# Perplexed in Monument Valley

I just finished playing Monument Valley. It's a beautiful game that uses M.C. Escher style impossible geometry to create a mesmerizing series of challenges moving a character around the screen. It's no wonder that Apple awarded it one of its coveted design awards this year.

This game evoked for me many of the ideas that Dan Meyer shared in his latest blog post and talk about video games and math class. Its tremendously easy to get started: tap on a spot, and the character goes there if doing so is possible. There are many ways to find a solution - an open middle, in his words.

One other attribute is that there is no sliding backwards, so there is little to no penalty for making mistakes. Once you've solved part of the puzzle, you never die and have to start over (unless you quit the game.) This means there's no practice involved (which is where the math class analogue of independent practice might be applied with care) which is a good thing. This game is consequently pure problem solving, replete with many moments of realization and discovery of how to make progress. I was in the position below for a while before realizing that a single rotation would allow me to reach the striped target and complete the level.

This game got me thinking about designing lessons with similar levels of constructive confusion and forcing new ways of thinking. If you are looking for an enjoyable way to feel the type of perplexity that we strive to offer our students, give the game a try. It's a few hours time very well spent.

If you haven't seen Dan Meyer's talk on using the structures of video games to make math class resemble things students like, you need to do so now. You could wait until after Christmas, I guess, but not too much longer.

There's an interesting mix of comments on that blog post. The thread that interests me most is that on the relationship between the story telling aspect of video games, and the equivalent story telling that happens in good math problems. I'm not convinced that there needs to be a good backstory for a game to be compelling, just as a real world context doesn't tend to be sufficient to get most students enthusiastic about a particular problem.

One comment from Kevin Hall, however, tapped into an idea I've also been mulling over since finding one of my own Choose-Your-Own-Adventure books during a trip back home in November. Here's Kevin writing in a comment on Dan's post:

I’ve thought about embedding videos in a Google Form so students can choose their own adventure and see the consequence of their choices. For example, if each pizza is \$6 and delivery is \$1.50, you could ask how much it would cost to get 2 pizzas delivered. If a student selected \$13.50, you’d take them to a video of a single delivery guy bringing 2 pizzas. If the student said \$15, you’d show a guy bringing 1 pizza, driving back to the pizza place, and bringing the other pizza separately. But it’s a lot of work and, I think, a critical aspect of making math more like video games.

The work of putting together such a task is not to be ignored. I do think though that getting students thinking about their thinking in a way that doesn't require whole class discussion is worth investigating. Some carefully crafted questions, ones that we might ask the entire class based on student responses, might also have some power for individual students to go through before sharing thoughts with others.

I also recently learned about an online tool called Twine that takes away some of the difficulty of putting these together. You can edit your adventure in the browser, link pages together without too much hassle, and add links to pictures or videos online using standard HTML. If you know Javascript, you can use it to add even more interactivity to the story. The tool allows you to piece together a truly individualized path.

I'm interested in piecing together some activities using Twine as a starting point for some explorations next semester. I've done things like this on paper before, but the limitations of paper are such that it's impossible to progressively reveal questions based on student responses. The way that Twine reduces the friction for doing this seems just enough to make this an option to explore. I'm writing this out now as a way to get some of you to push me to actually do it.

I'd love to see what happens when the math-twitter-blog-o-sphere gives Choose Your Own Adventure a try. Give it a go, and let me know what you create. I'll be here.

# Analyzing IB Physics Exam Language Programmatically

I just gave my IB physics students an exam consisting entirely of IB questions. I've styled my questions after IB questions on other exams and on homework. I've also looked at (and assigned) plenty of example questions from IB textbooks.

It got me wondering - what non-content related vocabulary does occur frequently on IB exams to warrant exposing students to it in some form?

I decided to use a computational solution because I didn't have time to go through multiple exams and circle words I thought students might not get. I wanted to know what words were most common across a number of recent exams.

Here's what I did:

• I opened both paper 1 and paper 2 from May 2014, 2013, 2012 (two time zones for each) as well as both papers from November 2013. I cut and pasted the entire text from each test into a text file - over 25,000 words.
• I wrote a Python script using the pandas library to do the heavy lifting. It was my first time using it, so no haters please. You can check out the code here. The basic idea is that the pandas DataFrame object lets you count up the number of occurrences of each element in the list.
• Part of this process was stripping out words that wouldn't be useful data. I took out the 100 most common words in English from Wikipedia. I also removed some other exam specific words like instructions, names, and artifacts from cutting and pasting from a PDF file. Finally, I took out the command terms like 'define','analyze','state', and the like. This would leave the words I was looking for.
• You can see the resulting data in this spreadsheet, the top 300 words sorted by frequency. On a quick run through, I marked the third column if a word was likely to appear in development of a topic. This list can then be sorted to identify words that might be worth including in my problem sets so that students have seen them before.

There are a number of words here that are mathematics terms. Luckily, I have most of these physics students for mathematics as well, so I'll be able to make sure those aren't surprises. The physics related words (such as energy, which appeared 177 times) will be practiced through doing homework problems. Students tend to learn the content-specific vocabulary without too much trouble, as they learn those words in context. I also encourage students to create glossaries in their notebooks to help them remember these terms.

The bigger question is what to do with those words that aren't as common - a much more difficult one. My preliminary ideas:

• Make sure that I use this vocabulary repeatedly in my own practice problems. Insist that students write out the equivalent word in their own language, once they understand the context that it is used in physics.
• Introduce and use vocabulary in the prerequisite courses as well, and share these words with colleagues, whether they are teaching the IB courses or not.
• Share these words with the ESOL teachers as a list of general words students need to know. These (I think) cut across at least math and science courses, but I'm pretty sure many of them apply to language and social studies as well.

