[Three Act Physics] Introduction

I read a lot of teaching blogs.  There are just so many good ideas out there, and they inspire me to constantly improve the way that I teach.  Today I want to focus on one particular teaching method, the Three Act Method, which is the product of Dan Meyer and his awesome math colleagues.  If you didn’t click the link, you should do it now; it will be well worth your time.  Seriously, I’ll wait…

Okay, are you back?  To summarize, the basic idea of the Three Act Method is to take a cue from the world of storytelling, which often uses the three-act structure as a model.  Stories are typically divided into three acts: The Setup (Act 1), The Confrontation (Act 2), and The Resolution (Act 3).  Applied to teaching, it could look something like this:

Act 1: Here we introduce a conflict to spark curiosity.  This should be simple and concise while still clearly outlining the problem.  This act should lead to natural questions.

Act 2: Now that we know what the problem is — and we have a question — we need to figure out how to solve it.  Here we provide the necessary information and resources to begin calculations using principles and prior knowledge.

Act 3: Finally, we can resolve our conflict and figure out if our predictions and calculations were correct!

Sequel: We may have answered our main question, and probably some others along the way, but what else can this situation relate to?  What if we introduce something new or take something away?  How does a slight change affect the outcome?  Here we can continue to make connections to how what we learn applies to our lives every day!

My favorite part of the Three Act Method is how it can spark curiosity, even with topics and situations that people normally might not care about.  See these if you want some examples.  Dan Meyer and his colleagues have done a wonderful job coming up with their own library of Three Act Math tasks, and I wanted to join in on the fun.  So this summer I started working with an undergrad student, Michael Russo, to develop a series of Three Act Physics tasks.

So without further ado, I would like to introduce Three Act Physics.  It is still a work in progress, so please leave comments.  Any feedback you could provide would be greatly appreciated.

(By the way, I recently discovered that I am not the only person interested in Three Act Physics.  Neil Atkin has started his own series of videos, so check him out as well.)

[Lessons from Game Design] Piggybacking

This is from a series of posts called Lessons from Game Design in which I apply some of the lessons of game design to the art of teaching.  For some background as to why I am doing this and why I think game design is relevant to teaching, see my Introduction post.

Piggybacking

Several years ago, the makers of Magic noticed that they were having a problem holding onto new players because of the growing complexity of the game.  The designers’ response was to take advantage of something known as “piggybacking”.  The idea of piggybacking is to design around an already well-understood concept.  This reduces the cognitive load required to process a certain concept.  Take the following Magic card text as an example of what something could look like without piggybacking:

Confused?  What does this card do?  There may be a lot of unfamiliar terminology and syntax here.  Let me show you the rest of the card to see if that clears things up at all.

Despite the fact that you still may not understand what some of those terms mean, you probably have a much better idea of what the card does simply because you are familiar with Medusa.  Medusa turns people into stone by looking at them.  Stones are perfectly capable of acting as obstacles, but they certainly can’t attack you.

Another great example of piggybacking (which is described in the linked article) comes from the game Plants vs. Zombies, which is an implementation of a game style called tower defense.  In a tower defense game, you must defend something from an incoming attack force by strategically placing immobile defense units.  As the game goes on, the attack force becomes more dangerous and you get access to more powerful defenses.  One of the particular defense units in Plants vs. Zombies is called the Pea Shooter, which shoots peas at incoming zombies.  The upgraded version of the Pea Shooter deals more damage, but as a designer how do you convey the fact that it deals more damage in clear, obvious way?  The solution was to call the upgraded version the Repeater, and it shoots two peas at a time.  The designers are piggybacking off of the familiar concept that two is more than one.

