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!

The Science PLC at our school is considering what students should know about atoms in 8th and 9th grade science classes (including Physics First).  Just recently, Amber (Strunk) Henry posted on Twitter:

This is my attempt to arrange the ideas.

Map of the Territory of Things to Know

Next Generation Science Standards (NGSS)

Here are the progressions found in Appendix E of the standards.  I do digress into talk of matter and substance when it supports later understanding of atoms.  I’ve expanded these to list ideas explicitly and separately.

ESS1.A The universe and its stars

• (Grades 9-12) Light spectra from stars are used to determine their characteristics, processes, and lifecycles. Solar activity creates the elements through nuclear fusion. The development of technologies has provided the astronomical data that provide the empirical evidence for the Big Bang theory.
• Excited atoms/molecules emit light of particular frequencies and wavelengths (collectively called the emission spectrum of an atom/molecule).
• The frequencies and wavelengths of light emitted by atoms/molecules depend on the structure of the atom/molecules.
• Atoms/molecules absorb light at particular frequencies and wavelengths (collectively called the absorption spectrum of an atom/molecule).

PS1.A Structure of matter (includes PS1.C Nuclear processes)

• (Grades K-2) Matter exists as different substances that have observable different properties. Different properties are suited to different purposes. Objects can be built up from smaller parts.
• Matter can be made of different substances.
• Substances have many properties, each with their own uses.
• Objects are made of smaller parts.
• (Grades 3-5) Because matter exists as particles that are too small to see, matter is always conserved even if it seems to disappear. Measurements of a variety of observable properties can be used to identify particular materials.
• Indivisible particles of matter are too small to see.
• Measurements of properties characterize substances.
• (Grades 6-8) The fact that matter is composed of atoms and molecules can be used to explain the properties of substances, diversity of materials, states of matter, phase changes, and conservation of matter.
• Molecules are made of atoms.
• Matter is made of atoms and molecules.
• Different atoms and molecules explain different substances.
• Atoms and molecules behave differently in different states of matter.
• Atoms and molecules change their qualitative behavior at phase transitions.
• Matter is conserved because atoms are not destroyed in physical and chemical processes.
• (Grades 9-12) The sub-atomic structural model and interactions between electric charges at the atomic scale can be used to explain the structure and interactions of matter, including chemical reactions and nuclear processes. Repeating patterns of the periodic table reflect patterns of outer electrons. A stable molecule has less energy than the same set of atoms separated; one must provide at least this energy to take the molecule apart.
• An individual atom has structure explained by electromagnetic and nuclear interactions.
• The structure of the atom explains:
• arrangement of atoms into molecules
• chemical reactions
• nuclear processes
• trends in periodic table
• Energy is required to remove electrons from an atom.
• Energy is required to break molecular bonds.

PS1.B Chemical reactions

• (Grades K-2) Heating and cooling substances cause changes that are sometimes reversible and sometimes not.
• (Grades 3-5) Chemical reactions that occur when substances are mixed can be identified by the emergence of substances with different properties; the total mass remains the same.
• Mass is conserved in chemical reactions.
• Measurement of properties of substances identifies when chemical reactions have taken place.
• (Grades 6-8) Reacting substances rearrange to form different molecules, but the number of atoms is conserved. Some reactions release energy and others absorb energy.
• Chemical reactions result in different molecular arrangements of atoms.
• (Grades 9-12) Chemical processes are understood in terms of collisions of molecules, rearrangement of atoms, and changes in energy as determined by properties of elements involved.
• Chemical reactions occur when molecules collide and atoms rearrange.
• Changes in energy during a chemical reaction depend on properties of the atoms involved.

Let me know if you think I’ve forgotten anything here!

AAAS Science Assessment

The AAAS has a great website under the auspices of Project 2061 that lists ideas and misconceptions related to Atoms, Molecules, and States of Matter.

Arnold B. Arons. Teaching Introductory Physics

Arons identifies four lines of evidence necessary to build an early quantum model of the atom:

1. Bright line spectra of gases.  This requires understanding of how accelerated charged particles can emit light, how charged particles can absorb light.  It should include the Balmer-Rydberg formulae for hydrogen.
3. Size of atoms (electron cloud and nuclear).  Evidence from multiple sources.
4. Photoelectric effect and photon concept

How should this knowledge be arranged?

TODO: I’d like to work on a Learning Landscape, Knowledge Packet, or Learning Progression synthesizing these sources, but that will have to be added later.

