Teaching with Modeling in AP Physics

Modeling is a student-centered, inquiry-based, very successful teaching method originally developed at Arizona State University and now maintained by the American Modeling Teachers Association.

The clearest evidence that AP Physics and Modeling are a great fit is seen in the AP Physics Science Practices. These are embedded in each course, outlining the skills that should be developed by the students. Each AP Exam question incorporates one or more Science Practices. This is described in detail in the Course and Exam Description for each course. There is a set of SPs for AP Physics 1 and 2 (see below), and a slightly different set for AP Physics C Mechanics and Electricity and Magnetism.

In this post, I’ll take you through the Science Practices for AP Physics 1 and 2, and I’ll list one example of a connection with Modeling for each practice.

Science Practice 1, Modeling

“The student can use representations and models to communicate scientific phenomena and solve scientific problems”

What could be more clear! Science Practice #1 is “Modeling” and the Modeling Method for teaching physics is about training students to see science as the process of constructing conceptual models to explain nature.

In teaching with modeling, students begin most units by examining paradigms (standard examples) of each model in a student-designed lab. The students represent the behavior of the paradigm with four types of representations, mathematical, graphical, pictorial, and verbal. That means Science Practice 1 is embedded in every Modeling unit right from the start.

Science Practice 2, Mathematical Routines

“The student can use mathematics appropriately.”

In AP Physics 1/2 this Science Practice is often used to indicate an exam question that requires calculations by the student. But it is also used to indicate cases where a student has to explain WHY an equation (or a graph) makes sense, or why a representation models a physical situation. Here is an example from the 2019 AP Physics 1 released exam questions:

link to the 2019 AP Physics 1 questions

In teaching with Modeling, we use classroom discourse to accomplish the same ends. The teacher (and even other students) ask deep questions that cause students to justify the graph that they constructed, or the mathematics that they used to solve a problem. The whole class participates in this discussion, so that everybody understands WHY the techniques that were applied to create the model or solve the problem make sense. I wrote this blog post describing some of the popular whiteboarding techniques.

Science Practice 3, Scientific Questioning

“The student can engage in scientific questioning to extend thinking or to guide investigations within the context of the AP® course.

This science practice has three components:

3.1 The student can pose scientific questions.

3.2 The student can refine scientific questions.

3.3 The student can evaluate scientific questions.

In teaching with modeling, many units begin with a student-designed “paradigm lab.” Teachers demonstrate an interesting system, the “paradigm” (a pendulum, in one unit), and students (with lots of guidance and some limitations) choose what they want to investigate about the physics of the paradigm. Students pose observations and questions about the system in a whole-class brainstorm. They refine the questions in deciding what variables to test and how they can test them. And they evaluate the questions in the model-building discussion that follows the lab, where students decide what their lab results mean.

Typical graphs that students have to explain after the pendulum lab.

Science Practice 4, Experimental Methods

 “The student can plan and implement data collection strategies appropriate to a particular scientific question.

On the AP exam, this is assessed in a question where students must design a lab to answer a question. In the modeling classroom, this is a component of nearly every unit. Modeling-trained teachers give students leeway to create and carry out their own labs. This is excellent practice for AP experimental questions.

Don’t try this at home!

Science Practice 5, Data Analysis

The student can perform data analysis and evaluation of evidence.

In modeling, students must frequently collect data, construct a table, graph the data, produce a mathematical model that represents the data (and the physical system), and then explain in their whiteboard presentation their whole process and findings.

A student group’s whiteboard

And here’s an example of how the AP Exam assesses the skills developed from teaching with inquiry and modeling, also from the 2019 AP Physics 1 Free Response questions:

Science Practice 6, Argumentation

 “The student can work with scientific explanations and theories.

Argumentation involves justifying, constructing explanations, making claims, and evaluating explanations. One place on the AP Physics Exam where this Science Practice is often assessed is the “Paragraph-Length Explanation” question. There is one of these on every AP Physics 1 and 2 exam. In the Paragraph Length Explanation question, students tie together several different ideas in physics to explain the behavior of a physical system. This is quite challenging!

Modeling students should be well-trained in these skills. The skilled modeling teacher is constantly demanding that their students justify and explain physics.

Science Practice 7, Making Connections

The student is able to connect and relate knowledge across various scales, concepts, and representations in and across domains.

Isn’t this the goal of all science teachers, but especially modeling science teachers? A great example of this is the placement of the projectile motion unit in the modeling workshop I attended. Instead of being in the first unit or two, projectile motion was placed in unit 6. This was so that students could use all of the tools they have been taught in the early units: graphical models, mathematical models, pictorial models motion maps (the infamous “dot diagrams” that bedevil so many students), free-body diagrams and the whole force concept. Instead of projectiles being a scary, painful assault of obscure equations, students see it in the context of the course. It becomes both easier to understand and less scary by this simple adjustment.

Here is an example (from the released 2018 AP Physics 1 Free-Response Questions) of how the AP exam assesses both Argumentation and Making Connections. In answering this question, students must put together two areas of physics: momentum and oscillation.

I hope this all makes sense. Please comment or ask questions if you feel the need.

Go to the AMTA website (modelinginstruction.org) and check out all of the resources for modeling, if you’re new to it. A modeling workshop is great background for teaching the Science Practices in AP Physics.

