Averages vs histograms

With graphics being so easy to add to documents these days, why don’t we show more histograms in place of the typical approach of representing very complicated data with one or two numbers (eg average and standard deviation)? Sure, if your data is normally distributed, then those two numbers really are a great distillation of the data. However, lots of things aren’t normally distributed, and I’m lobbying for more use of histograms instead of (or, I suppose, in conjunction with) the numeric characteristics of the data set.

Here’s the example that got me thinking about this today. At my school student evaluations of instructors are very important. We use a seven-point Likert scale on questions such as “The instructor encourages me to learn actively” and “This course was a valuable learning experience.” Quite often reviews of faculty are peppered with means and occasionally standard deviations of evaluation data for the reviewed faculty member. However, the data is not normally distributed at all! It can be bimodal (some hate me, some love me), or highly skewed in other ways. I’ve been working lately to provide an interface for our evaluations to help people on the tenure and promotion committee make wise recommendations. Instead of having to click through to each course, I’ve made a nice table that shows the average for the class on each question. The table rows are the various courses the faculty member has taught. But while thinking about the notion of showing histograms in addition to averages, I hit upon using PHP to dynamically create SVG’s with the histograms. Here’s what it looks like:

5 courses for an anonymous faculty member. Each column is a different question on our standard evaluation.

5 courses for an anonymous faculty member. Each column is a different question on our standard evaluation.

I feel like you learn a lot by looking at the (tiny) histograms. Take the three “4.44”s that are in the third class. The middle one is much more bimodal than the other two.

What am I lobbying for? I’d love it if many more reports/journal articles/newspaper stories did this kind of thing. The graphics generation and inclusion is really not that hard, and I think it communicates the whole story, not just a distilled version.

One downside is the inability to describe the data very easily. I was showing this to my partner and I was trying to say “this one is different than that one” and I had to point to them. I couldn’t easily describe them. So I resorted to saying “the 4.44 one . . .” etc. I suppose this is backing up my point that the data sets are complex and resist easy description, but I know my colleagues on the tenure and promotion committee like to really discuss these evaluations a lot.

Here’s another interesting point from a friend of mine (who’ll remain anonymous):

Averages and SDs are **NOT** appropriate for categorical data. They assume the “distance” between each category is equal, as if the numerical choices were locations on a spatial scale. They are not. You’ve got two choices: Report number of responses in each bin (as you’re playing with); or turn to Rasch analysis, which is designed for exactly this problem. But it’s not for the faint of heart…

Interesting, huh?

Your thoughts? Here are some starters for you:

  • This is great. I totally agree that representing all of the data is much better than any distillations. I would even go further by suggesting . . .
  • This is dumb. We use the distillations for several very good reasons . . .
  • Why do you use evaluation data at all? They’ve clearly been shown to be problematic.
  • Why a 7-point Likert scale? How about a 2-point Love-ert scale?
  • How did you make those SVG histograms in PHP?
  • PHP?!!? I’m never reading this blog again.
  • Wait, I thought you only knew how to use Mathematica.
Posted in math | Tagged , | 3 Comments

Wave equation first

This semester I kick off my general physics 2 course with waves. I really want the early focus to be on what waves are, and, more specifically, what the wave equation means. The reason I want to do this is because the wave equation is, for me, the biggest hallmark of a system being able to support waves. If you look at a system and find any parameter whose spatial curvature is proportional to its acceleration, you know it can support a wave and you can determine the speed of the wave from the proportionality constant.

When teaching about the speed of a wave on a string, which is often the first example that texts “cover,” I get frustrated with the various approaches to determining the speed of the wave, since often it’s a very contrived situation. Typically it’s considering a situation of moving one end up at a constant speed. That leads to a non-calculus calculation of the speed, but I’ve always thought it felt too contrived. I much prefer convincing the students that the wave equation is what to watch for and to simply look at the proportionality constant.

What I thought I’d do is start by asking my students about examples of waves. I don’t really want to get bogged down in SHM stuff, so really my hope is that we land at something like “disturbances that travel through the medium.” Then I want to see how far we can get talking about why the propagation happens. For a string, that’ll be talking about portions of the string where there’s a curvature (or, really, a change in slope). The idea would be to realize that a portion of the string that’s a constant slope will not have a force pulling the string up (or down) since the (constant) tension will balance out. However, if there’s a change in slope, then there will be a net force up (or down). So, a change in the slope will lead to an acceleration. The wave equation!

