Uncertainty about Uncertainty in IB Science

I have a student that is taking both IB Physics with me and IB Chemistry with another science teacher. The first units in both courses have touched on managing uncertainty in data and calculations, so she has had the pleasure (horror) of seeing how we both handle it. For the most part, our references and procedures have been the same.

Today we worked on propagating error through the calculation \Delta x = \frac{1}{2}at^2 with uncertainties given for acceleration and time. The procedure I've been following (which follows from my experiences in college and my IB textbooks) is to determine relative error like this:

\frac{\delta x}{\Delta x} = \frac{\Delta a}{a} + 2 \cdot \frac{\Delta t}{t}

In chemistry, they are apparently multiplying uncertainty by 0.5 since it is a constant multiplying quantities with uncertainty. On a quick search, I found this site from the Columbia University physics department that seems to agree with this approach.

My student is struggling to know exactly what she should do in each case. I told her that everything I've seen from the IB resources I have in physics supports my approach. The direct application of the formula suggests that an exact number (like 1/2) has zero uncertainty, so it shouldn't be involved in the calculation of relative error. That said, the different books I've used to plan my lessons agree with each other to around 95%. There is uncertainty about uncertainty within the textbooks discussing how to manage uncertainty. Theory of knowledge teachers would love the fact that teachers of a generally objective field (such as science) have to occasionally acknowledge to our students that textbooks don't tell the entire story.

The reality is that there are a number of ways to handle uncertainty out in the world. Professionals do not always agree on the best approach - this conversation on the Physics Stack Exchange has a number of options and the mathematical basis behind them. For students that are used to having one correct answer, this is a major change in philosophy.

Thus far in my teaching career, I haven't delved this deeply into uncertainty. The AP Physics curriculum doesn't require a deep treatment of the concepts and roughly ignores significant figures as well. I talked about some of the issues with uncertainty with students, but I never felt it was necessary to get our hands really dirty with it because it wasn't being assessed. We also learned error analysis in my experimental design courses in college, and it was part of the discussion there, but it was never the class discussion. It's really interesting to think about these issues with students, but it's also really difficult.

It seems that the questions that have resulted both from class and for my own understanding are exactly the style of conflict that the IB organization hopes will result from its programs. The way this student throws her hands up in the air and asks 'so what do I do' and managing the frustration that results is the same difficulty that we as adults face in resolving daily problems that are real, and complex.

The philosophy that I shared with the students was to be aware of these issues, but not to fear them. It should be part of the conversation, but not its entirety, especially at the level of students that are new to physics. I'm confident that some of the discomfort will melt away as we do more experimentation and explore physics models that tend to describe the world with some level of accuracy. The frustration will yield to the fact that managing uncertainty is an important element of describing how our universe works.

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Graduated Assessment & Web Design

I decided to try teaching programming this year as a class, specifically HTML, CSS, and Javascript. My hope is to get students to the point that they can put together a basic Meteor app by the end of the year, along with a good set of skills for building web pages from scratch.

My assessment scheme for the class is through a series of projects. Some are small, some are bigger and more open ended. I noticed during class on Tuesday that students are cutting corners by copying HTML from files we used in earlier classes. I admittedly do this all the time, but I pay the price for doing so in time spent cleaning up fragments of code that I really could have written from scratch in less time. In the general series of trying to teach good habits, I decided to give a graduated assignment that went through the series of HTML concepts we have learned over the past two weeks.

The requirement is that students need to make one HTML file for each of the ten steps in this file. They have to start from a blank HTML template that has nothing more than the basic head and body elements. I also had students write out the code for the first three steps by hand.

Screen Shot 2014-08-28 at 7.44.02 PM

The effect today in class was a clear measurement of where each student stands in understanding how to piece together HTML from scratch. I collected the folders of files from students at the end of class and can see precisely where their difficulties are. Some of this comes from just knowing what step they were on at the end of class, but I also had some good conversations with students throughout the period today. My class, thankfully, was pretty honest in showing what they do and don't understand how to do. While there has been some code sharing in the class before, they seemed to appreciate this opportunity to step their way through the progression of what we've learned so far.

