# What if you had a teaching assistant?

I know how demanding teaching is, and I know that you need a break. Would you like a teaching assistant? I’m moving away from full-time teaching, but I’ll still miss it (except for the grading on the weekends). I always enjoyed creating educational artifacts, such as tables, graphs, diagrams, animations, and simulations. I’d like to keep these skills current, so I may have something to offer you. I will be your teaching assistant for a small fee (\$5?) yet to be decided. I’ll create an educational artifact for you, provide any source files to you, and at a time we agree on, I’ll release the work under an open license so that all teachers can benefit.

The only catch is that I’m doing this for fun. I can’t take every project, so I might start with the ones I think are most interesting. If I can’t get to the project, maybe someone else could. The first thing I probably need to do is set up a website of wishes and wish-granters, but meanwhile, you can just reply to this post. Teachers, would you be interested in something like this? What kinds of educational projects can you envision? Interested bystanders, would you volunteer your skills?

## What can I do for you?

Here’s a brief list of my skills.

• Physics
• Mathematics

### Diagrams and Tutorials

Need the perfect diagram and can’t find it? I’ll make it better.

• (Xe)LaTeX (PDF/PNG)
• PGF/TikZ (PDF/PNG)
• Asymptote (PDF/PNG)
• D3.js (HTML)

### Programming

Need a small interactive website, simulation, or program?

• HTML/CSS/JavaScript
• Node.js
• Meteor
• Python
• GlowScript
• Ruby
• C++
• GeoGebra
• Easy Java/JavaScript Simulations
• PhET simulations (HTML5 sims modified to support inquiry)

### Data Science

Need to analyze that concept inventory or unit test? Scrub the student information (replaced with teacher-chosen student IDs), and I can find the story that your data whispers.

• R
• Pandas
• Julia
• Excel (Ugh!)

### Something else?

I have other skills too, probably. Just ask. I would love to hear from you.

# 2015-2016 Sumner Academy of Arts & Science Job Postings

Due to retirement and more incoming students, we are looking for physics, chemistry, and biology teachers to fill two science positions at the wonderful Sumner Academy of Arts & Science, a grades 8-12 college preparatory magnet school within the Kansas City, Kansas Public Schools and an IB World School. If you want to teach at a school where you can make a difference in the lives of a diverse mix of inner-city kids, then this is it. If you don’t teach science, we’re also looking for other dedicated professionals; see below for links to job postings.

Homepage: http://kcksumner.schoolloop.com/

The dry statistics are here: http://online.ksde.org/rcard/building.aspx?org_no=D0500&bldg_no=8322 (or at least they are supposed to be when the server is not down)

We are consistently ranked as the number one school in Kansas by Newsweek, Washington Post, and U.S. News & World Report, but these metrics are nothing next to the chance to work with other teachers curious about science and committed to their craft, teaching students who merit the best teaching.

Opportunities for high-level curriculum development abound. New teachers will most likely teach some combination of Science 8, Physics 9 (only a general KS science certification needed), and Biology (currently 10th grade). See below. Chemistry teachers are also encouraged to apply, to teach Science 8, Physics 9, and (in a later year) Chemistry 10. During our PCB transition, we will need people who know chemistry. Not all courses have traditionally used Modeling, but two of our teachers have been trained in Modeling Physics and use it, and the others are receptive to Modeling.

• Grade 8: Science 8. This summer we will be transforming a memorization-heavy Earth & Space Science course to include more experimentation, guided inquiry, and laboratory skills to support further science study through International Baccalaureate (IB) science courses. We plan to include physics and chemistry themes used in later courses.
• Grade 9: Physics 9. This Physics First course is currently taught using Modeling Physics, with which we have been pleased, but since we are switching later courses to include chemistry before biology, we would like to interleave modern applications.
• Grade 10: Chemistry 10. Chemistry is currently taught in the 11th grade but in the next several years will be moved to the 10th grade, and we will be doing the curriculum development in-house.
• Grade 11: Biology 11. Biology is currently taught in the 10th grade but in the next several years will be moved to the 11th grade.
• Grade 12: Physics 12. This is a more advanced physics course that satisfies Kansas requirements for physics. This is currently taught using Modeling Physics.
• Grades 11-12: International Baccalaureate science classes. Students who choose to take our two-year Standard Level and Higher Level science courses generally double up on chemistry and biology in the 10th grade. We currently offer Physics; Chemistry; Biology; and Sports, Health, & Exercise Science. We are also considering developing an IB Career Certificate program.

