Desmos Activity: Electric Field Due to Point Charges

Two of my main goals when teaching students about electric fields are getting them to understand superposition and vector addition.  I usually do this by having them sketch several examples, but it is difficult for me to provide good feedback.  So I decided to create my own Desmos activity: Electric Field Due to Point Charges.  The basic idea is that there is a green region, and you have to maneuver charges until the electric field vector falls entirely within that region.  (By the way, Desmos is quickly becoming one of my favorite teaching tools.  The activity builder allows you to create scaffolded activities that are still interactive.)

Screen Shot 2016-01-19 at 11.36.32 AM

Screenshot from Desmos activity: Electric Field Due to Point Charges

I tried to use design elements to make the activity feel as natural as possible.  For example, positive charges are red and negative charges are blue.  Each type of charge produces an electric field of its corresponding color, but the combination of a red charge and a blue charge will produce a purple electric field.  The process of design is still pretty new to me, though, so if you have any suggestions please let me know in the comments.

Sharing Whiteboard Work with Mathematica and Instagram

I love using portable whiteboards for group work in class, but the ephemeral nature of the students’ work means that students will not have a written record to refer back to later.  One solution I tried last semester was to take pictures of the whiteboards with my phone.  Then after class I would upload the pictures onto Google Docs that contained the corresponding questions.  That was workable but a little less efficient than I would have liked.  

This semester I am preparing my notes and in-class activities on Mathematica slideshow presentations.  In trying to figure out efficient ways to upload pictures to the documents, I discovered that Mathematica integrates with Instagram.  With just a couple lines of code I can import any image I want.  So here is the plan: at each point in the presentation where I want to insert pictures of student work, I write a couple lines of code that search Instagram for photos with a particular tag (a tag that I can remember and that is unlikely to be used by anyone else).  Whenever I take a  picture of a whiteboard, then, all I have to do is put that particular tag as a comment for the picture.  Then I hit Shift+Enter on Mathematica and the pictures instantly appear!    

Thoughts?  Is there a better/easier way to do it that I am missing?

Curricular Structure

A typical week in my classroom used to look like this:

Stuff More Stuff

I have always been slightly bothered by this approach, though, because it makes it difficult for the students to determine what is important and what is not. All of the material more or less blends together in one constant stream.

This year, I am experimenting by adding a regularly structure to my weekly plan. It looks something like this:

weekly structure

The first day of each week is about assessment, lab skills, and epistemology. We start with a quiz based off of the previous week’s material. It lasts about 15 minutes, then we spend a little time going over the answers. Next, we do a lab that typically starts with a single investigative question, like “What is the relationship between the mass on the end of a spring and the period with which the spring oscillates?” The students determine the procedure, carry out the experiment, then create a linearized plot of the data. In the end, they will have an equation for the relationship in question. The goal of this lab activity is to introduce the topic of the week and to show the students that physics knowledge ultimately comes from experiment, not an authority figure.

On the second day of class, we flesh out the topic, and students work on establishing a conceptual understanding of the material. I start by lecturing for about half an hour, using the equation that the students’ determined in lab as a jumping-off point. For the next hour, students break into groups and practice qualitative questions (we use Randall Knight’s Student Workbook). The questions typically involving ranking tasks, proportional reasoning, etc. Before the end of class, we reconvene as a group, and individual groups show their answers to one of the questions on a whiteboard.

On the third day of class, we add a level of complexity to the material, and students work on honing their quantitative problem-solving skills. I start by answering student questions and filling in details of the content that I didn’t have time to fit in on the previous class day. The next hour or so is fairly open-ended, but the focus is on quantitative problems. Sometimes these are typical end-of-the-chapter problems, and sometimes they are more interesting challenges.

There is a very clear delineation between new content, practice, and lab work, and I think that helps the students “chunk” what they learn in class. I also like that the structure helps me focus my content delivery. Limiting my lecture time helps me focus on what is really important. This obviously requires sacrificing breadth for depth, but that is a sacrifice that I am willing to make.

I am pretty happy with how this class structure has affected my classes so far. It is not without its faults, and I have some ideas for improvements, but I will save that for a future post. Have any of you tried implementing a regular structure like this? Are there things that you would do differently? Let me know in the comments.

Summer Research Project

I’m doing a summer research project at Union College with a student, and I need as many people as possible to fill out a survey that we created. If you complete the survey by 11:59pm (EST) on Sunday, August 11, 2013, you will be entered into a raffle to win a Google Nexus 7 Tablet (32Gb), and you will receive an additional entry into the raffle for each person that completes the survey and lists you as a referrer. You can find the survey at http://tinyurl.com/q7pmzlh. It should only take 5-15 minutes. Please share this with anyone you know. Thanks!

[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.