I think there's an analogue in math and science here - I've given leveled practice sheets before in various mathematics topics. The willingness to push through misunderstanding and admit difficulties seems to be a lot more substantial in a programming context.

Here's the full exercise:
day5-Step Instructions

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Rambling about Desmos, Meteor, and the Math-Twitter-Blogosphere

By my last week in the states this summer, I had made it to San Francisco. Before getting to the hard work of eating sourdough and tinkering my way through the Exploratorium, I made two stops that were really special.

The first was a chance to meet the Desmos team at their office, arranged by Dan Meyer, who was planning to be at the office. I walked into the office while the team, not two days from the successful release of their newest activity Central Park, was on a conference call discussing the next project. As my time with them went on, I periodically felt a wave of giddiness at the fact that I was sitting with some of the people responsible for making Desmos what it is.

The four people that I met there, two thirds of the entire team, had their hands in making a difference in hundreds (if not thousands) of classrooms around the world. Jason shared that his changes to some code had resulted in a substantial increase in the code speed. Jenny showed her prototypes for a beautiful new user interface. Eric repeatedly referred to the guiding principles of Desmos as they made decisions about moving forward. The careful, deliberate work done by this group of passionate people is the reason Desmos is able to create the collaborative learning experiences for which they are known.

At one point, David Reiman, one of the team members and a former teacher himself, asked me what they could do for me. Honestly, all I could muster was that it was an honor to learn from them and see their workflow. They put a lot of energy into making sure their tools are useful for reaching objectives in the classroom, not for the sake of merely being used in the general category of technology. I really appreciate Dan, Eric, Eli, and the rest of the team for arranging to spend time with me.

The next day involved a visit to Meteor headquarters for their monthly Devshop. This is a meeting that gets Meteor coders and entrepreneurs in one room with the goal of everyone helping each other. It was impressive to meet in person some people that I had really seen only as Twitter handles. They were all incredibly genuine, humble people that worked really hard on work that mattered to them. I gave a lightning talk on coding for the classroom (posted here on YouTube) and using code to make my life as a teacher easier. Mine was one of a series of such talks. They were streamed live on the internet, but it seemed much more intimate in the actual room. Each person had three minutes to talk about an idea that mattered to them. It was also a treat that people that came up to me to chat afterwards - some of them teachers themselves - to talk about teaching, coding, and the challenges of teaching effectively with technology.

The theme that struck me after both days, a theme that I think resonates strongly with the beauty of the existence of the Math-Twitter-Blog-o-sphere, is not just that individuals (and teams) are doing interesting, thought-provoking work. That has been true for a long time.

The people at Desmos and Meteor are designing tools that enable others to not just explore their ideas, but develop, build, and share them. Just as these tools are created iteratively (Meteor released version 0.9 today) they encourage others to make the most of what is out there to put ideas in front of an audience and make them better over time. That audience might be a classroom of students. It might be an audience craving a useful online tool that targets their unique niche. Everyone at these companies (and in classrooms) is hoping that the next idea they try is one that gets more people excited than the last. Teachers work in a similar vein hoping that their next idea for tweaking a lesson gets more students engaged and making connections than the last.

I've spent the past three academic years interacting with people through this blog, Twitter, and other online channels. I've shared ideas here and have gotten feedback on them from a number of different perspectives. All of us are working hard. We have ideas and share them because ideas sprout new ideas. This process is addictive. We all have our pet projects and obsessions, and need to be brought back to reality from time to time about what will really work most effectively. We listen to each other and value the conversations that happen.

