The Book of Arons – Chapter 4

For the teachers in our reading group, here are some discussion questions for Chapter 4 of Teaching Introductory Physics:

1. What it is not
At numerous points in the book, Arons expresses…
“In order to understand what something is, one must also understand what it is not.”
Is this built into your teaching? If so, how? How does it affect students’ understanding? If not, why not? Do you think building it in would be useful?

2. The Crossover Condition
Come up with 2-3 situations (other than the ones that Arons mentions) where analyzing beyond the “crossover condition” may be helpful for students’ understanding of the phenomenon in question. Think about how you might incorporate these into class this year.

3. Arnold’s snarky remark of the week
Find some dry bluntness, well-placed snark, or something clever that made you LOL.

4. Arons Gold
What did you find in this chapter that you think is pure gold (in terms of teaching strategy)?

5. Also, I could use some help with equations 4.10.1 and 4.12.1 on pages 126 and 129!

Go team physics!

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Science Night 2014

This year our science department decided to invite our community members to the high school to learn about science. Not only was this a chance for us to bring the joys of science to the public, it was a chance for our students to share their knowledge outside of class. We decided to focus the event by choosing a theme that we thought would tie together all of our different scientific disciplines. We decided on ‘climate change’ because we thought that climate science was fascinating and was also an important issue that all people should learn about.

climatechange science night

After proposing this idea to our students we took a day early in the year to bring all of the science students to our auditorium to hear a presentation on climate change. We then went back to our separate classrooms and had students study different aspects of climate change that related to our content areas. Physics students studied human energy use, chemistry students studied ocean acidification, biology students studied the evolutionary implications of climate change, etc. Students then put together projects on their research questions that they could present at Science Night.

We invited guest speakers – a climate scientist and local meteorologist. We marketed the event around the school, in the local newspaper, and in the school newsletter. We also asked our students to invite as many people as they could.

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We hosted the event on a Friday evening in May. The first hour of the event included a presentation from local meteorologist Ross Ellet on Toledo’s weather history.

Photo May 09, 6 10 20 PM

…I also gave a presentation on climate change and had students come up and help me with some demos.

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…and students had a live Skype conversation with climate scientist Richard Alley.

Photo May 09, 7 13 00 PM

We then invited everyone out to the lobby to join us for cookies and coffee while talking to students about their projects.

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Overall, it was a positive event that we hope to build on in the future. It gave our community a chance to learn science and our students a chance to share their knowledge outside of the classroom. Many departments like art, music, athletics, and theater all  invite the community out to appreciate their crafts…why not science!?

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In defense of Newton, but…

For the past 5 years, my students (mostly high school seniors) have spent the majority of the school year learning Newtonian Mechanics – a way of thinking about how things move and why they move that way. We’ve dabbled a little in other areas like light, sound, electricity, and magnetism…but most of the year has been devoted to mechanics.

There are legitimate criticisms of this approach:

Lack of exposure to modern topics. Lack of student choice in the curriculum. Some students lose interest. Little on the history or nature of science (something most K-12 science courses are slim on).

There are also benefits:

Robust, coherent, lasting understanding (Evidence: FCI). Greater likelihood of success in college science courses (Evidence: Success in Intro College Courses and FICSS). Understanding that can be used to problem-solve  (Evidence: FCI and MBT correlation)

Some general thoughts:

I would truly like to incorporate more modern topics. However, most modern topics make little sense without at least a semi-quantitative mathematical and graphical understanding of motion. At the very least, we should strive for this as part of the course. Also, motion must be related to the physical world. Some have tried calling motion a “math topic”. I suspect that this often neglects the development of these concepts in relation to reality and typically without careful operational definitions of concepts (position, velocity, time). As for forces, I could see them being treated more qualitatively, but again they must be developed, defined, related to real situations that we can observe with our senses, represented with multiple diagrams, and connected to students’ understanding of motion. Forces make little sense without understanding motion.

