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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.

Just before the exam, students came to me with some questions on vocabulary that had never come up before. It could be that they hadn’t looked at the problems as closely as they had before this exam. What struck me was that their questions were not on physics words. They were on regular English words that, used in a physics context, can have a very different meaning than otherwise. For these students that often use online translators to help in decoding problems, I suddenly saw this to be a bigger problem than I had previously imagined. An example: a student asked what it meant for an object to be ‘stationary’. This was easily explained, but the student shook her head and smiled because she had understood its other meaning. On the exam, I saw this same student making mistakes because she did not understand the word ‘negligible’, though we had talked about it before in the context of multiple ways to say that energy was conserved. Clearly, I need to do more, but I need more information about vocabulary.

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.

Revising my thinking: Force Tables

I’ve avoided force tables as a lab in the past. This is primarily because when I first started teaching physics and saw some collecting dust in the lab equipment room, the activities that were written for them seemed so formulaic that I was bored by them. I didn’t know then what I might do to make it more interesting.

In making an activity using them today, I actually played around with them a bit. They are a bit tricky to set up, but once you have the weights balanced, it’s oddly satisfying to see the ring in the center floating there:

The theme of my lesson planning is a search for this type of gold: how can we play with this?

I’ve done activities involving ‘find the unknown mass’ before, and the force table offered an efficient way in to doing this.

I asked students to figure out the mass of the weight circled in blue. I asked them to decide what information they needed to do so, and they requested the other two masses, which I provided.

Students worked quickly using their knowledge of forces and equations of equilibrium. They figured out pretty quickly that the angles between the threads were approximately equal, a fact I didn’t notice until I looked from above:

Their predicted answer of 290.9 grams was impressively close to the actual answer of 292.2 grams. We discussed that the assumption that the angles were the same might contribute for the error.

On the whole, this was a fun way to put to use a piece of equipment that I’ve kept out of my classroom for largely silly reasons. I think I’ll definitely add this to the playlist for future units on equilibrium.

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: 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. <p\> 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.

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?

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.

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:

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:

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.

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:

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:

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.

Standards Based Grading: Bridging the Gap

I ended last semester feeling pretty discouraged about my implementation of standards based grading. I still felt pretty good about what it was doing for students. For the students that were actually taking advantage of the system and initiating reassessments, it seemed to be helping. Some examples:

Students were getting frequent assessment over the different standards of the course through quizzes, and got feedback on their learning the same day since the quizzes were short.
Some students understood that they could request reassessment on their own to show progress on standards that previously were not marked as proficient.
On a day that I gave one of these standards quizzes, I was guaranteed to have a conversation on content, albeit sometimes a short one, with every single student. I can’t guarantee that I get to every student, every period, though I’d like to think that I do.
Students seemed to be less frustrated or scared by unit exams, and I received (anecdotally) fewer blank problems since students had an incentive to try anything.

By the end of the semester, I had 248 student-initiated reassessments. I don’t know how that compares to others, but that number seemed to be an indication that something was going well. Then I looked at the numbers. Of those reassessments, eighty-eight of them were in the last week of the semester. Roughly 1/3 of the total were taken by the top five most frequent assessors.

I wasn’t getting to many of the students. Despite my efforts to constantly ask students to do so, talk about opportunities to reassess in class, and target students that needed extra help with suggestions to come see me after school, some students didn’t know that they could reassess. Some students didn’t make the time. In fact, most didn’t. I was also tolerating a fairly heavy end of semester reassessment rush that seemed higher than what I’d like to see happen.

The other concept that also bugged me was that in this system, I wasn’t placing value on those behaviors that would lead to higher standards scores. No, I wasn’t about to go back to a system of checking homework, and giving extra credit – the grades reported through standards were a pretty good measure of what students knew. On an end of semester survey, a majority of students confirmed this fact. Students also understood that reassessment without preparation wouldn’t result in increased scores. I had students that said, however, that doing homework, getting help after school, teaching concepts to other students – those things that result in improved understanding – weren’t accounted for in the grade. If I valued those as part of the process, why was I not assigning any value to them in the grade?