As this year is getting underway, I'm going to work to keep something in mind this year. We all have governing principles that help us decide what work to tackle at a given point in time. We often wait to share ideas until they are fully formed, but that's not really when we need the most feedback. I hope to share more ideas when they are raw and still forming. Bad days, especially when they are still smarting from an unsuccessful lesson, are revealing. It's in these situations that we stand to grow the most. What makes innovative companies like Meteor and Desmos successful isn't that they have the best ideas from the beginning. It's that they know how to cultivate ideas from beginning to end, and aren't afraid to make mistakes along the way. They acknowledge that there are lots of starts and stops and hiccups before ending up on the idea that will make a difference to people.

Have a great school year, everybody!

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Picasso's Bull - Not Just for Design Thinking

I came across the New York Times article on the Apple's training program and its use in describing their design process. I hadn't seen it before, but saw it also as a pretty good approximation for mathematical abstraction.

I used the lithographs 1 - 11 from http://artyfactory.com/art_appreciation/animals_in_art/pablo_picasso.htm and put them together like this:

Picasso - The Bull Lithographs 1 - 10
We have shortened classes tomorrow (20 minutes) and I think it might be good material for a way to introduce the philosophy of the IB Mathematics and Math 10 courses. Some potential questions floating in my head now:

  • How does this series of images relate to thinking mathematically?
  • What does the last representation have that the first representation does not? How is this similar to using math to model the world around us?
  • Can you do a similar series of drawings that show a similar progression of abstraction from your previous math classes?

This seems to be a really interesting line of thinking that connects well to the theory of knowledge component of the IB curriculum. I see this as a pretty compelling story line that relates to written representation of numbers, approximations, and the idea of creating mathematical models. Do you have other ideas for how this might be used with students?

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The Nature of Variables for Students vs. Programmers

Dan Meyer has provoked us again with this post questioning the meaning of variables in programming compared with how they exist in the minds of our students.

I previously wrote about something I tried at the beginning of last year with my students that probed this question a bit. My contention then was that writing expressions is something that occurs with students only in math class world, and that it is an inherently non-interactive process. The spirit of what variables do is something with which students have familiarity. It's the abstraction of the mathematical representation that pushes that familiarity away from them.

I'm going to use a different expression problem since the one in Dan's post doesn't do it for me.

Dan estimates that around 3/4 of any group of people drink soda.

I'd start with this activity that students would be able to answer:
Screen Shot 2014-07-24 at 7.01.57 PM

Students could each click on the people go through the process of figuring out how many in each group drink soda according to Dan's estimate, and would record the number in each group. The third group serves to construct a bit of controversy for discussion purposes. In doing this four times, students are presumably going through a similar process each time.

Mathematics serves to create structure for this repetition, but on its own, is not necessarily in the realm of what our students would do to manage this repetition. Programming provides a way to bridge this gap using the same idea of variables that exists in the mathematical realm, and here is where the value sits for this discussion.

In the post I mentioned previously, I said that I briefly showed students how to type expressions into a spreadsheet and play around with inputs and outputs so that they match concrete values. In a non 1:1 laptop classroom, I might start with this:

Screen Shot 2014-07-24 at 7.22.34 PM

A calculation links the outputs to the inputs in each of these tables. Students have concrete values sitting in front of them, so they will notice that each of these tables must be making the wrong calculations, even though they each have one correct value. Here, we have the computer making the same calculation each time, but these calculations do not work in each case. This is the wrong model to match our data. The computer is doing exactly what we are telling it to do, but the model is wrong.

How do we fix this, class? Obviously we use a different computational model. I might have students decide in a group what calculation I need to do to correctly reproduce the values from the exercise, and elicit those suggestions from them.

Once we establish this correct model, this calculation we are making is common to every set of data. We can show that this calculation makes an interesting prediction of 7.5 people liking soda in the group of 10. We can use this calculation to predict how many people in a group of 28 drink soda (and in a 1:1 classroom, I'd have them go through this entire programming process themselves.)

I might now generate a table hundreds of entries long and ask whether there is a better way to represent the set of all possible answers to this question. The table will work, but it is tedious. We need a better way. How do we do this? Here is where variables come in.