From my experience, Newtonian mechanics is going to take many first-year physics students at least half of a typical high school course to understand, remember, and be able to use the concepts. If our goal is for students to understand, remember, and be able to use Newtonian Mechanics, then we need to be willing to give them the time and pedagogy necessary to accomplish this. If our goal is exposure (some call it “Pseudoteaching“), then Newtonian Mechanics can be “covered” in a week.  I’m not saying that exposure is bad. Exposure to any physics concepts, whether Newtonian or Quantum Mechanics, is a good thing…but we have to know when we’re exposing students to ideas and when we’re helping them to understand, remember, and be able to use those ideas. There are days when I absolutely feel like cutting short Newtonian Mechanics, giving it the “one week” treatment, and jumping into modern topics with students. I still might one of these years. Priorities…

A couple of years ago at a modeling workshop, Mark Schober posed a question that I found to be a useful way to think about what we choose to teach. He asked…

“If you weren’t allowed to give the test until one year after the lesson/s…what would you teach and how would you teach it?”

“Newtonian mechanics” and Modeling Instruction  have been my answers to his question. BUT…I don’t think I’d answer the following question in exactly the same way…

“If you were trying to inspire students to continue studying physics either at college or independently after they leave your class…what would you teach and how would you teach it?”



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Scientists on science education


Are we listening?

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How my students used physics to save the world

I showed pictures of ancient fossils. I told them a story about large beasts that once roamed the land. We talked about the very bad day they had 65 million years ago. Could it happen again…?


We watched video of the giant rock that exploded over Russia recently.



We talked about the space rocks that hit the earth every day. How could we stop a big one? What tools would we need? What knowledge would be necessary? 

An asteroid was headed our way.

We had to stop it.

We prepared. We decided to knock it off course.



We studied the motion of our ramming spacecraft and the asteroid. We built a model. We wondered whether our model would be good enough. We practiced. We planned.

We waited…

The day of the asteroid came. Would our knowledge be enough to stop it?

Could we save the world?


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A look back at my 4th year of teaching

Here are some highlights from the past year.

FCI Results

FCI updated chart year 4Honors physics averaged 86% and regular physics averaged 72% for an overall post-test average of 78%. Last year I wrote a post about how some of my practices changed throughout my first years of teaching and why I think they contributed to improved understanding of Newtonian mechanics…but why did they do better this year than they did last year? What did I do differently? Honestly, much of what I did this year was similar to my 3rd year.  Here are a couple of key things I think may have contributed to better understanding this year:

  • Weekly physics journal responses (only 1st trimester) – While we only used these during the 1st trimester, they were a great window into student thinking, gave students the opportunity to reflect, organize, and articulate their ideas.  Perhaps they encouraged students to be more reflective from the start of the year.
  • Better use of Standards Based Grading – This was my 2nd year using the assessment system and perhaps I explained it better and used it more effectively to promote 2nd, 3rd, & 4th attempts at mastery.  Students also weren’t too resistant this year due to a heads-up from the students the previous year.
  • Better discussion facilitation – I was perhaps more consistent in promoting scientific discourse this year.  Students were encouraged to articulate their ideas to each other more frequently and I more consistently expected contributions from all members of the class during class discussions. I also was lucky to have some smaller class sizes this year, which I think contributed to more frequent and meaningful interaction with each student.
  • Focus on the underlying model – I often would ask students to “zoom out” of the problems we just discussed and think about the main concepts behind them.  I’d also ask them what was similar about all of the problems, focusing their attention on the underlying model being deployed.  Maybe this is just a result of experience. I think I am doing a better job of emphasizing what’s ‘most important’ about each set of problems.


Project Based Learning and Modeling 

This year I tried to incorporate meaningful, long-term, creative opportunities into the modeling cycle. Students had to make or do something that mattered with the science model they developed.  I’m still trying to figure out how to best plan and carry out these projects, but I’m happy with what students did this past year.

Project 1: Weight Room Posters

After initially developing a model for torque (see how here) we decided to apply this model to the school’s weight room and make safety posters for weightlifters. This included spending a couple of days in the weight room bulking up, taking measurements, doing calculations, and in other words “getting to know the balanced torque model” really well. From the video above, you can hear the rich conversations this context provided.  So many questions came up that would never have come up if we were only using ‘book problems’. We also spent some time in the computer lab designing posters to keep those weight lifters safe!

IMG_2338 IMG_2331





Project 2: Human Energy Use and Environmental Impacts

We started by watching some episodes of “Beyond the Light Switch” and the recently released “Do The Math” video about human energy use and climate change.