### How to Apply

Please first email a resume and cover letter to our principal, “Mr. Jonathan Richard” <Jonathan.Richard@kckps.org> . You are welcome to refer to this posting by “Brian Vancil”. Then, apply for a job listing (not all of the three jobs have yet been posted) in the Kansas City, Kansas Public Schools database at https://kckps.tedk12.com/hire/index.aspx . For instance, https://kckps.tedk12.com/hire/ViewJob.aspx?JobID=3482 . You have to click on the posting to see the “Anticipated Location(s): Sumner” field. Here are direct links to the job postings:

We’d love to work with you!

It’s been a while since I took thermodynamics and statistical mechanics, so I’m using this post partly as a way to refresh my memory—please tell me I’m wrong! It’s also a way for me to start a conversation on definitions of temperature, some of which are abysmally bad. Because science has a misconception problem, we ought to think of a good way to progress toward more sophisticated notions of temperature throughout one’s educational timeline and to make clear when we break from the naïve notions and why.

One has only to google “definition of temperature” to realize the problem: Once one skips the dictionary definitions about temperature being a scale of hotness (which, as I will argue, is arguably better than what follows), one gets to definitions that say something about how temperature is a measure of the average translational kinetic energy of the atoms in a substance.  (I won’t link to these because I don’t want to increase their Google PageRank.)

### Bad definition 1: Temperature is a measure of the average translational kinetic energy of the atoms in a system.

Compare to NGSS draft 2: DCI PS3.A: “Temperature is a measure of the average kinetic energy of particles of matter. The relationship between temperature and the total energy of a system depends on the types, states, and amounts of matter present.”
It’s a nice picture.  It’s just not hard to break.  For instance:

• What would happen to the temperature if you threw the system?

### Bad definition 2: Temperature is a measure of the average translational kinetic energy of the atoms in the rest frame of a system.

Even if you try to correct for this naïvely by specifying that the kinetic energy be measured in the center of mass frame:

• What would happen to the temperature if you split the system in two pieces and threw them in opposite directions?

Or even worse:

• What would happen to the temperature if you spun the system?

### Bad definition 3: Temperature is a “measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules”.

HyperPhysics has the best bad definition of temperature.  However, I wouldn’t go as far as they do and call it an “operational definition”.  What is “kinetic energy associated with disordered…motion”?  What counts as disordered motion?  Is a sound wave (phonon) disordered?  It’s what we might think of as a vibration (which many texts cite when they talk about temperature).  How do we measure disorder for the purpose of calculating the “associated” kinetic energy?  Why doesn’t rotational energy count?  What do we mean by “measure” (another problem with calling it an operational definition)—even if I account for all the “disordered” kinetic energy, what value do I put down for temperature?

What’s the simplest system we could envision that breaks this definition? Note that to break the measure part, there must be a non-monotonic relationship between temperature and kinetic energy.  Candidates include:

• photon gas (Many thermal systems include EM radiation.  How do we measure the temperature of light when it isn’t made of atoms?)
• low-temp quantum solids???
• diatomic gases???

### Good definition 1: Temperature is the rate of change of energy with entropy (TODO: specifics on how this is defined) (with volume and the number of particles fixed)

HyperPhysics also gets credit for this good definition.  However, the authors don’t give any examples where the behavior of temperature differs drastically from the simplistic $T\propto U$ idea.
The standard definition in thermodynamics is:

$T=\frac{Q_\textrm{\scriptsize reversible}}{\Delta S}$

However, the standard definition of temperature in statistical mechanics is:

$T=\left(\frac{\partial S}{\partial U}\right)_{N,V}^{-1}$

Does this always work?  What does it mean? Without teaching entropy well, this might be hopeless. However, I recently read an interesting paper on a simple model to introduce the need for entropy as a thermodynamic variable:

• Abreu, Rodrigo de, and Vasco Guerra. “Introducing Thermodynamics Through Energy and Entropy.” American Journal of Physics 80.7 (2012) : 627–637. 4 Jan. 2013. <http://link.aip.org/link/?AJP/80/627/1>.

## How could we make the teaching of temperature better?

I envision a tripartite system of teleological, conceptual, and operational definitions, where we scale up the complexity of the conceptual definitions (i.e. develop new models for temperature) as a student progresses through the system. This has to be explicit, or students won’t understand either the nature of science or why their old ideas are not quite right.