Models of Atoms

1. BB Model of Atoms and Molecules (hard, indivisible balls)
• Needed to explain phases of matter.
2. Dalton Model of Atoms (hard, indivisible balls that can combine)
• Needed to explain chemical reactions in integer ratios.
3. Plum Pudding Model / Thompson Model (negatively charged electrons embedded in a positively charged medium)
• Needed to explain static electricity.
4. Planetary Model / Rutherford Model
• Needed to explain the Geiger-Marsden gold foil experiments.
5. Bohr Model / Rutherford-Bohr Model
• Needed to explain why electrons don’t fall into the nucleus after radiating EM waves.
• Needed to explain the Rydberg formula.
6. Bohr-Summerfeld Model
• Needed to allow elliptical orbits
7. Schrödinger Model / Electron Cloud Model
• Needed to explain more satisfactorily why electrons don’t fall into the nucleus after radiating EM waves
• Needed to explain atoms with more than one electron
• Needed to explain periodic table trends
• Needed to explain spectra of large Z atoms
• Needed to explain intensities of spectral lines
• Needed to explain Zeeman effect from magnetic fields
• Needed to explain spectral splittings (fine, although this could be done with Klein-Gordan equation and is really a hack onto the non-relativisticSchrödinger equation, and hyperfine) Note: I need to go back to my QM books on this one.
8. Swirles/Dirac Model
• Needed to explain spectra of large Z atoms better
• Needed to explain the color of gold and cesium
• Needed to explain chemical and physical property differences between the 5th and 6th periods
9. Quantum Field Theory Model
• Needed for ???
10. Nuclear Shell Model / Goeppert-Mayer et al. Model

About the biggest controversy is disagreement over the need to teach pseudo-historically these models.  This is leaving out all the really bad ones.  However, the terrible picture that society has adopted as the meme for atom (see below) affects student perceptions of the atom.

Stylised Lithium Atom by Indolences, Rainer Klute on Wikimedia Commons.  Note that this is only a model, based loosely on the Bohr model.  Also, these 3 electrons couldn’t all occupy the same circular orbit.

It would be nicer if students came into classrooms with the following conception of an atom.

Helium Atom QM by Yzmo from Wikimedia Commons. This is a much better rendition of the electron cloud but might be as bad for the nucleus. However, it is nice that it shows scale.

Physics teachers tend to like the Bohr model in that it can quickly (although magically) explain the Rydberg formula.  However, there are many reasons to dislike the Bohr model.

Classroom Experiments

TODO: What classroom experiments or simulations could help students to progress in their knowledge of atoms?

Unit Conversions as Gauge Transformations?

I recently read through a very nice blog post, references of which led me to reread Redish’s 2006 paper about how math is used in physics.  The following quote jumped out at me:

In introducing the concept of units to my introductory classes, I tell them that a quantity has a unit when we have an operational definition for assigning a number to it and that the number that results depends on the choice of an arbitrary standard. Since the standard is arbitrary, we may only equate quantities (or add them) if they change in the same way when we change our standard. Otherwise, a numerical equality that we obtain might be true for one choice of a standard but not for another. An equation that has physical validity ought to retain its correctness independent of our arbitrary choices.

Many physicists will recognize in the above the “scent of Einstein” – the idea that “a difference that makes no difference should make no difference.” Einstein, Poincaré, and others around the turn of the last century introduced the idea of analyzing how physical measurements change when you change your perspective on them – rotate your coordinates (in the case of identifying vectors and tensors), hop onto a uniformly moving frame (in the case of special relativity), or make a general non-linear coordinate transformation (in the case of general relativity).

Of course, the transformations that we use with units do not depend on spatial coordinates, but considering the symmetry transformation explicitly punched me in the gut because I realized that we don’t teach this explicitly to students in science classes.  Students trying to to convert units typically try either of two strategies where I work.  The first (used with metric conversions) is to consider how many factors of 10 there are between the units (like km and cm) and then move the decimal place that many times.  If students remember this procedure, they as often move the decimal point the wrong direction.  The second is to use the unit-factor method, wherein they often try “fun” factors like $\frac{100\,\textrm{m}}{1\,\textrm{cm}}$.

At least for proportional units—let’s leave affinely related units for another time—we can regard a quantity as a pair $(n,u)$, where $n$ lives in some mathematical space, and $u$ is our unit, a physical “arbitrary standard”, as Redish calls it, which lives in some torsor for the multiplicative real numbers $\mathbb{R}^\times$.  On this space, we can define an equivalence relation for physical equivalence, $(n,u)\equiv(\Lambda^{-1}\cdot n,\Lambda\cdot u)$, where $\Lambda\in\mathbb{R}^\times$ is a scale-factor.  In my mind this leads to the following exercise:

The width of a desktop is measured in units of cm and found to be 134.4 multiples of 1 cm, or in other words, 134.4 cm.  If, instead, one had measured it in a different unit, how many multiples of the new unit would the length be?  Try for as many different units as you can.

This gets at two ideas.  Students don’t always think in terms of 3 cm being 3 multiples of a centimeter length.  They also don’t often get to choose what measurements they use, or the teacher has them convert in predictable ways.  Here they can see that (134.4, cm)≡(134.4/10,cm*10)≡(134.4*10,cm/10).  Would this help them build a chain of understanding of units?  I realize that when I convert, I explicitly play the epistemic game in my head, “m is a bigger unit than cm, so it takes less of that length”.  Do all students have that understanding?

The other epistemic game I play in my head is to think, “134.4 cm is about 100 cm.  I know 100 cm is the same as a meter, so 134.4 cm is a little bigger than a meter.  It’s definitely less than 2 meters, since 2 meters is the same length as 200 cm.  I’m pretty sure that 134.4 cm works out to 1.344 m.”

How do you teach students to understand units in elementary, middle, and high school?  I’d love to know what conceptual tools or epistemic games you give students.