The project (guidelines here, final self eval. rubric here) was then introduced as a motivator, then we developed and deployed the conservation of energy model using the modeling materials for about 1.5 weeks, then we used what we learned to apply it to making products and planning presentations to community members.  I’m telling you, have your students present to groups outside of your class!  The motivation was way higher and students didn’t see this as “just an assignment”.  They knew that they were doing something that mattered by presenting to groups in the community.  Most students wanted to present to younger kids at the other schools in our district.  What leadership! Also, I was still able to watch the presentations via video. In their final papers, many students talked about how much they enjoyed this project and that I should continue to do this in my class.




Nature of Science for 9th graders


We spent some time working with a black box that would output different amounts of colored water when water was poured in.  We collected data, designed models to explain the data, collected more data, refined our models, and then presented our models to each other to defend them.  In the process, students acted like real scientists and learned about what it meant to ‘do science’. I also introduced many scientific terms and ideas to them during this investigation.  We constantly referred back to this activity throughout the semester as we did other science investigations.  It really seemed to stick with students.


I’m really happy with how this portion of the class turned out.  I’ve really come to appreciate the idea that students must understand how scientific ideas (models) are developed in order to appreciate the scientific discipline and what it’s all about. Here’s a packet we used to guide our discussions and data collection.

Much of this unit was taken from or based off of work from MUSE. They’ve done some really excellent work in designing progressive science curricula.


Balloon Launch

Also…we went to space.

What’s next?


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Model vs. Theory vs. Law, What’s the difference?

I’ve been thinking about this for a while.  I’ve read through Hestenes’ articles (see below) and ended up in the same place that I started. Sometimes he uses ‘model’ as a verb and sometimes as a noun. I’m confused.  Can anyone help?  The articles are below, with some parts quoted.

1st Article: Modeling is the name of the game

Here’s a quote:

“To summarize, a conceptual model in science is defined by specifying the following:

(1) Constituents: Names for the thing of interest and the things in its environment.

(2) Descriptors: Object variables, State variables, Interactions.

(3) Laws: Laws of change, Interaction laws.

(4) Interpretation: Relates descriptors of the model to properties of the object.

A great variety of models can be constructed for any given thing, depending on the purposes of the modeler. Scientific theories supply advice on what variables and laws to use. No single model characterizes a concrete thing completely. Nor would such a model be desirable, because its complexity would make it too cumbersome to be useful. One of the most important objectives of modeling is to focus on the most significant or relevant properties of a thing by constructing simple models that eliminate or suppress minor details. ”


Here’s a quote:

The defining axioms of Newtonian theory are called laws, because they
have been empirically tested and validated in a broad empirical
domain. That domain is so broad, in fact, that they were believed to
be universally valid (or true!) throughout the eighteenth and
nineteenth centuries. Only in the twentieth century have definite
limitations of the validity of Newtonian theory been set by
relativity theory and quantum mechanics. The axioms of the theory
cannot be empirically tested either directly or independently. They
can only be tested indirectly through their implications for model
building. Only models can be tested experimentally, models of
physical phenomena which can be studied experimentally. Thus,
theories are empirically validated only by validating models derived
from them. The confusion is rampant in science, I find.  My intent is to help
bring clarity.”

Here’s my attempt at a summary from these articles:

“Theories inform the creation of models, and laws are part of models.”  …?

Here’s what I think:

Scientific conceptual models are ideas or sets of ideas (encoded somehow in neurons in the brain that we can create, access, and use to interpret sensory information) that are used to represent or explain parts of physical reality. Physical representations (drawings, diagrams, symbols, physical objects) can be used to represent and communicate the conceptual model. To me, theories and laws also fit this definition of a conceptual model. The articles seem to imply that laws are somehow only part of a model and that a theory is somehow outside of a model. What do you think?


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Favorite quotes on education

Here are some of my favorite education-related quotes.

“Education is not preparation for life; education is life itself.” -John Dewey

“Education is not the filling of a pail, but the lighting of a fire.” -W.B. Yeats

“If you want to build a ship, don’t drum up people together to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea” -Antoine de Saint-Exupery

“Trust that the natural world is far more interesting that anything you can toss up on a whiteboard, and then step back.” -Michael Doyle (@BHS_doyle)

“The greatest enemy of understanding is coverage.” – Howard Gardner

What are your favorite ed-quotes? Share them in the comments.

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Weekly Physics Journals

This year I’m asking my physics students to write a weekly journal response for our class.  Here are the questions they are answering.

1. What did I learn?
2. How did I learn it?
3. What questions am I wondering about?
4. If I were the teacher, what questions would I ask students to see if they understood the most important ideas of the week?