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Marc Reif’s 2020 AP Physics Summer Institute Presenting Schedule

~hover over the text to find links to course, site, and geographic location~

Online! AP Physics  1 and 2 combined Registration Link on this page

Pamphlet here

15 June to 19 June 

University of TexasEl Paso


Online! AP Physics C (Combined Mechanics and Electricity and Magnetism)

22 June to 26 June

Walton HSMarietta, Georgia


Cancelled. AP Physics C (Combined Mechanics: Electricity and Magnetism)

6 July to 9 July

University of North TexasDenton


Online! AP Physics 2

13 July to 17 July

University of ArkansasFayetteville


Online! AP Physics 1 for New Teachers

20 July to 24 July

Rice UniversityHouston, Texas


Cancelled. AP Physics 2

27 July to 30 July

Silver State APSI

Liberty HS, Henderson, NV

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Electricity Visualized! Teaching Circuits in AP1 with ideas from the CASTLE Curriculum.

A student puts their own spin on the Modeling version of a CASTLE activity.

CASTLE stands for Capacitor-Aided System for Teaching and Learning Electricity.

It is a conceptual curriculum available for download from Pasco Scientific (go to https://www.pasco.com/prodCompare/castle-kit/index.cfm and scroll down to find the downloads). The curriculum is a basically complete set of activities, demonstrations, student classwork, homework, and quizzes.

A teacher guide is available by contacting me (or Pasco Scientific).

It takes a lot of time for students to complete the whole curriculum, but there are benefits. The curriculum is student-guided and inquiry-based, and emphasizes deep conceptual understanding (there are virtually no calculations and equations). Because of time constraints, my students, even my students in “on-level” physics where there is less time pressure, don’t do all of the activities. I am presenting some of the useful ideas here, so that you can see the benefit of the curriculum and perhaps make use of some of the ideas even though you don’t use the whole thing (which would be ideal, but won’t work for everyone).

Any of these activities that use a capacitor and bulbs to visualize what is happening in a circuit will not work with ordinary capacitors. As far as I know, Pasco.com is the only source for the capacitors that are utilized in the CASTLE curriculum. But, many of the activities below do not require the CASTLE capacitors

1.2 Activity:  “Using the compass to investigate a closed loop.”

A compass is placed under one of the wires in a circuit. 

  • The deflection of the needle indicates something is happening in wires.
  • Reversing the battery reverses the deflection – whatever is happening has a direction.
  • Moving the compass to different parts of the circuit shows the same deflection – indicates that whatever is happening in the wires happens everywhere. Charge is everywhere in the circuit. The battery provides energy that makes charge move/causes charge to do work, but is not the source of charge (See also Activity 8.1).

1.11 Activity: “Lighting a bulb with a single cell”

Students are given a miniature bulb, a D cell and a single wire. They are challenged to light the bulb using only those materials. Students are given a “dissected” light bulb to examine. 

  • An incandescent bulb must provide a single conducting path for charge to move through the bulb, including the filament
  • Charge must enter and leave through conducting parts of the bulb
  • Insulating parts of the bulb separate the conducting parts to provide the single path

2.3 Activity “Additional Symbols for Circuit Diagrams”

Try drawing “starbursts” to represent bulb brightness:

And drawing “Arrowtails” to represent current magnitude and directions:

2.6 Activity “Examining filaments under magnification” and 2.8 “Comparing the resistance of a bulb to a wire”

This is done after students observe that adding resistors or bulbs in series to a circuit decreases the brightness of a bulb. They examine the filaments of incandescent bulbs using magnifying lenses. The filament wires are much thinner than the support wires and connecting wires (alligator clip leads). Adding a long wire to a circuit does not appreciably change the brightness. Connecting a wire in parallel with a bulb causes the bulb to go out, as nearly all of the flow stays in the wire. Students deduce that most of the resistance is in the bulb.

  • Most of the resistance is in the bulb
  • The filament of the bulb is much thinner than other parts of the circuit
  • Thinness appears to equate with increased resistance
  • In a series circuit, a long bulb is brighter than a long bulb – since current is the same in the series circuit, the brightness of the bulb must depend on the resistance of each bulb. The filament of the round bulb must have less resistance than the filament of the long/the filament of the round bulb is thicker than the filament of the long bulb a thin filament has high resistance (see pictures below)
Round bulb (image by Charles Mamolo)
Long Bulb (image by Charles Mamolo)

2.7 Activity “Detecting the resistance of straws to air flow”


In this activity different sized straws are used as an analogy for conductors in a circuit. Air is a compressible fluid that serves as the analogy for electric charge in the circuit. Coffee stirrer straws, ordinary drinking straws, bubble-tea straws, and paper towel tubes are all useful for this activity. Students blow through the straws and observe that resistance to airflow decreases with diameter. Putting like straws together with tape illustrates the series and parallel relationship with resistance. 

  • Resistance to flow decreases with increased diameter
  • Resistance to flow increases with increased length
  • Resistance to flow decreases when “resistors” are arranged in parallel, increases when they are arranged in series.

2.8 Activity “Comparing the Resistance of Wire with a Filament”

Students insert a long wire into their circuit and observe that the compass needle deflects the same as before. Then they insert a second bulb in series into their circuit, and observe less deflection. This leads to the conclusion that wire has negligible resistance and bulbs have significant resistance. 

4.2 Activity “Exploring air as an analogy”

Two linked hypodermic syringes (minus needles) show how pressure equalizes in a circuit. Potential difference (voltage) in a circuit acts like pressure differences in the syringes. 

  • When circuit elements are connected to a source of electric pressure (a battery, for instance), the pressure quickly equalizes
  • Although the elements may be different, the pressure equalizes if it can. 

4.7 Activity: How below-normal air pressure behaves (Air Capacitor)

In this activity, students work with an air capacitor (shown above in schematic and below in a photograph).

Blowing air in or out causes the balloon membrane to move, displacing air and/or changing the pressure within the capacitor. This is analogous to the flow of charge into and out of a capacitor. Air/Charge is already present in the capacitor, and is displaced from one side or the other, rather than moving through the capacitor. The balloon membrane acts like a dielectric, insulating one side from the other. 