### Teleological definition: Temperature is a scale that tells us the direction of heating when two systems (both in equilibrium) come into contact with each other.

Even this isn’t obvious and needs some justification. If we have three systems in equilibrium, A, B, and C, why couldn’t A heat B, B heat C, and C heat A if they were brought into pairwise contact?
It does get the point across why we care about temperature, which helps to ground our other definitions and provide continuity in the notion of temperature.

### Operational definition 2 (later elementary): Temperature is what a thermometer measures.

This should be connected to the idea of heating and reference temperatures (from special systems with understood behavior). It can later include the idea of different scales. The idea of absolute zero should come from an extrapolation of gas law data from a student experiment.

### Conceptual definition 1: Temperature is a measure of how frenetic and disordered the motion of atoms/molecules in a substance is.

Note that we’re pretty close to a bad definition but that it’s always augmented by our teleological and operational definitions. This is not worth getting to until students understand that matter is made of molecules. Students should see simulations of matter at different temperatures to get a feel for what we’re talking about. It’s simplistic and qualitative.

### Conceptual definition 2: Temperature is a measure of the distribution of energies in a substance given by $T=\left(\frac{\partial S}{\partial U}\right)_{N,V}^{-1}$.

That is, roughly, it’s the ratio of added energy to the change in entropy that results. We’re moving past our bad definitions.

### Conceptual definition 3: We should define a new “temperature” as an inverse energy scale $\tau=-\beta=-\frac{1}{k_B T}=-\frac{1}{k_B}\frac{\partial S}{\partial E}$

Regular absolute temperature fails our teleological definition at negative absolute temperatures. This new definition gets the direction of thermal transfer right when two systems come into contact. See, for instance:

• Braun, S. et al. “Negative Absolute Temperature for Motional Degrees of Freedom.” Science 339.6115 (2013) : 52–55. <http://arxiv.org/abs/1211.0545>

# Numeral systems, Or Until I get a proper math blog…

I have a young daughter and have been thinking for the past few years about how we count in the United States.  While there are many interesting alternative number systems, not all of these are useful for teaching a young child to count.  Many commentators on mathematics education have cited the? Chinese system for its monosyllabic digits and ease of composing them into the numbers 0-99, and others have pointed to other interesting mnemonic? features.  However, what I have in mind is inspired by what the late Tom O’Brien has done (paywalled).  I think that for older students, we can use the positional system without the extra letters, but I’ll leave them in for now. So, here’s my version of his system.

Digits 0-9 (monosyllabic versions)
Symbol Name
0 rho (as in zee-rho)
1 one
2 two
3 three
4 four
5 five
6 six
7 ven (as in seh-ven)
8 eight
9 nine
Base units (monosyllabic versions). If the SI prefix for ten were just one syllable, I might consider using it instead of “T”. I also don’t like the mixed distribution of uppercase and lowercase prefixes in SI. I would like to switch up the long vowel sounds (for powers of 10 greater than 0) and short vowel sounds (for powers of 10 less than 0), but I’ll save that for later. In particular, regard anything beyond ty=T as provisional.
Place value Symbol Name
10-3 k kū (pronounced koo)
10-2 h ta (pronounced tah)
10-1 t te (pronounced teh/oak)
100 U (not normally used) tu (not normally but pronounced tuh)
101 T ty (pronounced tee
102 H to (pronounced toh/toh)
103 K ku (pronounced kuh)
104 TK ky (pronounced kee
105 HK ko (pronounced koh)
106 M mu (pronounced muh)
107 TM my (pronounced mee
108 HM mo (pronounced moh)
109 B bu (pronounced buh)

## Putting it all together

• To get a sense of where this meets our current system, 43 becomes 4T3 and is read “fourty three”.
• To get a sense of where this enforces uniformity over tradition, 37 becomes 3T7 and is read “threety ven”.
• Try counting from 0 (rho) to 3T (threety).
• For a more complicated example, 73029 becomes 7TK3K7T8 and is read “venky threeku twoty nine, but we would probably leave off the base units and write it in the traditional way with 0 (rho) as a placeholder.
• For an even more complicated example, 3.142 becomes 31t4h2k and is read “three onete fourta twokū”, but we would probably also leave off the base units and write it in the traditional way.