How can we use piggybacking in order to prevent our students from disengaging when they encounter difficult material?  Here are some ideas that come to mind, some of which may be obvious as established teaching methods, and some of which may be new to you:

  • Use metaphors and analogies.  Better yet, have students develop their own analogies.  That way, you don’t run the risk of dated pop-culture references — when discussing how I solve physics problems, I used to ask my students to imagine the blank white room from The Matrix; that reference is becoming less useful with time — and the analogy is more likely to be remembered by the student.  One of the most successful analogies in my years of teaching came from a student when we were talking about RC circuits; he said that a discharging capacitor was like a water balloon with a hole poked in it.  A thicker hole would cause the balloon to empty faster.  Similarly, a resistor with a large cross-sectional area will cause a capacitor to “empty” faster.  The subsequent exam showed an unprecedented level of understanding of RC circuits for virtually everyone in the class.  By the way, an important step to any analogy is also to discuss where the analogy starts to break down.

  • If a particular student is struggling, try to use what you know about the student to create a situation that is more familiar to that student.  For example, let’s say that Bob is having a difficult time doing a projectile motion problem involving a cannon shooting a cannonball off of a cliff.  You remember that Bob is on the basketball team, so you cosmetically change the problem to one where he is shooting a basketball into a hoop.  The effect of cosmetic changes like this may not be intuitive, but it is true nonetheless; I once talked to a New York State Regents physics exam writer, and he told me that they have a list of words and phrases that they are supposed to avoid because those words and phrases have been found to create demographic biases in scores.

  • Put the concept before the name.  Most lessons naturally build off of previous lessons; however, if you start the day by saying, “Today we are going to learn about something called X”, then you are creating a new chunk in the brain for “things related to X”.  If you decline to give the topic a name, then the student is more likely to try to understand the new information by assimilating it with what is already there.  This helps the student piggyback the new information with old information.  For example, let’s say that you want to introduce your students to the concept of multiplication.  One approach would be to ask the question “How many is five fours?”.  In the absence of a definition for multiplication and its rules, students are likely to answer the question in the only way that they know how, which is to do 4+4+4+4+4=20.  When the term “multiplication” is introduced after several examples, the term is more likely to be understood as a form of addition rather than a new operation with its own separate set of rules.

  • Introduce an idea with concrete examples rather than starting off in the abstract.  Dan Meyer has written a lot of excellent material on this subject, and I highly recommend it.  As teachers, often our goal is for students to transfer what they learn from one example to a wide range different (but similar) examples.  This requires having a general understanding of the topic/rule/law.  In other words, an abstract principle is applied across a variety of specific contexts.  A common teaching technique is to start off in the abstract, then demonstrate the utility of the abstract idea by working a concrete example.  The problem with starting in the abstract, though, is that the students have no prior knowledge with which they can piggyback the abstraction.  A solution that takes advantage of piggybacking would be to start off with a concrete example, then build up with an example that requires abstraction.  For example, lets say that you want to teach how to sum all of the integers from 1 to N.  The general answer is that the sum is N(N+1)/2.  You could start with the abstract notion of the sum as well as the generalized answer for the sum, then have the students work a concrete example.  Alternatively, you can start with a concrete example that piggybacks off of something familiar, say the number of bowling pins in a bowling triangle, then work toward the abstraction by showing this:

Who wants to count that?  They’ll be begging for a generalization.  Once again, Dan Meyer is a treasure trove of wonderful ideas in this vein, and I will be talking more about the Three-Act method in later posts.

Are there other ways you can think of to use piggybacking?

[Lessons from Game Design] Introduction

I love games and puzzles.  My favorite game is called Magic: The Gathering, which I have been playing for almost twenty years.  For those who are not familiar, Magic is a trading card game; in fact, it was the very first trading card game, and it has been extremely successful.  The reason I bring this up is because for the past twelve years I have been reading a weekly column by the game’s head designer, Mark Rosewater, and I am interested to see if I can apply some of what I have learned about game design to the classroom.  After writing for a little bit, I realized that I have a lot to say on this subject, so this will simply be the introduction to a long series of posts.

Why are games relevant to teaching?  When people play games, they are voluntarily presenting themselves with a challenge in the hopes that they will receive some kind of reward for that challenge (this reward can be very different for different people).  In school, ideally students choose to challenge themselves for exactly the same reasons.  Unfortunately, that is not often the case in school, but that is also why I am writing this.