4.9 Commentary “Color Coding for Electric Pressures in a Circuit”

In this section, students use colored pencils to represent levels of electric potential in a circuit by color-coding schematics of the circuit. Once students understand what is expected, it is very quick to determine which bulbs in a circuit will be the brightest, or identify any bulbs that will not light (because both ends are at the same “electric pressure”). Try color-coding this circuit: 

See below for a CASTLE-style representation of an RC circuit charging. 

8.1 Activity “Circuit with a Conducting Island”

Build the circuit, predict what will happen, and connect it. The bulbs light and then go out. Charge that lights the bulbs must not have come from the battery, since the capacitor has insulators that don’t let charge through. Charge everywhere in the circuit moves until the electric pressures are all equalized. Energy is stored in the capacitors when they charge, but not a net charge. 


There are twelve sections in CASTLE. The later sections delve into advanced topics, such as electric fields, semiconductors, magnetism and induction, and electromagnetic signal propagation and detection. All without making significant use of mathematics and equations. There are great teaching ideas in those sections, I just chose to highlight some sections that may be more broadly applicable.

You can download the curriculum from Pasco.com. Or leave me a message below /send me an email and I can share the entire curriculum, including a few things that are not available on the Pasco website.

Pasco Scientific is a convenient source of good-quality materials for the CASTLE kit used by students in the curriculum. You may be able to find everything in the kit cheaper elsewhere, but the capacitors. I have never seen those specific capacitors (High Capacitance, relatively high Voltage, and non-polar) anywhere else. 

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I learned a very simple, powerful technique for engaging students’ interest, sparking intense classroom discussions, and guiding students how to think like a physicist from the book Peer Instruction  by Eric Mazur. What’s more, if you use this technique in AP Physics you’ll be incorporating a version of scientific argumentation into your instruction, something the College Board says we must be doing in AP Physics.

PI_coverIt’s a skinny volume, but it does contain a description of the Peer Instruction method, a discussion of the results of using PI, “Climate Setting” tools (techniques for getting students to buy in to inquiry) and ConcepTests for using PI in an introductory physics class.  There is good advice in here, but I will get you started using this technique right here.

The Peer Instruction technique is fairly simple to describe and has been discussed in many places (see here, and here, for example). This post is an outline of how I use this technique, with some tips from my experiences with high school students.

Step 1. Present to students an interesting multiple choice, conceptual question.


Paul Hewitt’s Next-Time Questions contain many great examples (the link takes you to Arbor Scientific’s website where you can download all of them; or, send me an email and I can send you a link to my Google Drive folder of them all). In the example above, students would vote  (A) for 100 N, (B) for 200 N, (C) for Zero N.  I usually project the question. If you are a non-physics teacher reading this post, I can assure you that physics students will get into a very intense discussion about the question above.  

Step 2. Students silently read the question, and the teacher collects the anonymous responses.

My current favorite approach for gathering the responses is Plickers (“paper clickers”). Plickers are free, and fast. Students are assigned a card with a number and a pattern on it. They vote by holding up the card in one of four possible orientations, while a phone or tablet scans the room. They can change their answer on the fly, and the website records their responses. This usually takes only about 2 minutes, including scanning the plickers.


image from https://plickers.com/

Other high-tech methods include socrative, polleverywhere,  or dedicated remote answering systems (“clickers”).

Low-tech approaches include students voting with a stack of colored plastic cups, colored post-it notes, colored index cards, or a show of hands. These are not as good, because they are not anonymous. Some students will hesitate to vote, or just as bad, copy their neighbor’s votes. You want everybody voting their own ideas so you have the option of discussing all ideas!  

Step 3. The class views the first graph of responses.

A good question will have some respondents on every (or nearly every) choice. For the plickers website,  I have created generic (no text, no image) 2, 3, and 4-choice questions that I use over and over again, rather than typing the question text into the plickers library. The graph after responses are collected from plickers.com looks like this:


Notice the vote with plickers is anonymous. I can’t stress enough how much this improves discussions. If the vote is by a show of hands, for instance, watch your students and you will see them hesitate until others have voted, or change their vote based on what their neighbors are doing. This is not what you want! You want all ideas represented in the discussion. I either place my phone under the document camera, or switch to the Plickers website “Live View” to display the graph. If I have to use the low-tech approach, I always sketch the bar graph of the responses I see on the board. This step takes about 30 seconds.

Step 4. Students discuss their own answers and the first class graph with their neighbors.

This takes several minutes on most questions, and  longer on a tough question or ambiguous question. Tell your students they must use physics to convince their neighbors what the right answer is. This is where the real power of the approach comes in. Everybody (hopefully) has committed to an answer and (again hopefully) has something to discuss. Looking at the graph is a powerful moment where they realize there are multiple ideas out there. You want them to discuss. Even discussing a guess is likely to be better than just listening to other people. Make sure everybody talks physics during this time.  The teacher roams and discusses with various groups. This is your opportunity to ask probing questions, force students to defend their reasoning, make sure everybody is engaging in the argumentation. Move quickly and check in with everybody you can. Help guide their discussion by asking “interesting” questions when they are stuck. This will also help you gain a sense of which groups to call on for Step 7. You may want groups to explain both correct and incorrect reasoning. It is important not only that students understand what makes a correct answer correct, but what makes an incorrect answer incorrect.

Step 5. Students answer again, after agreeing with their neighbors on an answer.

I command “Hold up your card for your second answer, and you better be prepared to defend your group’s answer!” This takes another 30 seconds.

Step 6. The class views a graph of the second set of responses.