To figure out that the proportionality constant is related to the speed of the wave, I really want them to have a sense that any function f(x) simply turns in to f(x-vt). I’ll try to get to that by getting the students to comment on the similarities and differences of the motion of different portions of a string that has a disturbance traveling down (for now without friction). I’ll be hoping for thoughts like “they all do the same thing, only delayed” and “they’re delayed by how long it takes the disturbance to get there.” 

If I can do both of those last paragraphs, then getting that v=\sqrt{T/\mu} should be relatively straightforward.

So what about using this approach with other systems? Sound in air, for example? Well, what causes sound. Again you have to have a change in the pressure distribution or nothing happens. Again you’d have a second order spatial change proportional to an acceleration (of the air particles, say). I think it could work, but it’s not as clear cut as the string example.

Where this approach will come in handy is when we get to Maxwell’s equations and light. You futz with Maxwell’s equations and you end at a proportionality between the second spatial derivative of E (or B) and the second temporal derivative of E (or B) with the permeability and permitivity of free space sitting there as the proportionality constant.

Your thoughts?

  • Why do you put the word “cover” in quotes?
  • I really like the “one end moving up at a constant speed” approach. I like it better than this because . . .
  • I, too, don’t really like the “one end moving up at a constant speed” approach. What I do instead (which is MUCH better than your plan) is . . .
  • I don’t get all this. Just give them the equation and assign some homework.
  • With friction the notion that “everyone does the same thing, only delayed” doesn’t work. How do you deal with that?
  • In multiple dimensions the notion that “everyone does the same thing, only delayed” doesn’t work. How do you deal with that?
  • I like this approach a lot. Please let us know how it goes!
  • With sound in air, here’s a good way to get students to think about a second spatial derivative needed . . .
  • For light, it’s not an acceleration. Will your students be ok with that?
Posted in physics, teaching | Leave a comment

What if they don’t do it?

I’m still refining yesterday’s idea of having one day a week for assessment/review/integration in my General Physics II course. As often happens, I’m narrowing in on an idea/approach that I think could really help students learn, but there’s always the fear that they won’t do what’s necessary to get enough out of it.

An example of that is my traditional flipped class approach from a few years ago. I carefully crafted some screencasts trying to elucidate some of the harder issues in the text and came into class hoping we’d all be ready to hit the ground running. Unfortunately I never seemed to have more than about 1/3 of the class ready. Looking at viewing statistics backed that up, though it was interesting to note that the vids were viewed a ton leading up to any assessments.

So here’s my pie-in-the-sky thoughts about this weekly assessment day. First I would respond to the top 5 few questions from the weekly Google Moderator series. Those would be questions entered throughout the week on the content of the week. That would take 15 minutes. Then we’d do a 15 minute quiz. Then the students would collectively identify the additional resources they’d need to help them understand the material better for future reassessments (note that the whole Google Moderator series would likely help in that conversation).

Why do I call it pie-in-the-sky? Because it really relies on students doing a number of things throughout the week

  • Use class time to explore the landscape of the material and request useful resources that I would provide before the end of that class day’s day (that sounds confusing).
  • Utilize the resources I provide to learn more of the details of the content. This should be heavily interspersed with working as many problems as they can to get ready for the quiz
  • Both submit and vote on questions/issues in the Google Moderator series.
  • Working together in the last 30 minutes of the assessment day to figure out what they need to improve their understanding of the material
  • Commit to doing reassessments (these can be videos, office visits, virtual office visits, etc)

If some or all of those break down, the assessment day is a big waste of time (except the 15 minute quiz, I suppose). I’m very cognizant of that because I’m proposing doing 18 chapters using only 28 days of instruction time.

The hope is that the students will see the value of all of the proposed activities. They’ll see how all class days are really opportunities for them to request specific resources that will help them (worked example problems are surely going to be very popular). They’ll work problems with an eye toward doing well on the quiz (oh, and to learn, I suppose). They’ll use Google Moderator to make sure that class time isn’t “wasted” on less important issues (note: in student evaluations in the past I’ve had students complain that I answered every question and wasted class time working on what were really easy ideas).

One concern of course is that they’ll do everything and ace the quiz, making the second half of the reassessment day a waste of time. I’m not really concerned about that, but I could imagine stronger students thinking that way.