Why should I be listening to the lessons of this one guy?  Because the game of Magic has been ridiculously successful.  In fact, due to some changes and innovations in the game, sales roughly doubled over the 2-3 year period after the recession began, and Magic is currently Hasbro’s top-selling brand. Clearly, he (and the rest of the team that he speaks for) knows something about getting people interested in learning something new and sticking with it.

I think that Magic is a particularly good analogy to physics because of the structure of the game.  At its core, Magic is not a very complicated game; the rules could probably be summarized on one page.  The fact that there are over 12,000 unique cards, though, means that there are going to be some strange interactions that require a more detailed understanding of the rules.  In fact, there is a list of rulings on individual cards that takes up thousands of pages.  It would be silly, though, to think that playing the game of Magic would require knowing all of these individual rulings.  First off, these rulings are not in fact new, separate rules but rather are specific cases of more general rules.  Second, the rulings for specific card interactions are not likely to show up often in a typical game.  In real life, physics is the set of rules that describes the interactions between objects.  The basic set of rules is not that long, but the fact that the universe is so big means that there are a ridiculous amount of possible interactions.  I think the mistake that many novice physics students make is to think that in order to play the “physics game”, they need to have a detailed knowledge of all of the individual “rulings” for all of these possible interactions.  My favorite example of this was when a student of mine raised her hand during an exam and said, “I don’t have the equation for the acceleration of a tethered box on a ramp; could you give me that equation?”  I said, “Fnet=ma”.

To be clear, I am not advocating “game-ifying” teaching.  By “game-ify”, I mean turning the learning process into an actual game.  I can’t remember the citations at the moment (maybe someone can help in the comments), but I remember reading that making games out of learning makes students very good at that game, but very little of that learning transfers.  Instead, I am simply trying to apply lessons of game design to designing lessons in class to increase student interest and engagement in class material.

Are the lessons of game design something you’d like to see?  Am I entirely off-base in creating a link between game design and teaching?  I’d like to hear what you think in the comments.

Job Hunt

Being a Visiting Assistant Professor means that I am perpetually searching for new jobs, and I am discovering that applying to teaching jobs is a tricky process.  I decided some time ago that my strategy for setting myself apart from the crowd would be to emphasize my use of non-traditional teaching methods and my desire to constantly improve the way that I teach.  By all accounts, this strategy has been very successful in getting me phone interviews for visiting positions.  If the phone interview goes well, I end up having an exchange with the search committee that usually goes something like this:

Search Committee: Congratulations!  We were impressed with your phone interview, and we would like to invite you to visit our campus and give a talk in front of our faculty and students that demonstrates your teaching style.  Please provide us with a name for your talk so that we can advertise it.

Me: Excellent!  The name of my talk is Implementing Non-Traditional Teaching Methods in the Physics Classroom.

Search Committee:  That talk is not really appropriate for what we are looking for.  We are looking for a talk that demonstrates your ability to make a complex topic understandable to undergraduates.

Me: Okay, I understand.  How about Black Holes and their Formation?

Search Committee:  Capital! (Okay, nobody ever said that, but how cool would it be if they did?)

Did you catch the subtle shift there?  First, they ask for a talk that demonstrates how I teach, then they ask for a talk that demonstrates my ability to make a complex topic understandable to undergraduates.  In my mind, those are not the same thing.  I’m not the one offering the job, though, so I go along with it.

So I go and give my black hole talk, and it goes gangbusters.  I get to show my enthusiasm for the subject and my personality, and the audience is reeling from all the crazy things about black holes that they just heard.

On two occasions, the search committee accepted my first talk, so I talked to them about some of the non-traditional teaching methods that other people/institutions have used and the evidence that shows the benefits of non-traditional teaching.  Both times I was ridiculed by people in the audience.  They attacked the validity of the supporting evidence and called the methods childish.  That’s not to say that there weren’t people in the audience that supported me, but being ridiculed like that in front of a group of people tends to stick in your mind.