Really good discussions in Step 4 may lead to nearly everybody switching to the best answer. This doesn’t happen every time. Sometimes they nearly all switch to what is not the best answer! That is also an opportunity for a good discussion. If the responses are still dispersed, you can decide, based on the quality of the discussions in the groups, to have them discuss again, and vote again. This might be a point where you provide a strong hint. For instance, in discussing the Paul Hewitt question above, a lot of students might decide that the best answer is 200 N. If this is the case, I might say to the class “If the tension is 200 N, do the masses remain at rest? Discuss again, and we’ll vote again!”

Step 7. A whole-class discussion on the final set of responses, with the goal that the class decides what is the best answer.

Have some student or students explain the reasoning for every choice, if you feel you have time. If time is short, or the discussion is dragging, you may quickly explain to the class what you heard from the groups about some choices. For instance, I might say “I heard that everybody excluded Zero newtons as the answer because everybody was sure you could feel some tension in the string, so let’s not discuss that one.” I try to get the students to reach consensus, without needing me to tell them the answer. A representative speaker is called on to defend their answer, and they are encouraged to engage in some (respectful) back-and-forth about what is the best reasoning. I try my hardest to stay out of the discussions as much as I can, interjecting only when I feel it is necessary. At the end, I try to never give up an answer, but I will say “It’s time to move on” when I feel that no more discussion is necessary. At this point they may demand an answer, but I repeat “I’m ready to move on.” Some kids really want me to explain the answer to them again, but what’s the point? They’ve already heard the answer.  If a student doesn’t get it, usually another student will say to them “Whatever we last said was right, or he wouldn’t be ready to finish.”

If a student asks, I would take the time (or have a student take the time) to summarize the reasoning we agreed upon by writing it on the whiteboard. But I don’t often initiate this. In my mind the discussion is the goal, not memorizing a solution.

I never grade these discussions for accuracy,  although I often keep track of who contributes to the discussion using ClassDojo.

Peer Instruction Links

Wikipedia page



YouTube video of Peer Instruction in use




YouTube video with Eric Mazur talking about PI

Peer Instruction blog

Peer Instruction network (nothing much there, yet)

A paper on Peer Instruction in Calculus

The Amazon page for the book

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“Nothing is too wonderful to be true” – Michael Faraday’s Law


By Thomas Phillips (Thomas Phillips, 1842) [Public domain], via Wikimedia Commons

Science is moved forward by observations and experiments, yet some observations are too subtle and some experiments too complicated to reproduce in the classroom.Michael Faraday’s discovery of electromagnetic induction combines observation and experimentation yet requires nothing expensive or complicated. It is intriguing, easy to reproduce, and provides insight into the intellectual leap from observation to model-building.

The equipment is economical enough that many teachers could buy a set for every student. Below is a picture of the equipment I use when I do this as a demonstration. The stuffed gorilla is not absolutely necessary.


Batteries can be substituted for the power supply, the primary-secondary coil set comes with the core and costs less than fifty dollars, and a small galvanometer costs less than ten dollars.

The procedure is extremely simple, and mirrors Faraday’s. In class, we have already observed that electric charge moving in a wire produces a magnetic influence around the wire, which deflects a compass needle. This is known as “Oersted’s Law.” To begin the activity I raise the question, “If moving charge in a wire can influence a magnet, can a magnet make charge move? It seems likely, doesn’t it?”

At this point I’d introduce the apparatus. The galvanometer is a sensitive, uncalibrated meter. If an electric current runs through it, the needle deflects in one direction. If a current runs through in the opposite direction, the needle deflects in the opposite direction. The secondary coil has a lot of turns of fine copper wire. When we connect the galvanometer to the coil, we have made a device that can detect the motion of small amounts of charge within the coil.

I start out by showing when the galvanometer needle doesn’t deflect. Inserting one coil in the other does nothing. Inserting the core may make a small deflection, if your core is slightly magnetic, like mine. Inserting or dropping a small magnet through the coil makes the needle deflect first one way, and then the other. A moving magnetic field can make a current flow!

The real excitement occurs when you energize the coil that is not connected to the galvanometer by running a small electric current through it. Then insert it into the other coil. The galvanometer needle will deflect very noticeably, and even more so when the core is inserted into the energized coil, which becomes an electromagnet. The magnetic field of the moving charge in the energized coil has caused charge in the other coil to move in an electric current. Any change in the magnetic field in the primary coil causes charge to flow in the secondary coil. This phenomenon is known as electromagnetic induction, and its discovery is one of the most consequential discoveries in the history of science. Electric motors, generators, and transformers all depend on it. Our modern technological society owes as much or more to this discovery as any other.

This is a moment for the teacher to act a bit, and show real enthusiasm or feign surprise. The deflection of a tiny needle is neither explosive nor glamorous. You have to be excited or students will not get it. Channel the excitement of Michael Faraday when he made the original discovery after years of work. Proceed to show the effect of changing the current through the energized coil, adding the core, and moving the two coils at different speeds relative to each other. Note that the direction of the galvanometer needle motion is tied to the direction of the motion of the coils relative to each other.

Pretend to be finished. Turn the power supply off, and say “Hey, did you see that! The needle really jumped when I turned the power off.” Turn the power supply on again, and be surprised when the needle jumps in the opposite direction.

Much later, all of these observations were summarized as Faraday’s Law by incorporating the magnetic flux model, but I suggest not jumping right to the equation. Take a few minutes to talk about the excitement Faraday must have felt, and the trepidation at explaining such a mysterious phenomenon. What one model could explain all of these different observations? How would you explain it? Perhaps you will introduce magnetic flux later, but put students in Michael Faraday’s shoes for a few minutes.

