Archive for the ‘mindset’ Category
I’ve seen research cited that suggests demonstrations are not always effective because students often remember what they think they are going to see, rather than what they actually see. That is, prior conceptions can overwhelm actual observation. Thus, it is better to have students actually touch the apparatus, take the data and “see for themselves.” That’s what I do by using Modeling Instruction in Physics. But just taking the data isn’t enough, as was demonstrated today in my class.
My class had produced system schema and free body diagrams for a series of situations involving two carts in contact. These situations included constant and non-constant velocity, equal mass carts and unequal mass carts and even a collision between carts of unequal mass. While the students tried to puzzle out the FBD’s together, great questions about the relative magnitudes of the forces on the two carts come up. We then moved into the lab where the students were set up force sensors mounted on carts so they can try out each of the situations for which they’ve been drawing FBD’s. After data was taken, we went back to the classroom and each lab group whiteboarded one of the situations and explained what they found regarding the force that each cart exerts on the other cart.
The first group that reported on a non-constant velocity situation reported that the force that cart A exerted on cart B was, in fact, larger than the force that cart B exerted on cart A. The class sat silent while this sunk in. I asked if everyone’s observations coincided with this group’s observations. Total silence. After a bit of prodding to take a stand, they all admitted that they had measured the two forces to be equal. At that point, the group presenting admitted that their own data showed equal magnitude forces, but they just thought they should be unequal, and “kinda remembered” that they were unequal.
This led to a great discussion about our ability to fool ourselves, and how science can be thought of a set of behaviors designed to avoid fooling ourselves. The important point, I think, is that only by allowing students to present and defend their results (making mistakes and owning up to the mistakes in the process) does such an opportunity come up. Today’s class felt like a huge win, and I sincerely hope my other section of Honors Physics makes some kind of mistake just this good tomorrow.
A recent thread in the Modeling listserv sought to tease out whether there are any innate differences in us that lead to more efficient learning in physics. In making the argument for some kind of “natural ability,” many of my colleagues use world-class performers as their examples. This kind of reasoning is, I believe, misleading to the application of the ideas of whether talent is in-born or grown. Yes, it is true that no amount of hard work is going to turn a 5’4″, 130 lbs. adult into an NFL lineman. And there are definitely certain physical characteristics that Michael Phelps possesses that help him in the pool (perhaps it is because I’m a swimming coach that others bring up Michael Phelps to me). It is equally true that Ryan Lochte possesses a different set of physical characteristics, but he manages to beat Michael Phelps on a regular basis.
But to take the conversation right to world-class, or even lower level championship-class, performances confuses the issue of whether there are substantial differences between students’ abilities to understand physics. I am not teaching high school physics only to create world-class physicists. If I were, I might want to work at a school that doesn’t demand so much of the students in the way of extensive writing or playing of afternoon sports. And I might want to prepare to be disillusioned a lot of the time. I am more interested in giving students who want to excel in science the foundation to do so, and to introduce students bound for careers as artists, lawyers or historians the skills to think rationally and scientifically. Can every one of my students achieve these lofty goals? I think so. The question comes down to whether they have the time to spend on becoming strong at physics.
The problem with citing world-class performances is that world-class performances are the result of many diverse factors. Some would argue that at least a few of these factors are innate, and we could have a good old time debating to what extent quickness, agility, reaction time, strength and a host of other factors are innate or developed. Likewise, we could debate the extent to which some kind of innate “smarts” are responsible for the work of Richard Feynman and Albert Einstein (both of whom famously denied any such advantage, citing the power of hard work). In the end, such debates have little to nothing to do with my students and me. I just don’t see enough difference in my students’ abilities to attribute it to anything other than differences in their backgrounds. Even if I’m wrong, I’m not too far wrong, and they can certainly get better at whatever they put their minds to improving.
One response to my warning the listserv conversation away from discussing world-class performances was to say that world-class performers make good examples for our students and athletes. They sure do–I would not deny that. We have our swimmers watch Michael Phelps’ butterfly stroke. We encourage our students to read about famous physicists. We bring outstanding scientists and historians and artists to our campus to talk to and meet our students. My uneasiness with discussing talent in terms of only the very best in each field does not mean I don’t want to study and learn from the best in each field.