I spent a lot of time thinking about this over the winter break. In my system, there was a fundamental gap between the behaviors I wanted students to develop, and the way I was measuring the learning happening in my classroom. Students understand the system this way:

There is a visible wall between what students know I value and what they see measured in their grade. This is the philosophical basis of standards based grading – the grade is a measure of learning content, not necessarily of completion of activities. It is fundamentally different from other grading systems. We don’t see it this way as teachers, however.

We see it like this:

I have the conversation with students all the time about the difference between these two conceptions. They do understand. It just doesn’t fit with the rest of what they have been told in school, where learning sometimes takes second fiddle to being a student.

This is a communication design problem. After a lot of thinking and designing, I came up with a new computer based system using the Meteor JS framework that I’ve been using since January.

Some parts of it have helped bridge this gap (and other problems) in some ways that have been quite productive – I’ll go through them piece by piece.

Problem 1 – Google Forms are not reliable in China.

I previously used a Google form to collect reassessment sign-up data. Students would frequently (and with good reason) say that they couldn’t log on to sign up because of this issue. While there are still internet issues with the new site, this is less of a problem. They can log in with their own email address, their own secure password, and I can control the input/output of information much more reliably since it’s a database, not a spreadsheet.

Problem 2 – I don’t want students signing up for reassessments the same day.

I really want students planning ahead. The Google form didn’t have the option of limiting which days they could sign up for based on the time of sign up, at least I didn’t see how to do this easily. It’s true that I could simply see which students signed up from the Google form results spreadsheet, but that involved scrolling, searching, and mentally filtering results. That was more work than I wanted to be doing.

With some Javascript, I make it impossible to do this. Students log in, click on ‘Reassessment Sign-up’ and see this form:

Problem 3 – Students forget which standard they signed up to reassess on.

I received an email every time students signed up for a reassessment through the Google form. I never figured out a slick way to do this through forms – I’m sure it’s possible. With this system, students can click on ‘My Reassessments’ and see what they’ve signed up to do:

If they miss the bus and have to reschedule for later the same day, they can log in and edit the reassessment themselves. Because of Meteor’s realtime system, those changes instantly show on my browser when they happen.

Problem 4 – Students sign up to reassess without any preparation.

This was a big one I wanted to solve. On my previous form, there was just a check box that said “I promise to prepare for this reassessment” along with a box where they describe what they did to prepare. I wasn’t directly able to check this, and usually didn’t have time to do so beyond noting that it was more substantial than ‘I studied’.

When students log in and sign up for a reassessment now, they see a little badge called ‘Reassessment Credits’. Each reassessment costs them one credit. What happens when they try to sign up for a reassessment without any credits left?

They can’t do so. No way around it, at least without learning some Javascript to hack my system.

This is where I find I am doing the work to educate students in what I am looking for. I value the work that they do in preparing for reassessments. I show that value through giving students credits, a token for whatever it is they choose to do to improve their understanding. These credits then directly convert into opportunities to show what they have learned through reassessment. I have the flexibility to give credits for different things that students do – tutoring other students, sitting in the classroom and doing homework with me, or simply showing me the homework they did after the previous class. This value is separate from the grade. Students have also found that through doing the work to earn a credit, I have directly increased their standards grade because I’ve seen evidence of higher understanding there.

Problem 5 – Students don’t know that their peers are reassessing.

I’m not ashamed to say that I also wanted to call upon the fact that students (and all of us) are influenced to some extent by our social community. I added one more part to the page that some students have reported has pushed them to sign up and complete reassessments.

When I first added this feature, a student said she was disappointed when she saw her proportion of the total decreasing, so she felt compelled to figure out what she might reassess over based on her progress.