My good friend Bret Benesh commented on my last post about the usefulness of giving students lots of time to understand material. I thought about maybe pushing the quiz on this week’s material off to next week. But, in my experience, that just means the students will push off to that week the work needed to do well on that quiz. That could work, of course, especially if we pushed off the google moderator series too, but I think I want all of that happening in the week when they’re seeing all of this in class.

So, what could I do if the students don’t do what’s best for their learning? Here are some starters for you:

  • I’m in this class and I’m intrigued. What happens if . . .
  • I’m in this class and I’m worried. What about when . . .
  • If the students don’t do the work, it’s their problem. You should plow ahead and . . .
  • If the students don’t do the work, you’ll have to change the approach toward . . .
  • I like Bret’s idea, here’s how you could make that work better . . .
  • They’ll never do any homework problems is you don’t collect them. Here’s an idea that’ll make that work in your Standards-Based Grading system . . .
Posted in sbar, sbg, syllabus creation, teaching | 6 Comments

Assessment Fridays

Long-time readers of my blog know that August and January often feature posts with crazy syllabus brainstorms. This is one of those.

I’m teaching calc-based General Physics 2 this fall (yes, gen phys 2 in the fall, deal with it) for the first time in four years. A ton has changed in my teaching in those four years and I’m trying to figure out what to put into this class. I’m committed to doing Standards-Based Grading, and I think I know how I’ll do my standards list. What I’m thinking about today is how to structure the class days. Last time I taught the course I did a pretty “traditional” flipped class approach. This time I want to do my new back flip approach. Here’s what I’m kicking around so far:

  • Use 2 days per week as content days. That leads to something like 25 standards for the semester
    • We’d start with some sort of exploration
      • Maybe a chapter problem to learn the new vocabulary
      • Maybe a demo where I ask them to make predictions
      • Maybe an online demo where I ask them to predict what various things do
      • Maybe a discussion of their experience with the new topic if that makes sense
      • Some or all of this could be done in small groups
    • Develop a list of the big ideas that will need resources
      • break down a typical problem to figure out the approaches/facts/issues involved
      • Figure out whether we should spend class time/scast time/or book time on these
      • work some simple problems in small groups
        • report (kind of like a board meeting in the Modeling curriculum)
    • Determine the standard of the day
      • “I can . . .” will be the structure
      • this could lead to debate over things like “I can calculate” vs “I can derive” vs “I can explain”
  • Use the third day of the week as a free-for-all review/connect/assess day
    • Use Google Moderator to collect the questions/issues that students have throughout the week
      • GM is great because the students can crowd-source the priorities of these
    • Build groups of students who want to focus on different things
      • Have them determine an assessment
        • student-built problem, oral assessment, something
        • I might possibly have them all do a paper quiz instead or in addition
    • I’m not quite sure what I would do beyond going around and occasionally engaging with different groups
    • I’m also not sure if students will really know where they would need to be

I’m a little nervous that only having 2 hours of new content time per week will be tough, but I love the notion of an assessment day. I’m also really excited about a weekly Google Moderator series happening, because they’ll see the value in up-voting the things that they really need help with.

Your thoughts? Here are some starters for you

  • I’m scheduled to be in this class and I think this is great. Here’s why . . .
  • I’m scheduled to be in this class and I think this sucks. When are you in your office to sign my drop card?
  • A free-for-all assessment day could be a good idea. Here are some ways you can really make it work . . .
  • A free-for-all assessment day is a really dumb idea. Here are some better uses of your (and they students’) time
  • Squeezing the content into two days will help the students keep an eye on the big picture. I think that’s great and here’s how to make it even better . . .
  • Squeezing the content into two days will tell the students that only big ideas matter. They won’t learn problem solving skills
  • How will you handle reassessments?
  • Why do you like bullet points so much?
  • It’s late in August, what have you been doing? [ANSWER: refactoring my home-built LMS]
Posted in sbar, sbg, syllabus creation, teaching | 3 Comments

1 standard per day

I’m often involved in conversations with people about Standards-Based Grading where we focus on how many standards we should have. I’ve settled recently on a “1 standard per day” approach that works for me and I wanted to get my thoughts down about it here.

