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.

About Andy Rundquist

Professor of physics at Hamline University in St. Paul, MN
This entry was posted in glodal physics department, teaching, twitter. Bookmark the permalink.

14 Responses to Breadth vs depth

  1. bretbenesh says:

    Because I am completely self-centered, I am going to take your blog post, hijack it, and use it as an opportunity to talk about myself.

    I am going to turn the question into “what I want from high school mathematics.” The answer I would tell people is very similar to what you would say: depth is better than breadth, and I want them to really understand the mathematics that they see.

    But I also really want them to have basic algebra skills. I want them to be able to do very basic factoring (i.e. I want them to understand the distributive law really, really well), I want them to know the basic graphs of functions, and I want them to have a solid understanding of slope.

    I don’t think that these two ideas are mutually exclusive. In fact, I like to them that they support each other, and it may not be possible to have one without the other.

    But if I had to just choose one—and I feel bad saying this—I think that I might choose the algebra skills. I feel bad about this.

    I hope that I feel this way because the traditional K-12 curriculum does not emphasize understanding, and so I have not yet come to expect this as a reality (“If they are not going to have a deep understanding, they may as well have good algebra skills.”).

    Is there any sort of analogous thing in physics? Do college physics professors complain about students not being able to do algebra or perform basic lab routines?

    • Andy "SuperFly" Rundquist says:

      Interestingly, math/algebra would go on my list of things I really need students to “know” coming into my physics classes. As for physics knowledge, I’m not sure. Some would say “Newton’s laws!” but I’m not convinced. If someone did what I suggest above (a deep project or 2 in high school) I’m not too nervous about them moving on.

      On Fri, May 16, 2014 at 9:50 AM, SuperFly Physics wrote:


  2. I teach both math and physics, and I will add that there is a lot of flexibility in HS physics because of no emphasis whatsoever on high stakes testing (although AP classes artificially add high stakes back in), while with math there is tremendous pressure from all levels to go with breadth rather than depth. There are ways to work within that system, but with far less flexibility than with physics. This makes it hard for math teachers to break out of the box of algorithmic memorization; the system, whatever that means, emphasizes it.

  3. wwndtd says:

    I teach chemistry, and wrestle with this depth-vs-breadth question a lot. I feel like in order to call my course “chemistry,” I’m supposed to cover a particular list of topics, such as balancing equations, sig figs, moles, and reactions. But most of this is mechanical stuff, and not super useful (or deep) until put into context. My students had a fantastic day yesterday, where they (mostly on their own) put all of these skills to use, and the next class is also being led by their curiosity.

    It’s pretty clear to me which type of skills they’re valuing more, enjoying more, and prefer (definitely depth). But they also need to know the mechanical stuff (mostly breadth) to do what they’re doing.

    If I’d structured the course in a different way (and with our school structure, it’s not very feasible), I’d love to do more of a modelling approach so that they could determine the types of skills they need first, then go and try it out.

    • Andy "SuperFly" Rundquist says:

      cool post! I’m now really curious what else is in that barn. I guess I’m willing to continue to have the conversation about what it looks like to scrap the mechanical except where its needed to go deep in a particular area. Some of that makes me nervous, but I at least want to have the conversation.

      On Fri, May 16, 2014 at 12:19 PM, SuperFly Physics wrote:


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  5. I teach high school Physics and Math. I have gone more towards the maker side….make a hovercraft & mousetrap car and explore ideas of 1D motion, build a trebuchet (though we have not gotten good at analyzing that), set up circuits & lets measure and have discussions….There are so many topics we could never hit all of them….and we dont get to some I love because it takes so long to build stuff (OMG building a 4 foot tall trebuchet like 6 weeks in class), so they will always encounter “new topics” – now what will they do when they hit something new. I think the State curriculum (which I do glance at) has too many topics and too much emphasis on motion.

    I was asked once if we should do AP Physics and I quickly said no. I dont like the pace and amount of memorization that it dictates. And as you say, all for skipping a class in college and building relationships with Ss & Ts. I dont think AP is right. Cant we just have good solid courses in high school and leave college to college.

    Let’s quit learning science and start doing science.

  6. Peter Bohacek says:

    Thought provoking post, Andy. This question still keeps me up at night. We were able to do messy projects because eight of the top students from my AP calc-based mechanics class asked if they could double-up and work on AP E&M second semester. After the GPD meeting, I suggested the projects instead. During their semester of independent study (for which I volunteered my time — the school can’t pay a teacher for a class with 8 students), we put in more time on these projects than in the AP class they were in. Plus, all the projects were extensions of topics we’d already worked on in class, so they had a base of knowledge on which to build. We were also able to take advantage of some pretty unusual equipment (high speed video) I’m lucky to have access to. All the students were able to generate novel, interesting, achievable project questions, and make excellent progress.

    So, for students who have already had a rigorous introduction to physics and math, who are motivated and already successful, and who have a teacher who has time to guide them, yes, projects seemed to be a better choice than a second AP test.