Faraday wrote these words much later:

“ALL THIS IS A DREAM. Still examine it by a few experiments. Nothing is too wonderful to be true, if it be consistent with the laws of nature; and in such things as these, experiment is the best test of such consistency.”

Laboratory journal entry #10,040 (19 March 1849); published in The Life and Letters of Faraday (1870) Vol. II, edited by Henry Bence Jones [1], p. 248.

I made a short video of this demonstration, if you’d like to see me perform it (albeit without students). PhET Interactive Simulations has two excellent, free simulations that help students visualize what they have seen in the demonstration. Faraday’s Law (written in HTML5, so it runs on nearly all devices) faradayand Faraday’s Electromagnetic Lab (which was written in Java, so it will not run on some devices).

Michael Faraday is one of the most important 19th century scientists, yet he was a of paradox. He began his scientific career as a lab assistant and rose to head the Royal Institution. Known for his careful observational experiments, he originated theories that are considered the crowning scientific achievement of his time. Briefly schooled, he knew little about mathematics, yet his ideas led to a mathematical synthesis of the cutting edge physics of his day, the theory of electricity and magnetism. The ring which he used to first observe electromagnetic induction is below:

Faraday's ring coil appratus

by Paul Wilkinson, from the Royal Institution of Great Britain

The Electric Life of Michael Faraday by Allan W. Hirshfield is a very readable, relatively short account of his life and work.

You can read Michael Faraday’s original lab entry on the induction ring on this page at the Royal Institution website.

Veritasium made an excellent video in which the host, Derek Muller, visits the Royal Institution and views Faraday’s equipment where he used it.levitatingbbq

In AP Physics 2,the relevant College Board Learning Objective is

4.E.2.1: The student is able to construct an explanation of the function of a simple electromagnetic device in which an induced emf is produced by a changing magnetic flux through an area defined by a current loop (i.e., a simple microphone or generator) or of the effect on behavior of a device in which an induced emf is produced by a constant magnetic field through a changing area. [SP 6.4]

And in AP Physics C Electricity and Magnetism:

“b) Students should understand Faraday’s law and Lenz’s law, so they can:

1) Recognize situations in which changing flux through a loop will cause an induced emf or current in the loop.

2) Calculate the magnitude and direction of the induced emf and current in a loop of wire or a conducting bar under the following conditions:

  1. The magnitude of a related quantity such as magnetic field or area of the loop is changing at a constant rate.
  2. The magnitude of a related quantity such as magnetic field or area of the loop is a specified non-linear function of time.”
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A Physics Teacher’s Strongman Trick

Strongman tricks often involve seemingly impossible tasks like bending iron bars, lifting gigantic weights, or pulling trains with your teeth. This “teacher trick” doesn’t take great strength to impress. Using a clever arrangement of a mirror and a laser, students can see that steel girders, concrete block walls, and other seemingly immovable materials flex when a force is exerted on them, even a force as small as the force exerted by a wimpy pinkie finger.

Most people don’t think at all about how “rigid” objects exert forces on other objects (the force that teachers often term “normal” force”).  Early in a unit on Newton’s Laws, it would have been asserted that the downward force of the earth on an object is balanced by an upward force of a surface on the object when we observe that the object is at rest. The terminology that is often used for this situation is problematic. Following Newton, the force of a surface on an object is often called a “reaction force.” But how can a table “react?” What do we mean by reaction? This is an issue that is often raised by students. If they don’t bring it up, I pose the question myself. This trick supplies the answer and the explanation.

The script goes something like this:

“Students, suppose I place a book on a table, and then ask you: “With how much force does the table support the book?” You would have no problem stating that since the book is at rest, the table must produce an upward support force equivalent to the downward pull of the earth on the book (the “weight” of the book). But what happens when we replace the book with something else? Now suppose I put a watermelon on the table. The same logic tells us that the table supports the melon with a force equivalent to the weight of the melon. A garbanzo bean? A feather? A fifty-pound catfish. . . Hmm. That’s a clever table. It always knows what to do. How did the table get so smart?”

At this point, I would likely pause, ask them to talk to their neighbors about “smart tables.” We discuss a few of the ideas (typically, nobody has a complete answer, but everybody agrees that the question is ridiculous). –Of course tables aren’t smart. They just “react” to what you do.

“But how does a table “react?” Wouldn’t that be interesting to know? Maybe simple things are more mysterious than we realized?

I make a proposal. “Let’s make a model table and see if we can observe how it “reacts.” The model table is constructed of light wood strips or meter sticks and some books.

I place something light on the model table (a feather or a marshmallow, say). “Did anybody see it react?” -No. And yet, it must have “reacted,” whatever exactly we mean by that. Then I place something heavier on the table, say a large mass, or a big physics book. We might see a slight sag in the table at this point.

Next, something even heavier, until there is an unmistakable sag in the “table:”


I could continue, adding mass until the table breaks, but it’s easier on meter sticks to just suppose we put something really large on the table. Suppose an elephant came in and sat on the table. What would happen then?” -A normal table would break. Tables have limits.

“How does the model table know how much force to exert on the objects? ” -It sags. “Is it possible that the table or the floor sags when you put something on it?” –Maybe “Could you ever see it sag? –I doubt it. “What if I could somehow magnify the movement? Would you believe it then?” –Maybe. “Would you believe I can make a steel girder (or a concrete block wall) move by just pushing with my little finger?” –Nope.