Programmers use variables because they want to build a program that produces a correct output for every possible input that might be used to solve a given problem or design. Mathematicians also want to have the same level of universality, and have a syntax and structure that allows for efficient communication of that universality. Computers are really good at calculating. The human brain is really good at managing the abstraction of designing those calculations. This, ultimately, is what we want students to be able to do, but they often get lost in both the design stage and the calculation stage, especially because these get divorced from the actual problem students are trying to solve.

If we can have students spend more time in the design stage and get feedback on whether their calculations are correct, that's the sweet spot for making the jump to using mathematical variables.

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Standards Based Grading, Year Two (Year-In-Review)

This was my second year using standards based grading with my classes. I wrote last year about how my first iteration went, and made some adjustments this year.

What did I do?

  • I continued using my 1-5 standard scale and scale rubric that I developed last year. This is also described in the post above.
  • As I wrote about in a previous post, I created an online reassessment organization tool that made it easier to have students sign up and organize their reassessments.
  • The new requirement for students signing up for reassessments involved credits, which students earned through doing homework, seeing me for tutoring
  • I included a number of projects that were assessed as project standards using the same 1-5 scale. the rubric for this scale was given to students along with the project description. Each project, like the regular course learning standards, could be resubmitted and reassessed after getting feedback and revising.

What worked:

  • My rate of reassessment was substantially better in the second semester. I tweeted out this graph of my reassessments over the course of the semester:Reassessment plot EOY

    BqAGuNKCAAAUZjW.png-large There was a huge rush at the end of the semester to reassess - that was nothing new - but the rate was significantly more consistent throughout. The volume of reassessments was substantially higher. There were also fewer students than in the first semester that did not take advantage of reassessment opportunities. Certain students did make up a large proportion of the total set of reassessments, but this was nowhere near as skewed a distribution as in the first semester.

  • Students took advantage of the project standards to revise and resubmit their work. I gave a living proof project that required students to make a video in which they went through a geometric proof and explained the steps. Many students responded to my feedback about mathematical correctness, quality of their video, and re-recorded their video to receive a higher grade.
  • Student attitude about SBG was positive at the end of the year. Students knew that they could do to improve their grade. While I did have blank questions on some unit assessments, students seemed to be more likely to try and solve questions more frequently than in the past. This is purely a qualitative observation, so take that for what it is.

What needs work:

  • Students hoarded their reassessment credits. This is part of the reason the reassessment rush was so severe at the end of the semester. Students didn't want to use their credits until they were sure they were ready, which meant that a number were unused by the end of the year. Even by the end of the year, more than a quarter of credits that had been earned weren't used for reassessments. I don't know if this means I need to make them expire, or that I need to be more aggressive in pursuing students to use the credits that they earned. I'm wrestling a lot with this as I reflect this summer.
  • I need to improve the system for assessing during the class period. I had students sign up for reassessments knowing that the last 15 - 20 minutes of the class period would be available for it, but not many took advantage of this. Some preferred to do this before or after school, but some students couldn't reassess then because of transportation issues. I don't want to unfairly advantage those who live near the school by the system.
  • I need to continue to improve my workflow for selecting and assigning reassessments. There is still some inefficiency in the time between seeing what students are assessing on and selecting a set of questions. I think part of this can be improved by asking students to report their current grade for a given standard when signing up. Some students want to demonstrate basic proficiency, while others are shooting for a 4 or 5, requiring questions that are a bit higher level. I also might combine my reassessment sign up web application and the quiz application so that I'm not switching between two browser windows in the process.
  • Students want to be able to sign up to meet with me to review a specific standard, not just be assessed on it. If students know specifically what they want to go over, and want some one-on-one time on it since they know that works well for them, I'm all for making that happen. This is an easy change to my current system.
  • Students should be able to provide feedback to me on how things are going for them. I want to create a simple system that lets students rate their comprehension on a scale of 1 - 5 for each class period. This lets students assess me and my teaching on a similar scale to what I use to assess them, and might yield good information to help me know how to plan for the next class.