Many teachers seem to get offended when you talk about different ways of teaching.  My intent is to make suggestions and inspire people to try something different, but some people take it as criticism.  I’m probably partly to blame; walking the line between suggestion and criticism is difficult, and my excitement invariably causes me to stumble.

It’s not all bad news, though.  Much of my success in getting people to try new things has been the result of people walking by my classroom and briefly watching.  For example, some people were intrigued by what I was doing with whiteboards, and now there are whiteboards in every physics classroom in the building.  My experiment with Standards-Based Grading has piqued the interest of some of my colleagues as well.

So I guess the lesson I learned is that I need to stop telling people what they should be doing.  I should just do what I do, and if it is successful, people will notice.

Review of My First Year of Standards-Based Grading

I just finished my first full year of using Standards Based Grading, and the results were mixed.  I still can’t imagine going back to a completely traditional grading system, but the details of the implementation of SBG are difficult to get right.  I already talked about what I liked about my first term of SBG, so here I am going to focus on what went wrong so that I can prepare a solution.

It seems to me that the biggest benefit of SBG is that students are able to incorporate feedback and use it to improve.  To take advantage of this, though, you need to assess each skill multiple times.  This presented the biggest challenge to me because I had a lot of content to teach and only 10 weeks (with 50 hours of class time) to do it.  My solution to this was twofold: reduce the number of standards, and offload assessments to homework rather than in-class quizzes.  The difficulty with the first solution was that it required a good amount of prescience.  There were times when I designed a really good question only to find that there was no way of grading it since it wasn’t on the list of standards. The second solution didn’t work as well as I had hoped, either.  Scores on tests were always much worse than scores on homework, which means that the homework was not as helpful to the students as I wanted it to be.

Another major issue was the amount of time that was spent recording grades.  In each trimester, I used a different system of keeping track of grades.  Each new bookkeeping system was created to solve problems of the previous iteration, but each presented its own new problems.  The end result of all of this extra time spent bookkeeping was that we ended up shortening the assignments, which made it harder to revisit old objectives, which eliminated the main benefit of using SBG in the first place.

One more thing that is difficult to do with SBG is to have problems that require synthesizing skills.  The student may have no problem using Skill X and Skill Y individually, but combining them together is a different issue entirely.  Do I give two scores for that problem, one for Skill X and one for Skill Y?  Do I create a separate standard that says, “I can synthesize Skill X and Skill Y”?  That seems reasonable at first glance, but it quickly gets out of hand, as there are many possible combinations of skills.  Then we are back to the problem of having too many standards to address, which therefore makes it harder to revisit standards, which eliminates the main benefit of using SBG in the first place.

Proposed Solution

It seems to me that the best way of solving all of these problems is to have one standard for each model rather than having one standard for each skill required to implement that model correctly.  For example, the ability to properly implement the Forces Model requires that you be able to identify forces, draw a force diagram, break down forces into components, write down a force equation, and solve the equation for unknown variables.  Rather than score students on those individual abilities, I want to try assigning scores based on their ability to apply all of them together.  I was glad to see recently that someone else came to the same basic conclusion and even came up with a very nice list of big-picture standards.  One thing I like about the setup of that list is that each model is accompanied by a list of the individual skills needed to successfully implement that model.

The one-standard-per-model system also means that synthesis problems will be the norm rather than a challenge that is given from time to time.  While it is true that students often have trouble with synthesis, this is where the beauty of SBG shines through; they will improve with repeated assessment and feedback.

Pre-Mortem

When coming up with plan, I find it useful to imagine myself in the future recounting all the ways in which the plan failed (If I remember correctly, I first heard of this idea from Thinking, Fast and Slow by Daniel Kahneman).  So here goes:

  • focusing only on the models meant that students didn’t get enough practice on the more basic skills

  • synthesis is difficult, so grades were low

  • the fact that there were so few “grade columns” meant that a poor score on one particular standard dragged that student’s grade down too much

Are there any other reasons you can think of that my plan failed?  How would you solve these problems?