For me, a standard is an important concept/idea/tool/ability that students should know by the end of the course. I tend to write mine in “I can . . .” statements like “I can derive the Euler-Lagrange equation.” Deciding how many to have in a course is difficult, especially as there are a lot of really good approaches out there:

  • Have a handful: the argument here is that students won’t remember the details years later, so try to decide what the 4-6 or so big ideas are and focus your course around them.
  • Have one per chapter: the book author has already broken up the material into similar size chunks, use it!
  • Have one per class period: This is what I do (lots of discussion lower in the post)
  • Have big and small standards: Have a handful of big ideas that then breakdown into smaller ideas. Josh Gates does this really well
  • Have one for every concept you can think of: this is how I started. Look through the material and write down every concept you would normally assess. This, for me, led to something like 2-3 per class period or ~10 per chapter

My general advice to people is to do what feels right and what you’ll be able to assess well. For me, the 1 per day approach checks those boxes and has a some other benefits as well.

One standard per day works out to ~30 for the whole semester. That’s well under the ~42 or so actual days we have, but I tend to use a bunch of days for oral exams. Probably my favorite thing about this approach is that it really focuses every class period. My students (and I!) know that the day has one major topic and we work to figure out what resources we have, what connections there are with other days/standards, what examples hit all the subtle nuances, etc. I end the day refining the language of the standard, but at the beginning of the semester I put a one or two word phrase on the calendar to let them know what’s coming (like “doppler effect” or “RC circuits”).

I also like the notion that I’m using equal time to help me figure out equal weight, since I tend to treat all the standards equally in the grade book. What’s cool is that I’ve been working my whole career on finding the right balance of how much to cover (uncover?) on each day. In the old days of plain lectures (and homework and tests etc) I really agonized over how much of each chapter to cover each day. I still do that! And often I come to the same conclusions. And, interestingly, I’m often right with the authors of the texts I use as far as how many days per chapter. This work involves looking at the complexity of the concept(s),  looking at the level of math involved, looking at the impact on the “big picture”, and lots of other intangibles. In the end, I feel like I mostly meet my goal of using each day as wisely as possible. That notion, for me, translates to figuring out what my standards should be pretty easily.

When I talk to others about this, some push back that I get is that just because a concept takes a while to learn doesn’t mean that it’s as valuable an idea as something that’s quick to learn. I find this to be a compelling idea, but, at the end of the day, I don’t think I fully agree. If it takes a while to learn AND we decide to teach it, taking the appropriate amount of time, we have decided that it is that important, haven’t we?

So what other push back is there? Here are some starters for you:

  • How do you deal with MWF vs TR classes? It would seem you’d have a lot more of the former.
  • Even 30 is way too many! Here’s why . . .
  • 30 is way too few! Here’s why . . .
  • How do you deal with labs? Here’s what I think you should do . . .
  • It takes you 40 days to teach them where Wolfram|Alpha is? That’s weird.
  • I’m a student in your upcoming class and I think this is great! What I’m especially excited about is . . .
  • I’m a student in your upcoming class and this makes me nervous. Here’s why . . .
Posted in sbar, sbg, syllabus creation, teaching | 7 Comments

doodle notes

A while ago I saw a news report about these guys. They specialize on providing note takers for big events (usually speakers). The note takers try to produce an extended doodle that captures the essence of what’s spoken. I thought it was pretty cool, I remember someone in the report talking about how, for him, it really helped him internalize and synthesize information from presentations. He concentrated on finding images that connected to the material and found some non-linear ways to represent all(?) the information.

This weekend I’ve been at a conference all about upper-division physics curriculum, and in the last session I thought I’d give this technique a try. I did it for a couple different presentations, but I purposely chose to do it for Melissa Dancy’s on the research about why PER ideas are slow to disseminate. I wanted to do it for her because I was sitting next to her and I wanted to show her what I created. She got a kick out of it, and I thought I’d post here both what I did and what I thought about the process.

Here’s the link to the pdf that my Surface Pro produced via OneNote.

I have to say that it was really fun to do it. I used a bunch of stick figures and some drawings along with the occasional keywords. What I really liked is how I 1) concentrated like crazy, but 2) didn’t feel stressed or exhausted doing it. I really liked how I had to come up with a cool/funny/informative/whatever way to represent something, often trying to connect the new idea to the existing doodle. Of course, OneNote and its infinite page size and ease of changing pen colors really helped, along with my super cool Surface Pro (I promise I’ll stop promoting that one of these days).

There were some times when I felt like just writing out a sentence would have worked just as well (or better) but I wanted to really give the doodling a chance.

Having tried it, I think I might try it some more about meetings etc. We’ll see, but I’m pretty excited about how it got my brain to engage in a different way. I’m really curious if any of you think this might be good to encourage students to do it.