I was recently asked by a student what kind of fun (but serious) science-y play he could do over the summer. He is bored, stuck at home, his summer camp experience having been unexpectedly canceled. This is a student who repeatedly did that little bit extra in physics class all year (he even completed the first two chapters of “SpaceTime Physics” by Taylor and Wheeler) . He is signed up for second year (calculus-based) physics next year. Thus he is going to be learning VPython over the summer anyway. And he will be doing video analysis as part of his physics class next year. So take a look at what I suggested to him, and let me know if there is more that I could suggest.
- Read The Talent Code by Daniel Coyle (ok, I tell everyone this).
- Get your parents to use that cash they saved on summer camp to buy a student license for Mathematica and start playing with it (I know his parents can afford this and I know that he already has the math chops and curiosity to make it worthwhile).
- Get started early on VPython and then dig a little deeper into lists, loops and conditional statements in Python.
- Go to ProjectEuler.net and use Mathematica and/or Python to solve some problems.
- Buy an Arduino starter kit and start making your computer control something.
- Download Tracker and make it work with the sample files.
- Try to create a document using LaTeX.
There has been some internet-based discussion recently amongst math and science teachers about the usefulness of Khan Academy videos in particular, and lecture videos in general. Derek Muller at Veritasium.com has created a short video about his research findings into the efficacy of using videos to teach introductory physics concepts. If you watch that quick video, you’ll get a snapshot of one thread of the recent discussion. The upshot of Derek’s argument is that videos which contain student misconceptions and show real people working with and through their misconceptions lead to more successful learning by the observer of the video than does a straightforward exposition of the proper concept.
A recent blog post by John Burk at quantumprogress discusses the idea of using video examples of problem solutions that include common student mistakes and/or misconceptions. The idea is for the students to identify the mistakes made, thereby potentially learning more than if they simply ceded control to the expert on the screen solving the problem. We’ve all seen the effect of students watching an expert solve a problem for them. The students watch the solution unfold before them, usually failing to notice the subtle (albeit clearly presented) steps that cite fundamental principles and call out the broad models or chunks of knowledge that lead the expert to appropriately set up the problem (they just see the problem set itself up). Then they are bewildered at the prospect of starting a problem themselves.
In the comments to John’s blog post, there are some fantastic observations. One is from Jim Doherty who mentions the possibility of giving a correct and incorrect solution to the problem, having the students select the correct one and explain the mistake in the incorrect one. He also mentions a device used by a colleague, whereby a troubled student (“Careless Carl”) appears in problems, making common mistakes. Joss Ives wonders in the comments whether such devices might lead to student frustration on a level that leads them to give up. I’d like to address 1) how I use Careless Carl and 2) how I avoid the “oh crap, I just agreed with this idiot, which means I’m an idiot, too, so I quit” syndrome.
Careless Carl makes appearances in my class all the time, as John Burk knows. He went by the name Bobo (what a clown) when John and I taught together, but now Kelly O’Shea has given him the name Throckmorton (apologies to the Throckmortons of Fort Worth/Dallas, Texas). Throcky (who is your cousin) is a bit more advanced than Bobo… what he says is often ALMOST correct, containing lots of good reasoning with some crucial boneheaded blunder buried deep inside. Sometimes students reluctantly agree with Throcky, dropping their head, wincing, knowing that they are in less than stellar company. But they generally don’t “throw their hands up in the air in defeat,” as Joss worries.
Here’s why: My students have a very strong conception of their scientific self as something that is fluid and ever-changing. They have this conception because we talk about it! Not for long periods of time, but it comes up at least once a week. They have heard again and again that what they know to be true about the world now will, undoubtedly, change as they become wiser, more skilled, more observant and more careful. In this way, they are just like established, expert, working scientists. Scientists expect their view of the world to change and evolve as they understand more about it.