I've had some great conversations with colleagues about the ways that standards based grading has changed my teaching for the better. I'm looking forward to continuing to refine my model next year. The hard part is deciding exactly what refinements to make. That's what summer reflection and conversations with other teachers is all about, so let's keep that going, folks.

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Making Experts - A Project Proposal

tl;dr A Project Proposal:

I'd like to see expert 'knowers' in different fields each record a 2-4 minute video (uploaded to YouTube) in which they respond to one of the following prompts:

  • Describe a situation in which a simple change to what you knew made something that was previously impossible, possible.
  • Describe a moment when you had to unlearn what was known so that you could construct new ideas.
  • What misconception in your field did you need to overcome in yourself to become successful?

I think that teachers model knowledge creation by devoting time to exploring it in their classes. I think we can show them that this process isn't just something you do until you've made it - it is a way of life, especially for the most successful people in the world. I think a peek behind the curtain would be an exciting and meaningful way for students to see how the most knowledgeable in our society got that way.

Long form:

One thing we do as teachers that makes students roll their eyes in response is this frequent follow up to a final answer: How do you know?

This is a testament to our commitment to being unsatisfied with an answer being merely right or wrong. We are intensely committed to understanding and emphasizing process as teachers because that's where we add the most value. Process knowledge is valuable. An engineering company can release detailed manufacturing plans of a product design and know they will remain profitable because their value is often stored within the process of building the product, not the design itself. This is, as I understand it, much if the power of companies dealing in open source technologies.

In a field like ours, however, students often get a warped sense of the value of process. They don't hear experts talking about their process of learning to be experts, which inevitably involves a lot of failure, learning, unlearning, and re-learning. In some of the most rapidly changing fields - medicine, technology, science for example - it is knowledge itself that is changing.

An important element of the IB program is the course in Theory of Knowledge (abbreviated TOK). In this course, students explore the nature of knowledge, how it represents truth, how truth may be relative, and other concepts crucial to understanding what it means to 'know' something to be true. From what I have heard from experienced IB educators, it can be a really satisfying course for both teachers and students. Elements of TOK are included as essential parts of all of the core courses that students take.

I can certainly find lots of specific ways to bring these concepts up in mathematics and science. Creating definitions and exploring the consequences of those definitions is fundamental to mathematics. Newton 'knew' that space was relative, but time was absolute. Einstein reasoned through a different set of rules that neither was absolute. These people, however, are characters in the world of science. Their processes of arriving at what they knew to be true don't get much airtime.

What if we could get experts in fields talking about their process of knowing what they know? What if students could see these practitioners themselves describing how they struggled with unlearning what they previously believed to be absolutely true? I see only good things coming of this.

What do you think? Any takers?

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Summer Updates

One of my favorite parts of summer is reflecting on the past year and brainstorming new ideas for the next. On my mind these days:

  • Refining my standards based grading system after this past semester and year's implementation
  • Building my IB courses for math(s) and physics, which will have both HL and SL in the same class period
  • Sharing ways that programming has made my teaching life easier and richer
  • Better making the most of in-class time, as well as maximizing the benefit of time students spend on their own

There are posts brewing in my head on each of these. At the moment, I'm on a road trip headed west and plan to enjoy my time enjoying the views and life, so these will likely live only in my head for now.

Stay tuned for the roll out.20140716-220459-79499383.jpg

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Curated review for finals

I really don't like reviewing for exams. I don't think I'm the only one that thinks this, by far.

If I create a the review sheet, I'm the one going through all of the content of the unit and identifying what might be important. It would be much more valuable to have students do this. I've also been filling the school server with notes and handouts of what we do each day, so they could be the ones deciding which problems are representative of the unit.