I wish I had thought to do this earlier in the year, but I wouldn't have had time to do this then, nor would I have thought it would be useful. As the semester draws to a close and I reflect, I'm finding that the free time I'll have coming up to be really valuable moving forward.

I'm curious what you all think in the comments, folks. Help me out if you can.

# You Don't Know Your Impact Until You Do.

There comes a time, often at the end of the semester, when you look around your classroom once the students have left, and let out a big sigh.

Am I doing the right things?

Am I helping students grow in ways that are best for them?

Then you get an email from a former student that says things like this:

I got selected to be a part of a research group in the department of PHYSICS! Can you believe it? The one subject I did not like at all is the first research opportunity for me!
...
All these great opportunities wouldn’t have happened to me if you didn’t have patience to make me understand physics. I now understand why you wanted me to figure out how to approach a problem all by myself instead of telling me what to do step by step.

I never realized how important it is to be able to do more than calculations until recently because I have been helping out a friend with her chemistry homework. However, I feel like that is all I do - help her finish her homework instead of helping her understand how to analyze a problem before jumping to equations.

I don’t want her to jump to equations because, at the end of the day, chemistry is a science, not math. We use math to help us, but a calculated answer means nothing by itself. It is the ability to analyze and interpret numbers than differentiates us from computers. Going to back to my friend and her chemistry homework, I noticed a lot of things that she says that reminded me of myself and physics.

For example, she would say “I don’t get it, it seems so easy, but I just don’t know which equation to use.” Then when I try to guide her to figure out which equations to use, she just interrupts me with “Just tell me which equation to use, and I can do the math.”

Doesn’t that sound like me in physics class? It frustrates me how she takes such a mathematical approach to a scientific problem. I mean it’s great that she can do math, but so can the computer.

I am telling you about my experience because I want to first let you know how much I appreciate your patience with me, and second, I want to apologize for that things I said about physics. It must not have been very pleasant to hear someone talk about something you are obviously interested in in such an aggressive tone.

I am sorry for complaining about physics the way I did last year, and if you students in the future complain about a subject feel free to relate my experience with physics to them. Also, I am very happy that you made me struggle with physics last year because now when I don’t see how to solve a problem immediately I know how to use the tools available to me to experiment to find the right answer.

Moreover, do continue to do explorations with your students because they are so helpful when it comes to critical thinking....

...I know you always take the opinions of your students seriously, and I know that you have stepped away from doing explorations because our class had such a negative attitude towards them; however, knowing how to use a different program can help student develop their problem solving skills, which makes them a more competitive student.

If you know me at all, you know that this hits many of the questions I have about my own teaching. One perspective is certainly not every perspective. I'm certainly not going to stop questioning. That said, this message made me grin with pride. It means a lot to hear that something you do in the classroom enables students to make opportunities for themselves.

With the student's permission, I was eager to share the email as a way to help others remember why we do this job. You might never know the impact you have as a teacher until you do.

Keep this in mind as you approach the last teaching days of the year, everyone.

# Releasing my IB Physics & IB Mathematics Standards

Our school is in its first year of official IB DP accreditation. This happened after a year of intense preparation and a school visit last March. In preparation for this, all of us planning to teach IB courses the next year had to create a full course outline with details of how we would work through the full curriculum over the two years prior to students taking IB exams.

One of the difficulties I had in piecing together my official course outline for my IB mathematics and IB physics courses was a lack of examples. There are outlines out there, but they were either for the old version of the course (pre-2012) or from before the new style of IB visitation. The IB course documents do have a good amount of detail on what will be assessed, but not the extent to which it will be assessed. The math outline has example problems in the outline which are helpful, but this does not exist for every course objective. The physics outline also has some helpful details, but it is incomplete.

The only way I've found to fill in the missing elements is to communicate directly with other teachers with more experience and understanding of IB assessment items. While some of this has been through official channels (i.e. the OCC forums), most has been through my email and Twitter contacts. Their help has been incredible, and I appreciate it immensely.

At the end of the first semester for Mathematics SL, Mathematics HL (one combined class for both), and Physics SL/HL (currently only SL topics for the first semester), I now have the full set of standards that I've used for these courses in my standards based grading (SBG) implementation. I hope these get shared and accessed as a starting point for other teachers that might find them useful.

For my combined Mathematics SL/HL class:
Topics 1 - 2, IB Mathematics SL/HL

For my combined Physics SL/HL class:
Topics 1 - 2, IB Physics SL/HL

The third column in these spreadsheets has the heading 'IB XXXX Learning Objective' - these indicate the connection between the unit standard (e.g. Standard 3.1 is standard 1 of unit 3) to the IB Curriculum Standard (e.g. 2.3 is Topic 2, content item #3). Some of these have sub-indices that correspond with the item in the list of understandings in the IB document. IB Mathematics SL objective 1.3.2 refers to IB Topic 1, content item #3, sub-topic item #2.

If you need more guidance there, please let me know.

## If you are a new IB Mathematics/Physics teacher accessing these...

...please understand that this is my first year doing the IB curriculum. There will be mistakes here. In some cases, I also know that I'll be doing things differently in the future. If these are helpful, great. If not, check the OCC forums or teacher provided resources for more materials that might be helpful.

## If you are an experienced IB Mathematics/Physics teacher accessing these...

...I'd love to get your feedback given your experience. What am I missing? What do I emphasize that I shouldn't? What are the unspoken elements of the curriculum that I might not be aware of as a first year? Let me know. I'd love it if you could give me the information you wish you had (or may have had) to be maximally successful.

I've benefited quite a bit from sharing my materials and getting feedback from people around the world. I've also gotten some great help from other teachers that have shared their resources. Consider this instance of sharing to be another attempt to pay that assistance forward.