps had the manufacturers logo on it so they did not have a perfectly smooth bottom. If it bothers me enough I may go back and file them smooth. I found that wrapping the PVC with a bit of masking tape increased the diameter of the pipe enough to fit in the hole in the disk snugly. Through trial and error I found about 3 times around worked well. Too tight and I was banging the axle against the ground hoping the disk's inertia would drive it down onto the tape, sometimes that worked. I put a second end cap on the other end of the axle for comfort.
In the end I had 8 tops for use. By the time I made them it was towards the end of the rotation unit but they were still helpful. When students were reviewing torque, angular momentum, etc. I left them out with their review sheets. Students would grab them to rotate and discuss vector directions with their partners.

I also played with the Physics Toolbox app's accelerometer by placing it on one of them and giving it a few turns. Next year I'd like students to investigate the acceleration recorded by the phone at different radii as they turn it with the same speed. Below is a quick video of the attempt.

I had considered sharpening down dowels to a point as the axles instead. But, I teach high school and a sharpened dowel through the center of this disk might become a spear with a shield so ... no.