At this point I set up the materials to show the movement of a girder, or concrete block wall:


The laser light is reflected off of the fragment-of-CD mirror so that a visible spot is seen on a wall or ceiling several meters away. A tiny movement of the girder moves the metal rod (“attached” to the girder or wall with a lump of modeling clay). Friction between the metal rod and the dowel rotates the dowel a tiny amount. This changes the angle of the CD, and the reflected spot of laser light moves. If you push on the girder  and then pull on it, you can see that the movement of the laser light changes direction. Here is a picture of one of my students getting ready to push the girder:

File_005 (1)

And here is a video of the laser spot moving. The motion is not so pronounced, but is usually still evident if you push and pull with a pinkie finger.

It’s even more impressive if you start out with the apparatus in a room connected to a concrete block wall, and then send someone outside to push from the other side.

At this point most students can explain that objects, no matter how rigid they seem, “exert” forces by deforming slightly. The greater the force, the more they deform.

When we go back into the room, I pull out the Pasco Matter Model:


The red plastic spheres represent simplified atoms/molecules, and the metal springs represent simplified bonds. This gives students a visual for what is going on when rigid materials exert forces. It is greatly simplified and quite a bit exaggerated, but also very memorable.

I could have pulled out the model from the start and said “Today I’m going to show you how matter behaves.” But, that wouldn’t be very dramatic, would it?

Physics Teacher Notes Below

This activity aligns with the College Board’s AP Physics 1 Learning Objectives 3.C.4.1 and 3.C.4.2:

3.C.4.1: The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces. [SP 6.1]
3.C.4.2: The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions. [SP 6.2]

I usually schedule this activity two or three meetings into the force unit. In class we would not have done much more than mention Newton’s Laws. The students would have learned how to name forces (using agent-object notation), and how to draw force diagrams.

I first learned of this demonstration from a fellow participant named Steve Brehmer (a physics teacher from Minnesota) at the Project PHYSLAB teacher workshop in Portland, Oregon. The format of the activity itself was inspired by the book Preconception in Mechanics by Charles Camp and John Clement, published by American Association of Physics Teachers. The 2nd edition is available in print from the AAPT Store or as a download from American Modeling Teachers Association when you join and gain access to their curriculum repository. If you buy the book, you’ll see that they have a more detailed strategy than I outline here.

If you would like to know exactly how much your wall (or girder) moves, I recommend this article from The Physics Teacher, “Demonstrating and Measuring the Flexure of a Masonry Wall: by Daniel MacIsaac and Michael Nordstrand.

Posted in about teaching and learning, AP Physics 1 and 2, Modeling., Teaching Ideas | Tagged , , , , , | 3 Comments

WHITEBOARDING TECHNIQUES (To promote a good classroom environment and possibly, inquiry)

I have about 10 – 20 large whiteboards in the classroom. These are made from “tile board” purchased at building supply stores. This material is “Masonite” coated with a smooth white surface on side. It is intended for inexpensive bathroom remodeling. Tile board comes in 4΄ x 8΄ sheets. I have them cut it down the middle of the long dimension, and then make two cuts across the short dimension, so that I have six boards from one sheet. Each board is approximately 24″x 32″. Students write on these with dry erase markers, and erase them with rags. Blue and black erase most easily. Other colors and writing left for a long time may discolor the boards. Whiteboard cleaners will help remove the leftover writing, but rubbing alcohol also works.


Labs are a big part of the physics classroom. In my classroom students generally share their lab results by presenting them on a whiteboard. If everybody has done the same lab, then I usually only pick one or a few groups with good or interestingly poor results to present. More often, each group has investigated a different dependent variable, and everybody presents. The students below are showing lab results from a pendulum lab.


They investigated period and starting angle (the angular displacement from the rest position). Notice how they have graphed it two ways. On the left is a “zoomed in” version, based on what their graphing calculator showed them when commanded to set the window to zoom in on the data. On the right is a view that makes more sense, the “zoomed out” view. The zoomed in view emphasizes the variation in the data. When discussing their results with me before the presentation, the students recognized that the variation in the data was very small, and agreed that the calculator view was not a fair representation of their data. I asked them to show both graphs, which led to an interesting whole-class discussion of how the representation of the data influences what people think about it.


This is a technique I first learned from Jeff Steinert and Jamie Vesenka at a Physics Modeling workshop at the University of New England in Maine. More about modeling workshops here.

Students are given a set of problems, often as a worksheet. They work through the problems in their groups, and then share their answers with the class using the whiteboards. This technique works best if all students have attempted all problems, so you may want to schedule the group presentations on a different day from the group work. The problems may be conceptual, mathematical, or data-based, but I prefer a mix, rather than all one type in a session. The biggest gains in understanding come when the problems are on closely-related topics, and when at least some of the problems highlight misconceptions. 

Rules that I use for presentations (which I generally do not grade):

All group members should

  • participate equally in the preparation of the presentation.
  • participate in the presentation by speaking.
  • be prepared to answer questions about the presentation.
  • be prepared to answer questions that extend the ideas in the presentation.

All audience members should

  • listen carefully throughout the presentation.
  • hold all questions until the end.
  • be prepared to answer questions about the presentation.
  • be prepared to ask questions about the presentation.

No Comments or Applause until the group is dismissed.

The best advice I think I ever got on moderating whiteboard presentations in the classroom was “Allow Only Questions.”  In other words, students cannot comment positively or negatively. Positive comments tend to shut off conversation from both the audience and the presenters. Negative comments tend to embarrass presenters and destroy their ability to engage in a constructive dialogue. If mistakes are made in the presentation, the students in the audience are challenged to find a polite question that causes the presenters to realize the mistake. “Could you explain your assumptions in part (b)?” “Does your answer seem about the right size?”