Problem 6 – Staying organized with reassessments from four different classes is difficult

This system is computerized, so it’s easy to sort which reassessments I have on a given day.

Rather than skimming a spreadsheet and figuring out which quizzes to prepare, I have an easy list that allows me to prioritize and plan which quizzes I need to have available for which part of the day.

I’ve taken a lot of the obstacles out of the way that have made it stressful for me to stay organized in reassessments, and for students to opt not to do so. I am not trying to make a point about quantity vs. quality here, but I’m really pleased with how the system has worked for students.

So far this semester, I’ve had 221 reassessments through the system at this point in the semester, and we’re only in the first quarter. Thirty seven out of 55 students have assessed multiple times. Eleven students thus far have not reassessed at all, and I’ve seen that information easily through some database queries, which has prompted some conversations with those students about why they haven’t. It’s far easier than it used to be to get this information out.

Students also have great ideas for making it better. They know themselves, and know what would help them stay on top of their needs. I enjoy the challenge of learning to build this for them, and they seem to appreciate the effort.

I am not sharing the URL quite yet since there is student user information in there, and haven’t built a nice sandbox login yet to see the features. That will come when I have the time, whenever that is.

Visiting the Museum of Math in NYC

I was reminded by John Burk that the Museum of Math had been opened since I was last in New York. A good friend was in town on a weekend getaway from summer coursework in preparation for starting teaching math this fall. It was the perfect motivation to make time for visiting the museum sooner rather than later.

I was really impressed with the museum when I first walked in. The message that mathematics can be a language of play and exploration is emphasized from the experiential exhibits on the top floor. From pulling a cart that rolled across various solids to working to tesselate a hyperbolic surface with polygons, there is lots to touch, pull, and do to play with mathematical concepts. Without a doubt, these activities “stimulate inquiry, spark curiosity, and reveal the wonders of mathematics” as the mission statement aspires to do. The general organizing idea of the activities on the top floor is to provide a really interesting, perplexing object or concept to play with, and then dip into the mathematics surrounding that play for those that are interested. One could miss the kiosks that explain the underlying concepts and still feel satisfied with the overall experience.

The museum had a good mix of activities from different fields of mathematics. Most exhibits were built around a visually defined task that required little explanation in order to start playing with it and understanding its rules through that play. For me, the activities with the largest initial investment/perplexity ratio were the line of lasers that made it possible to see the cross section of a shape and the wall that generates a fractal tree from images of you and a neighbor. Building objects that roll along a particular path was also incredibly engaging for me.

The challenge for a museum like this is to be intriguing without being tricky or elitist. Given that many people experience anxiety about mathematics for all sorts of reasons, I am absolutely sure that the museum’s exhibit designers worked extremely hard to make the bar for entry for these activities as low as possible with a high ceiling. To this end, I think the museum has done a fabulous job. Most exhibits make clear what they are all about and give visible feedback on a visitor’s progress toward reaching the goal. The only area for growth that jumped out at me was an expansion of the role of the staff circulating among the exhibits. They were extremely knowledgeable of the content of the exhibits and were really excited to share what they knew about them. Even as someone that enjoys mathematics, however, there were some exhibits that left me wondering whether I was playing with it correctly. I saw the Shape Ranger exhibit as a puzzle to figure out, for example. I could see others leaving it when the activity didn’t clearly define visually what the score of the activity represented. I envision an expanded role of staff members helping nudge visitors to understand the premises of the more abstract exhibits through careful questioning and good examples of how to play.

This was not a deal breaker for me, however, and didn’t seem to be for the crowd of people in attendance. The number of smiling kids and adults enjoying themselves is clearly the best indication that the museum is doing a great job of fulfilling its mission. This museum has the same sort of open-ended atmosphere that the Exploratorium in San Francisco creates for its visitors, and that puts it in very respectable company.

2012-2013 Year In Review – Learning Standards

This is the second post reflecting on this past year and I what I did with my students.