Suppose I do make a new set of review problems available to students. If students have this set of problems to work through during class, I spend my time circulating and answering questions and giving feedback, which is the best use of my time with students. Better yet, students answer each other questions, and give each other feedback. They lose the opportunity to see the scope of the entire semester themselves because, outside of the set of problems I prepare for them, they don't actually take the time to see that scope on their own. They only see my curated sample and interpret it according to their own understanding of the relationship between review problems I select and problems I select for an exam.

I've had students themselves create review sheets, but this always has its own set of issues. Is it on paper or online? If on paper, how does this sheet efficiently get shared with other students? The benefit of an online resource is the ease of sharing. The difficulty comes from (1) the difficulty of communicating mathematics on a computer and (2) compiling that resource in one place. It's a lot of work to scan student work and paste it into a document. Unless I am meticulous in making sure that all students are using the same program (which is a lot of work for a class of twenty-four students all with their own laptops) this becomes a lot of work (again) for me. I'll do it if I really believe it is worth the effort for students, but I'm always looking to be efficient in that effort. I also don't want to put this effort on the shoulders of a student to together. And before someone tells me to use Google Docs and its amazing collaborative tools, I'll bring up the governmental disruption of Google services and leave it to you to figure out why that isn't an option for me and my students.

In the end, I have to decide which is the most valuable for students relative to a review. Is it getting feedback on what a student does and does not understand? Is it going back over the entire semester's material and figuring out what is important relative to a cumulative final?

If I have to pick a theme of my online experiments this year, it has been the search for effective ways to leverage social pressure and student use of technology to improve the quality of the time we spend in the classroom together. In the past, I have been the one collecting student work and putting it in one place when I've tried doing things differently for exam review. That organization is precisely something computers do well if we design a scheme for them to use.

Here's what I have had students do this year:
Screen Shot 2014-06-10 at 4.35.37 PM

Each student has a blog where they post their own review sheet for one standard. They submit the URL of their post and their standard number through the same site through which they sign up for SBG reassessments. They see a list of the pages submitted by other students:
Screen Shot 2014-06-10 at 1.09.08 PM

This serves as a central portal through which students can access each other's pages. Each student controls their own page and URL information, which saves me the effort to collect it all.

Why am I really excited about this list?

  • I curate the list. I decide whether a page has met the requirements of the assignment, and students can see those pages with a checkmark and a WB for my initials. If a student needs to improve something, I can tell them specifically what isn't meeting the requirements and help them fix it. Everyone doesn't have to wait for everyone else to be finished for the review process to begin. I don't decide what goes into each page generally, but I do help students decide what should be there. Beyond that, I don't have to do any compilation myself.
  • Students (ideally) vote on a page if they think it meets the requirements. Students can each vote once for each page, and see a checkmark once they have voted. This gets them thinking about the quality of what they see in the work of other students. I have been largely impressed with what students have put together for this project, and students are being fairly generous with this. I'm ok with that at this point because of the next point:
  • Students have an incentive to actually visit each other's pages. I have no idea how many students actually use the review sheets we've produced together in the past. I doubt it is very many. There's some aspect of game theory involved here, but if a student sees that others are visiting his or her own pages, that student might feel more compelled to visit the pages of other students. Everyone benefits from seeing what everyone else is doing. If some review happens as a result, that's a major bonus. They love seeing the numbers adjust real time as votes come in. There is a requirement that each vote include a code that is embedded in the post they are voting for, just so someone isn't voting for them all without visiting the page.
  • Students were actually using the pages to review today. Students were answering each other's questions and getting feedback sometimes from the authors themselves.
  • I get to have valuable conversations about citing resources online.

Right now, students can vote as much as they want, but I plan to introduce one more voting option before this is entirely done which allows students to vote on their top three favorites in terms of usefulness. I am not sure how I would do this without it turning into a popularity contest, but I might try it and see how their sense of quality relates to mine. I would also love to use this next year as a Reddit style resource where students are posting problems and solutions potentially for specific standards and can vote on what is particularly helpful to them. Again, just an experiment.