Individual (or pairs or groups) of students present their attempts at homework solutions. An attempt, at a minimum constitutes a picture or diagram, summary of given info, summary of definitions, and (hopefully) an attempt at a solution. They transfer them to the whiteboard and make a brief presentation of their work.  If they are really struggling, they may present only their narrative of what they think they would try OR what they don’t understand that’s keeping them from solving the problem. Grades (if assessed) are based on how well they explain their attempt, either successful or “failed”.


32918025633_ce390634a2_oThis technique works particularly well for quick conceptual questions which can be answered with a graph or diagram (the students at left are working on Free-Body Diagrams, for instance). Students sit in a circle facing inward. It’s best if you really make them scoot in, so they are all in the circle. Either pairs or individuals have a whiteboard. Small “slate-sized” whiteboards may work better than the large ones, particularly if the group is small, the questions are not very involved, and you want to go quickly. The students complete a single question on a whiteboard, keeping their response hidden from the others. When the instructor, who is outside the circle, says “Go”, they hold up their whiteboards and examine them for differences and similarities. The teacher and students lead a discussion. Students must be gently persuaded by questioning to change their whiteboards until all agree on the best answer and every white board reflects the discussion. Only at this time should the teacher give the signal to go onto the next question. The goals are to quickly reach agreement for good physics reasons and move through a lot of conceptual material quickly. Sometimes the teacher sits in the group and marks their own answer on the slate with a strategic mistake.


This is a good way to mix it up a little. Students or student groups complete their whiteboards and then arrange then around the room in a gallery display. After the boards are complete, everyone strolls around the room and carefully examines the work in the boards. If they agree with the physics on the boards, they put a smiley face on the board. If they think the board has problems, they put a frowny face on the board. After everyone has finished rating the boards, a class discussion about the work and the ratings happens.


This is a technique I learned about from Kelly O’Shea’s blog:


I think she invented it. (BTW, if you are a physics teacher and you have not spent some time reading her blog posts, I suggest you do that. Lots of great information, thoughtfully and creatively presented.) I have only used “speed-dating” a few times, but students thought it was fun. Students are given a problem or problems. They have a short time to work on the problem on the whiteboard, and then they have to change to a different whiteboard. In Kelly’s blog post, she had the whiteboards stay in place while some students rotate clockwise and others rotate counterclockwise. See Kelly’s pic below (Definitely read her blog post to get the full story):


I have also tried having pairs of kids move around to different whiteboards. The problems need to be fairly deep, or on a topic new to the students, otherwise some kids will solve them so quickly that there is nothing left to do when the next students get there. It’s definitely worth trying if whiteboarding is getting stale.


Another Kelly O’Shea innovation (at least she is the person I think I heard about it from). Kelly does this a lot. In fact, in this blog post, she recommends doing it nearly all the time, in order to build a classroom climate that I call “constructive failure.” I do this when whiteboarding problems is getting a little stale. I instruct students to put an intentional mistake on their whiteboards. The teacher should walk around and ask students what mistakes they are putting on the board. Most groups will probably put something pretty trivial on the board, like a mistake in units, or significant figures. The teacher will want some of the groups to highlight misconceptions, such as “the force of motion” that persists for a long time in spite of determined instruction.


Students are given a diagram or a written situation, but they aren’t given a specific problem to solve. Instead they try to model everything they can about the situation, using whatever physics they have learned in that unit, or multiple units, if you wish. For instance, you could give your students this diagram,


(copyright Pearson, from the Knight textbook Physics for Scientists and Engineers: A Strategic Approach)

with a brief description, i.e., “a suitcase is being towed 100 m on a level surface by a force T, at a 45 degree angle.” I can see several ways I might use this picture as the source of a goalless problem.

Near the end of the study of forces, it would be a useful review problem. The command might be, “Tell me everything you can about this situation, using the physics that you have learned. I expect to see diagrams, graphs, equations, and words that describe the physics of the situation.” The students could address this goalless problem again after studying energy, and use techniques that they have learned in the energy unit to model the situation in a new way.

I usually give all groups the entire sheet of problems, but each group only presents one of the problems on the sheet. I walk around and help or ask questions.  It can take a while to work through the situations and then a fair amount of time to present the whiteboards, so we don’t always finish all of the problems.

A subset of goalless problems is the “Model a Story” whiteboard. I’ve only done this when we were studying motion, but it worked very well then. Students were instructed to invent a story, and then illustrate the story using the representations from the constant velocity and constant acceleration units. The results are often funny, as the students outdo themselves trying to be creative. The whiteboard on the left had something to do with squirrels and acorns. The one on the right has to do with speeding cars.


I learned about this from reading Dwain Desbien’s doctoral thesis on Modeling Discourse Management: http://modeling.asu.edu/modeling/ModelingDiscourseMgmt02.pdf

The idea here is that students often respond better to a question or comment from a student than from the teacher. Teachers walk around to different groups or students and suggest questions for them to ask of the presenters.

If you have suggestions for things I ought to try, please post in comments below.

Frank Noschese wrote this post some years ago, which got a lot of attention and is an excellent overview of the reasons why physics teachers love whiteboards so much.



Posted in Labs, Modeling., Teaching Ideas, Uncategorized, Whiteboarding | 2 Comments

Pinterest Boards for Teachers

Last year, inspired by my oldest daughter’s obsession with Pinterest, I started making Pinterest boards for high school physics teaching. Pinterest is a website that allows you to create “bulletin boards” of images (with a snippet of text) “pinned” from websites. The boards are themed, and viewers can click on the images to visit the websites that they come from. Pinterest itself feeds you pins that it thinks you may be interested in, and there is a social media aspect to the whole thing. Users are encouraged to follow each other, sharing boards and pins. A lot of boards are themed around fashion, accessories, food, home furnishings, and luxury objects. Mine are themed around science books and lab equipment (insert nerd emoji here).