Side note about technology: I had my Surface out for nearly the whole conference, mostly taking notes in OneNote in full-screen mode, but admittedly occasionally checking email etc. What was interesting is that I think I appeared more engaged with the conference than I would have been using the keyboard (as opposed to the stylus). My screen was flat to the table, not blocking anyone’s view of my pretty face. I only used one hand to take notes, though I’m not sure if that’s meaningful. It’s interesting how many people have talked to me about the recent study showing how laptop note-taking seems not to really help people. I felt that my Surface enabled me to take digital (and thus easily saved, searched, not lost etc) notes in a format that is incredibly flexible (handwriting/doodling) while maintaining the ability to do other things too (yes, I’m talking about checking email :)

So what do you think? Here’s some starters for you:

  1. This is cool! Could you come to a meeting with me on …
  2. This is dumb. Melissa (or whomever) can just post her slides and you could fully engage without writing anything.
  3. This is cool. Here’s how I do something similar . . .
  4. This is dumb. I can’t figure out anything from those notes. I bet you won’t be able to either after a few days.
  5. This is cool. What would it be like to lecture like this?
  6. This is dumb. I don’t know how to draw.
  7. Wait, you didn’t mention how Mathematica played a part.
  8. I’m Melissa and I think this was really cool because . . .
  9. I’m Melissa and I’m mortified that this post exists because . . .
  10. You’re using technology, so the study about laptop notetaking applies directly to you.
Posted in teaching, technology | 10 Comments

Breadth vs depth

This tweet really got me thinking recently:

In the Global Physics Department we talk about this quite often, though we usually focus on students who will continue with physics or at least science. For that audience, we seem to always come to the conclusion that depth is better than breadth. For me it comes down to noticing how strong students can be in college if they’ve done a deep project in high school. That’s true even when that project restricted their depth a little. It seems that when they’re presented with something in college that their classmates have seen before but they haven’t, they seem to take it in stride quite well.

Casey asked later in the twitter conversation about non-majors, though, and I’ve been thinking about that too. Again I think I land on depth. I want students not to just know the results of science, but to understand how we got those results. If a student studies something, anything, deeply, they’re likely to really understand the scientific process. They’ll stumble, they’ll grope, they’ll make leaps, they’ll see connections, and they’ll see how our crisp, clean textbook results are really dirty, messy, and hard.

One of the physics teachers at the school my kids will go to has come to the Global Physics Department a bunch. He’s heard us have these conversations and he’s decided to try to find more ways to give students opportunities to do these messy, deep projects. I’m not sure if they necessarily take away from the breadth he covers, but I don’t care. I’m happy they’re doing science, not just taking it. (By the way, his name is Peter Bohacek and he just won a very cool award.)

Two things seem to creep up in conversations like these. The first is those dumb Harvard students on graduation day who don’t know what causes the seasons.

My friend Brian Frank has taught me that you can use those misconceptions to really talk about science and to learn about other possible explanations. Here’s my point: I don’t care if people know what causes the seasons (heresy, I know). What I care about is whether they can talk about it and think about it and brainstorm about it. Can they think about what evidence they have, seek out other evidence (not just do a google search for “the answer”), and/or ask good questions? It would seem that doing a deep project would prepare them well for that.

The second issue that creeps up is the AP physics curriculum and exam. I will certainly stipulate that you need breadth to do well on those exams. But I don’t care. Yay, you got a 5 and can skip a course in college. Skip an opportunity to build relationships with physics faculty and students. Skip a chance to see material in a different way, with different questions, with different labs. Great. Good for you. And to do it you had to go at a breakneck pace in high school to see all the physics “facts” that are available. No, I say. I say do a cool project. Look into how a slapshot really works. Wonder whether Godzilla can iceskate. Twirl some beads.

I know some of this won’t sit well with some. And that’s ok. I wanted to get my thoughts down so that a conversation could continue. Here’s some starter comments for you:

  1. I agree. We should just not teach science at all. Instead we should . . .
  2. I disagree. Students need to be facile with all kinds of things. Here are some examples . . .
  3. I agree. AP is overrated and also . . .
  4. I disagree. AP is the single greatest thing since sliced bread and here’s why . . .
  5. I agree. Just teach them Mathematica
  6. I disagree. If we just do AP physics in 9th grade, they’ll be set up AP chem and then AP bio after that.
Posted in glodal physics department, teaching, twitter | 14 Comments