My first post is located here. I wrote about this year being the first time I went with standards based grading. One of the most important aspects of this process was creating the learning standards that focused the work of each unit.

What did I do?

I set out to create learning standards for each unit of my courses: Geometry, Advanced Algebra (not my title – this was an Algebra 2 sans trig), Calculus, and Physics. While I wanted to be able to do this for the entire semester at the beginning of the semester, I ended up doing it unit by unit due to time constraints. The content of my courses didn’t change relative to what I had done in previous years though, so it was more of a matter of deciding what themes existed in the content that could be distilled into standards. This involved some combination of concepts into one to prevent the situation of having too many. In some ways, this was a neat exercise to see that two separate concepts really weren’t that different. For example, seeing absolute value equations and inequalities as the same standard led to both a presentation and an assessment process that emphasized the common application of the absolute value definition to both situations.

What worked:

The most powerful payoff in creating the standards came at the end of the semester. Students were used to referring to the standards and knew that they were the first place to look for what they needed to study. Students would often ask for a review sheet for the entire semester. Having the standards document available made it easy to ask the students to find problems relating to each standard. This enabled them to then make their own review sheet and ask directed questions related to the standards they did not understand.
The standards focus on what students should be able to do. I tried to keep this focus so that students could simultaneously recognize the connection between the content (definitions, theorems, problem types) and what I would ask them to do with that content. My courses don’t involve much recall of facts and instead focus on applying concepts in a number of different situations. The standards helped me show that I valued this application.
Writing problems and assessing students was always in the context of the standards. I could give big picture, open-ended problems that required a bit more synthesis on the part of students than before. I could require that students write, read, and look up information needed for a problem and be creative in their presentation as they felt was appropriate. My focus was on seeing how well their work presented and demonstrated proficiency on these standards. They got experience and got feedback on their work (misspelling words in student videos was one) but my focus was on their understanding.
The number standards per unit was limited to 4-6 each…eventually. I quickly realized that 7 was on the edge of being too many, but had trouble cutting them down in some cases. In particular, I had trouble doing this with the differentiation unit in Calculus. To make it so that the unit wasn’t any more important than the others, each standard for that unit was weighted 80%, a fact that turned out not to be very important to students.

What needs work:

The vocabulary of the standards needs to be more precise and clearly communicated. I tried (and didn’t always succeed) to make it possible for a student to read a standard and understand what they had to be able to do. I realize now, looking back over them all, that I use certain words over and over again but have never specifically said what it means. What does it mean to ‘apply’ a concept? What about ‘relate’ a definition? These explanations don’t need to be in the standards themselves, but it is important that they be somewhere and be explained in some way so students can better understand them.
Example problems and references for each standard would be helpful in communicating their content. I wrote about this in my last post. Students generally understood the standards, but wanted specific problems that they were sure related to a particular standard.
Some of the specific content needs to be adjusted. This was my first year being much more deliberate in following the Modeling Physics curriculum. I haven’t, unfortunately, been able to attend a training workshop that would probably help me understand how to implement the curriculum more effectively. The unbalanced force unit was crammed in at the end of the first semester and worked through in a fairly superficial way. Not good, Weinberg.
Standards for non-content related skills need to be worked in to the scheme. I wanted to have some standards for year or semester long skills standards. For example, unit 5 in Geometry included a standard (not listed in my document below) on creating a presenting a multimedia proof. This was to provide students opportunities to learn to create a video in which they clearly communicate the steps and content of a geometric proof. They could create their video, submit it to me, and get feedback to make it better over time. I also would love to include some programming or computational thinking standards as well that students can work on long term. These standards need to be communicated and cultivated over a long period of time. They will otherwise be just like the others in terms of the rush at the end of the semester. I’ll think about these this summer.

You can see my standards in this Google document:
2012-2013 – Learning Standards

I’d love to hear your comments on these standards or on the post – comment away please!

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