Okay, so maybe this is a dumb idea, but unlike most of my dumb ideas, I’m not alone on this one:Capture

I currently have boards on AP Physics Essential Books:


AP Physics 1 and Physics C Mechanics Lab Equipment:


Electricity and Magnetism Lab Equipment:


AP Physics 2 Labs:


AND Outside Reading for AP Physics:


I have a couple more science teaching boards in progress, but they don’t have enough pins yet to count as much. I’m not a huge fan of Pinterest. Like most of the Web, it seems to exist mostly to get you to consume more. But, for the purpose of sharing teaching ideas, it has some advantages:

  • There is a browser add-on that lets you quickly add pins to your boards.
  • The search and social media aspects make it easy to see what other teachers are doing (although there don’t seem to be a lot of HS physics teachers using Pinterest right now).
  • The images make it more useful and more appealing than my old “Useful Links” page.

If you are a science teacher with a board for teaching, please share with me.

Posted in about teaching and learning, AP Physics 1 and 2, AP Physics C, Teaching Ideas, Uncategorized | Leave a comment

Racism and the past

Last summer I drove through the delta from Searcy, Arkansas to Pine Bluff, Arkansas. It’s a pleasant drive. The land is mostly farmland, dedicated to cotton, soybeans, and rice. The delta is an area of rich soils, plentiful water, and productive farms. Arkansas is the largest producer of rice in the country. Rice fields are particularly beautiful. The rice is a vivid green, planted in sinuous curves, and the fields are often flooded, the water reflecting sky and earth.

I passed through the tiny town of Des Arc, and spotted the Lower White River Museum State Park. The museum is in an unassuming tan metal building, only a few years old. It is spotlessly clean and little worn. There was a young woman in uniform, serving the state as museum staff. She told me that she grew up in Northeast Arkansas, near the Black River, a tributary of the White, and we chatted briefly about the exhibits. The few artifacts were largely quotidian, related to life near the river, but there were a lot of photographs, including many of riverboats, evocative of the era of Mark Twain. Exhibits highlighted the fishing, inland shipping, and mussel harvesting by which many subsisted off of the river in the past. The mussels were made into buttons. I discovered the origin of some odd mussel shells with holes drilled out of them that my father had owned. And there were works of contemporary art related to the river. It was a pleasant enough thirty minutes.

As I drove away, one thing bothered me. Look at the diorama below.


You are looking at the only purposeful mention or depiction of African-Americans in the entire museum. The only thing  clearly communicated by this mannequin is his inferior status. Poorly dressed compared to his white companions. Seated on a barrel looking up deferentially at the riverboat captain, while the white surveyor surveys and the white lady does whatever the exhibitor thought white ladies did by the side of the river.

Kids come into this museum, with their parents or with school groups. Kids of all races. As an educator, and a person who once worked in a history museum, it bothers me that there are no exhibits or words about the Arkansas African-Americans who played an important role in the history of the Lower White River. As they still do.

I wish I had thought to ask the young woman what her take on the exhibit was, and why there wasn’t more about African-Americans. But, I didn’t. It troubles me that a state museum would completely avoid the issue of race in Arkansas’s history but it doesn’t surprise me. If you’re the museum staff, it’s safer to avoid sticking your neck out. Often visitors come to museums to feel nostalgia. Museum staff don’t want to kill the nostalgia buzz. Those kids who come into the museum are going to learn a bit about Arkansas’s history. But the issue of racism, a problem that still holds us back nearly 200 years after we became a state, well, that’s just too tough.

I’ll leave you with an admittedly preachy quote from a writer my father was fond of, George Santayana:

Progress, far from consisting in change, depends on retentiveness. When change is absolute there remains no being to improve and no direction is set for possible improvement: and when experience is not retained, as among savages, infancy is perpetual. Those who cannot remember the past are condemned to repeat it.”

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The First Day of School: Marshmallows and Spaghetti

I have used this as a first-day activity for several years. Students walk in, and sit in groups of three or four assigned for them. The groups are given a large marshmallow, 20 sticks of spaghetti, about a meter of masking tape, the same length of string, and a scissors.

Spaghetti, tape, string, marshmallow


In 18 minutes, each group is to use these materials to build a structure that supports the marshmallow. The highest structure wins. Below  are a couple of groups working on their structure.



The marshmallow must remain whole, and the structure may only be connected to the tabletop. That’s it. That’s the whole activity, almost. I project a countdown timer, walk around saying encouraging words, and call out the measurements at the end. We talk about what they did that worked, about how important it is for a group to work together, and how they might do better next time, knowing what they know now.  A successful structure looks like this:


Most of these kids have never built any kind of structure, or even thought about what it takes to build a structure.  Building a stable structure out of spaghetti is tough in 18 minutes, but the marshmallow adds another dimension. Once you place the marshmallow on top, most of the structures don’t stand, or they lean over until they are barely above the tabletop. It’s fun, it’s exciting, and there are lessons to be learned from it.

I pitch it to the kids as a “model” of what they will be doing in this class:

  • they will collaborate in groups, often groups not of their choosing
  • the groups will be given unfamiliar problems to solve with familiar tools
  • failure is expected along the path to solving unfamiliar problems
  • failing publicly is expected during class
  • I expect them to learn from failure
  • trying is valued, not just success
  • success comes when you jump right in, apply what you know, and work together.

I didn’t invent this activity.There exists at least one website, devoted to it. In the TED talk posted on the website, Tom Wujec emphasizes how the including the marshmallow from the start leads to success. This is worth stressing to students in the physics classroom, as well.

Afterwards, we usually do something more traditional, a spring lab, or a pendulum lab. Talking about rules and procedures can wait until later. Getting right to work is more important.

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