    But what about for the rest of the students? Could we have done projects like these with five classes of 30+ students who’ve never taken physics before? And then, they’d never see magnetism? Sound? Like I said, it keeps me up at night.

    Interestingly, the College Board seems to agree that depth is king. The new AP1 course has far less breadth than the AP B course it replaces.

    • marcreif says:

      Hi, Andy. Nice blog post and an interesting topic.

      I am in agreement with Peter (and a big admirer of the Direct Measurement Videos – I never miss a chance to tell other physics teachers about them).

      Projects are great where you’ve got people like Peter Bohacek to lead them – but that is by far not most of the country. The College Board’s AP Physics B curriculum, whatever you think of it, has raised standards all over the country, even in unlikely places like rural Arkansas (I teach in Arkansas).

      And, I would argue that the new curriculum intends to go deeper than many college professors go. I am sitting in DFW on my way back from leading a workshop on AP Physics 1 with a group of experienced physics teachers, and they were deeply (pun intended) impressed with the new curriculum. One person, who has been teaching some 30-plus years, left saying: “I was thinking I was going to retire, but I’m going to stick around for a few more years to teach these new classes (AP Physics 1 and AP Physics 2)”.

      You can download a description of the new courses here:

      Take a good look at the sample exam questions and see if you don’t think it’s deep enough. I see no questions that I would can be answered with memorization alone.

      Marc Reif

      • Andy "SuperFly" Rundquist says:

        Thanks for the comment Marc! I’ve been pretty impressed with the AP changes too. I guess the question for me is what should an educated citizen know about physics. AP is supposed to be all about placement in college, though, in practice, it’s all about getting credits in college. That seems to be answering a different question. For my question, if people knew the AP curriculum, I’d be ecstatic! But I’m not sure that’s the goal I really have.

        On Sat, May 17, 2014 at 7:13 AM, SuperFly Physics wrote:


  7. Great discussion. I’ve done a lot to embrace the idea of creating genuine experiences for students to actually do something on their own and see where it leads them. A friend of mine shared his lab program with me when I was doing my observations for my graduate program, and I’ve been using it ever since I started teaching HS physics.

    The students work in small groups on a topic of their choice on an extended lab cycle that lasts for six 38-minute periods. The first period is dedicated to choosing topics (I provide a list that parallels class topics, but students can come up with their own, each group in a lab does a different experiment). The next three periods are spent working on the experiment. The 5th period is used to put together short presentations- used to be on handheld whiteboards, but in the interest of time we’ve shifted to an electronic format (SMART Notebook files saved on a common server). The students also use this time to print out their graphs and data tables for their reports, which are until they’ve mastered them and then they get the privilege of switching to informal handwritten reports (this can be taken away if they don’t perform). The final day is for presentations.

    An alum stopped by to see me last week. He said that his college physics course was super boring: “they not only told us what topic we had to investigate, but they gave us step-by-step instructions for what we were supposed to do! Where’s the fun in that?” he complained. I guess I’ve gotten so used to the way I run things that sometime I forget there is a different way.

    It’s successful to a large degree. Most of the groups jump in headfirst, but there are always a few who want their hands to be held the entire time and choose topics based on what will be easiest or which will produce the cleanest and most reliable data. some of the richest conversations we have are about what the data means and how it can be interpreted. They get past the idea of data showing a trendline equaling a “successful” experiment- much of their work produces messy or complex data.

    Recent topics include: using Genecons as arms to make a lego platform walk across the floor, impulse delivered by rocket balloons, strength of sand castles, Hulk-style t-shirt strength based on % cotton, gummi bear wave machine, etc. If anyone is interested I’d be happy to share my list. Many are of my own invention, but some come from TPT or other sources. Downside is a loss of time and coverage of traditional experiments, but I’d gladly take a student who can think on their own two feet over one who has memorized the steps of rote labs.

    By the way, not all states give physics a pass on high stakes testing. NY teachers’ evaluations partially depend on their students’ performance on the end of the year exam called the Regents. So we have some high stakes action coming into play.

    I teach AP C mechanics as a second-year course. I like it because it gives me a level that I know the students need to master. Toying with the idea of a bridge course for next year with a local college. I don’t really see it as getting them ahead- even my best students tend to take physics 1 over again in college, but it makes the first semester more reasonable than it might be otherwise. And for non-physics majors they can get a science credit and spend more time on things that interest them. Just my $0.02.

    • Andy "SuperFly" Rundquist says:

      I’m curious, how do your students do in AP C if their prep before that is more deep but narrow? Very cool list of projects, by the way!

      On Mon, May 19, 2014 at 8:08 PM, SuperFly Physics wrote:


      • Thanks! The students typically do ok on the AP mechanics test. We have a small pool and not everyone is concurrently enrolled in calculus, which is more of an obstacle than their previous coursework in physics. During their first course (Regents level) we spend a lot of time on mechanics and then cover electricity, waves, and modern for the state test. A majority usually pass the AP test, but we don’t have time in our year to be able to cover E&M too so they only take mechanics.

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