I was amazed at some of the things students said in their first journal prompt.  I can tell that many students (not all though) were thoughtfully reflecting on what they’d experienced during the week and took time to articulate and summarize their ideas.  Reading and responding to these using Edmodo took some time on my part, but I am convinced it was worthwhile after reading these this week.  Hopefully, they will continue to be useful as we move throughout the year. Below I’ve highlighted some of the more enlightening things students said.


“I found the few days we spent on discussing intelligence, knowledge, and learning to be very interesting- I was previously very rigid in my belief that intelligence is constant and an inherent trait, but now I believe otherwise.”


“Throughout the past week, I have gone from slightly confused to totally understanding the type of Physics class that I have taken participation. At the inception of the week, my thoughts were that the class was being taught about the behavior of pendulums. However, advancing through the week, I found that through actually observing the concept of the pendulum was to gain insight to the concept of models and experiments. By gathering data and depicting it on the graph through a single experiment (model), Mr. Evans was actually teaching us how to graph and plot data points, linearize a set of data and describe the difference between a model and an experiment. Genius I say!”


“This week I learned what a scientific model is, and how we can go about developing one. I learned this by doing an experiment and coming up with a set of rules with my group. I think it’s very helpful that we did everything ourselves because it was easier for me to remember what we came up with. If we were told to copy notes on the same subject, I’m sure that I wouldn’t have remembered it nearly as well as I did.”


“1. I learned that there are three types of uncertainty and that there are steps you can take to reduce them. Also, how to properly graph data with uncertainty ranges and what a model is. I learned that sometimes I need to think about concepts in general terms regarding their relationship to each other instead of always thinking about a problem numerically. 
2. I learned these things by doing the pendulum experiment and by using logger pro. I think that I understood concepts better when we talked about them as a group in our board meetings than I did by just looking at the experiment data so I will keep that in mind moving forward. 
3. Since there is no exact measurement for anything due to uncertainty I am wondering how people know how accurate they need to be when building something (a bridge or a space shuttle for example). 
4. If I were a teacher I would ask students why it is important to reduce uncertainty and the ways to do it. Also, I would ask them to graph data from an experiment and see if they could alter the axis to make it linear.”

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What is Modeling Instruction?

I’ve been struggling with this question for years!  My first three years of teaching looked very different from each other, even though I’d thought I was prescribing to Modeling Instruction (MI).  I’ve realized that simply reading an article (or even this blog post) about Modeling Instruction aren’t enough to paint the entire picture, just like reading about Karate won’t help you fully appreciate it until you’ve tried all of the moves.  A fresh explanation might be of some help to people though.  So here’s an attempt at answering the title question of this post…

What does Modeling Instruction look like?

Instead of conventional ‘units’ the course is divided up into the study of different scientific ‘models’.  A model is basically a ‘set of rules’ that exists conceptually in our heads that we can use to explain the things we observe.  The ‘set of rules’ can be represented with graphs, diagrams, words, equations, charts, etc. The whiteboard at the right was a summary created by students of a model called the ‘Constant Velocity Particle Model’.  We used it to explain how certain objects moved.

Each model takes approximately 2-3 weeks to study.  The study of each model includes two phases: development and deployment.  The things that typically occur in each phase are outlined below.

Development phase (takes ~2-5 days)

  • Students are introduced to a common physical phenomenon (car moving at constant velocity, ball rolling down a ramp, two objects crashing into each other, etc.)
  • After noting their observations, they decide which variables they could change that may affect the phenomenon, then choose which they’d like to investigate further by collecting data with available equipment.
  • Students work in groups to collect data about the phenomena.  If possible, they organize their data with tables, graphs, and equations.
  • Students then collaboratively consolidate their data and findings to share with the class.  They discuss everyone’s data to come to a consensus on a working model for the phenomena studied.
  • At this point, the teacher may introduce terminology and/or representations (force diagrams, energy bar charts, etc.) that can be used to represent the model, such that students are using scientifically consistent language and diagrams to communicate their ideas.
    Below is a short comic strip I drew up to highlight some important parts of this process.  There’s more to the development than this, but this might give you an idea of what I mean.