I really loved how engaged students were today in either developing their pages or working on each other's review problems. It was one of the most productive review days I've had, particularly in light of the fact that I didn't have to write a single problem of my own. I did have to write the code, of course, but that was a lot more interesting to me today than thinking of interesting assessment items that I'd rather just put on an exam.

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Testing probability theories with students

One of the things that has excited me after building computational tools for my students is using those tools to facilitate play. I really enjoyed, for example, doing Dan Meyer's money duck lesson with my 10th grade students as the opener for the probability unit. My experiences doing it weren't substantially different that what others have written about it, so I won't comment too much on that here.

The big thing that hampered the hook of the lesson (which motivated the need for knowing how to calculate expected value) was that about a third of the class took AP statistics this year, so they already knew how to do this. This knowledge spread quickly as the students taught the rest how to do it. It was a beautiful thing to watch.

I modified the sequel. I'll explain, but first some back story.

My students have been using a tool I created for them to sign up for reassessments. Since they are all logged in there, I can also use those unique logins to track pretty much anything else I am interested in doing with them.

After learning a bit about crypto currency a couple of months ago, I found myself on this site related to gambling Doge coins. Doge coins is a virtual currency that isn't in the news as much as Bitcoin and seems to have a more wholesome usage pattern since inception. What is interesting to me is not making money this way through speculation - that's the unfortunate downside of any attempt to develop virtual currency. What I've been amazed by is the multitude of sites dedicated to gambling this virtual currency away. People have fun getting this currency and playing with it. You can get Dogecoins for free from different online faucets that will just give them away, and then gamble them to try to get more.

Long story short, I created my own currency called WeinbergCash. I gave all of my students $100 of WeinbergCash (after making clear written and verbal disclaimers that there is no real world value to this currency). More on this later.

After the Money Duck lesson, I gave my students the following options with which to manage their new fortune in WeinbergCash:

Screen Shot 2014-05-21 at 5.17.26 PM

Then I waited.

After more than 3,000 clicks later, I had quite a bit of data to play with. I can see which wagers individual students are making. I can track the rise and fall of a user's balance over time. More importantly, I can notice the fact that just over 50% of the students are choosing the 4x option, 30% chose 2x, and the remaining 20% chose 3x. Is this related to knowledge about expected value? I haven't looked into it yet, but it's there. To foster discussion today, I threw up a sample of WeinbergCash balance graphs like this:

Screen Shot 2014-05-21 at 5.24.49 PM

Clearly most people are converging to the same result over time.

My interests in continuing this experiment are buzzing with two separate questions:

  • To what extent are students actually using expected value to play this game intelligently? If you make the calculations yourself, you might have an answer to this question. I haven't parsed the data yet to see the relationship between balances and grade level, but I will say that most students are closer to zero than they are their starting balance. How do I best use this to discuss probability, uncertainty, predictions, volatility?
  • To what extent do students assign value to this currency? I briefly posted a realtime list of WeinbergCash totals in the classroom when I first showed them this activity. Students saw this and scrambled to click their little hearts away hoping to see their ranking rise (though it usually did the opposite). Does one student see value in this number merely because it reflects their performance relative to others? Is it merely having something (even though it is value-less by definition) and wanting more of it, knowing that such a possibility is potentially a click away?

I had a few students ask this afternoon if I could give them more so they could continue to play. One proposed that I give them an allowance every week or every day. Another said there should be a way to trade reassessment credits for WeinbergCash (which I will never do, by the way). Clearly they have fun doing this. The perplexing parts of this for me is first, why, and second, how do I use this to push students toward mastery of learning objectives?

I keep the real-time list open during the day, so if students are doing it during any of their academic classes, I just deactivate them from the gambling system. For me, it was more of an experiment and a way to gather data. I'd like to use this data as a way to teach students some basic database queries for the purposes of calculating experimental probability and statistics about people's tendencies here. I think the potential for using this to generate conversation starters is pretty high, and definitely underutilized at this point. It might require a summer away from teaching duties to think about using this potential for good.

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