Deployment phase (takes ~1 week)

  • The students then begin using the model to predict how other similar physical situations may unfold.  This most often takes place through hypothetical scenarios ( ‘problems’ or ‘questions’) posed by the teacher on a series of worksheets or through an actual practicum, where students must predict how reality will behave.
  • In the process, they gain fluency in the use of multiple representations (graphs, diagrams, equations, words) for the model, which solidifies their understanding of the nuances of the model and how it applies to various contexts.
  • At different points in this process students may find that they need to refine or change the model (EX. Adding a new energy storage mechanism) to account for a new situation or refine/add a layer to their arsenal of representations (EX. Adding v-t graphs after initial use of x-t graphs, and then defining the area of v-t graph)

How does it all fit together?

MI gives students the opportunity to create and then use what they have created to understand their universe.  By doing this over and over again throughout the year, students eventually begin to think and act like real scientists! Each model becomes the backbone for the unit.  The teacher and students should always “keep one eye on the model” constantly looking back and forth between the model and reality to understand to what extent they can be superimposed on one another.  It is integral that the students understand this process and are engaged in all aspects of it.  The teacher facilitates the cycle carefully, armed with content specific knowledge and experience dealing with common student misunderstandings.  The teacher never tells the students what to think (if this is even possible), but rather invites them to evaluate their thinking, becoming a sort of metacognitive coach.  By doing so, the teacher helps give students the ability and confidence to think for themselves and to experience the thrill of a deep understanding of nature.

The entire curriculum is carefully woven into a coherent storyline, with one model picking up where the last one left off.  The failure of a model to explain a new situation motivates the development and deployment of another model.  This helps students understand science more clearly as a modeling process, where each model has its limits.  Ideally this helps dispel the common idea among students that science is a ‘body of facts’.  There aren’t ‘truths’ in science, only tentative models with limitations.  How is a student to understand this about science unless they experience it for themselves?

Why does this work so well in promoting lasting conceptual understanding?

While I’m no neuroscientist, I do have a few ideas about why MI is so effective. Throughout the modeling cycle, students are constantly shifting and affirming relationships amongst concepts in their minds. This process of shifting ideas around and adding to them takes careful and frequent thought with powerful representational tools.  It also takes time.  Both phases of the cycle give students the time and means (via observation, data collection, discussion, representational tools, etc.) they need to process these ideas and integrate them into their belief structure.  Throughout the cycle, students are constantly comparing their developed ideas (the model) to reality.  In this way, students come to believe in the model (or not, if it doesn’t work) and accept (or deny) it as part of their belief structure about the world.  Over time, the new model replaces their former notions about the world, but only if they come to realize that it fits reality better than their old ideas.  While it varies from student to student, coming to this realization typically takes most of the time and messiness noted above.  Students cannot simply be told what they’re supposed to realize about the world.  If science ideas are introduced didactically, most students are left in the dust and miss out on an important opportunity for authentic learning.

What makes modeling stand out from other “inquiry-based” approaches?

While I’m not entirely familiar with all of the flavors of “inquiry” type instruction out there, I do know that there are many different ideas and opinions amongst educators about what “inquiry” instruction is.  Often, in talking with others about modeling instruction, I can tell that they tend to attach my words about modeling to their existing ideas about inquiry, and rightfully so.  People learn by comparing and contrasting new ideas with what they already think. Unfortunately, this makes it difficult to simply explain what modeling instruction is, since it usually gets lumped together with other inquiry or ‘discovery’ approaches.  Often, my descriptions of modeling instruction are interpreted in the context of how single lessons are facilitated. This is part of MI, but is not the entire picture.  MI is more so a philosophy behind teaching science than it is a particular way of facilitating lab activities.  MI’s focus on the collaborative development and deployment of foundational scientific models is what sets it apart from other inquiry-based lesson-specific teaching techniques. Students “do science” like real scientists, not just during one ‘inquiry-type’ lab, but for nearly all of the course.  The design of the curriculum and the modeling cycle promote continuous scientific thinking and doing!  Other inquiry based approaches I’ve heard of do not take curriculum design to this level, or emphasize the building and using of models as a primary objective for teaching science.  In the modeling curriculum students repeatedly create models and then use them.  They don’t discover models.  Discovery has more to do with observing something new.  Model creation is different.  It is the intentional making of a conceptual “set of rules”(represented with graphs, diagrams, words, etc.) to describe or explain what was observed (ie. the ‘discovery’).  The heart of Modeling Instruction is all in the name.  MI is about making and using scientific models!


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