Many of my students, when faced with their own mistake, will say something like “Ok, that was my eighth grade science self. Let’s see what’s wrong.” In fact, “eighth grade self” has become a very popular phrase this year (although last year my students preferred to blame Aristotle, rightly or wrongly, for everything). This just happened yesterday, in the same way, in both of my Honors classes. We are about three days into studying the central force particle model (uniform circular motion). In each class, someone spoke up asking “Wait… if the speed is constant, how is there a net force on the object?” I asked what principle or model the student was applying and in both cases the answer was something like “My gut.” They know by now that their gut is not any better at physics than Throcky. The class then puzzled out the answer. About half knew right away what the mistake was, but, because they are extraordinarily kind and gentle, didn’t say anything until the answer emerged naturally from those having what they called an “eighth grade moment.” It was beautiful, mainly because the students expect this to happen.
I’m not saying none of my students get frustrated. I had a minor meltdown (including tears) to deal with after dinner two nights ago. But the student was much better when he realized that, even though he hadn’t truly learned how to use vectors to do momentum problems yet (even after three months), he had learned something very valuable about what kind of practice doesn’t work. And his assumption is that tomorrow he will understand more about momentum and vectors than he does today.
If there is one thing middle school teachers could instill in students that would help them the most in high school, it is the idea that their own conceptions of the world are bound to change. They should seek out the opportunities to change these conceptions and celebrate the replacement of old concepts with new. I have seen this trait in some students (locally, the Newark Center for Creative Learning teaches this habit fantastically), so I know it is possible to do. This makes students much happier and eager learners.
I have been trying to figure out the ways my colleague, Kelly, and I get our students to engage in deep practice (Daniel Coyle’s term) or deliberate practice (Geoff Colvin’s term) in the classroom and on their own when studying physics. This article by Stephen Chew nicely outlines the problems incoming college students have with mindset and study skills, arguing that they often lack the knowledge of what serious study looks like or feels like. While the work I’m trying to do with my students should definitely prepare them for studying in college, my more proximal concern is getting them to learn physics. I’m admittedly making an assumption that getting them to study in a more serious, deep and productive way in order to learn physics should serve them well in college, too.
Colvin’s book (Talent is Overrated) outlines some of the hallmarks of deep practice.
It is an activity designed specifically to improve performance, often with a teacher’s help; it can be repeated a lot; feedback on results is continuously available; it’s highly demanding mentally, whether the activity is purely intellectual, such as chess or business-related activities, or heavily physical, such as sports; and it isn’t much fun.
So what is it we actually do, as teachers, to improve performance?
Kelly and I do a lot of small group problem-solving sessions using whiteboards. Essentially the students do in the classroom what they used to do for homework. The reason I want them to use class time as practice time is that I can see exactly what is going on. In-class problem-solving also allows “continuously available feedback.” I started using class time as practice time after taking a course in Modeling Instruction, but my misgivings about homework started much earlier after deliberately watching students do homework (I work at a boarding school, so I am privileged to be able to witness this… in exchange for working a 15 hour day).
We have students present their work verbally. Talking one’s way through a thought process is fantastic practice. I need my students to do even more of this.
We let students, after plenty of scaffolding early in the year, design their experiments in the laboratory. Early in the year we give them a structure for designing an experiment (roughly: make and record initial observations, use that list of observations to decide what you can measure and how to measure it, pare that list down to what might be related and/or interesting to the phenomenon at hand, then decide what variables to hold constant, which to vary, and what you are going to plot), and we step through this structure, little by little handing off elements to the kids until they can design their own experiment with only a bit of coaching.
But what do we have students do that is “specifically designed to improve performance” when they aren’t with us. I don’t want to create students who depend on me being present in order to do physics. This makes me worried. How do I come up with something new, and does it really work? What evidence do I have? Is it working, but not yet? Does it seem to work, but then not lead to deep understanding that sticks? These are questions that bother me, leading me to stall while planning classes, my perfectionism becoming my procrastination tool of choice again, just like in college. Ok, I’m better than I was in college, but still… I don’t have good answers to these questions.
One hallmark of repetitious skills building is that the performance being worked on is altered in some way, and this is a possible solution to the problem of deliberate, solitary study. Problems are given with partial information, wind sprints are run uphill (even though the lacrosse field is flat), swimmers sprint tethered either to impeded them (the power rack) or to assist them (speed assist training), students create problems rather than just solve problems given them. The trouble is, I feel I can come up with many more ways we focus on performance in swimming (next post, I swear) than we do in the physics classroom. Maybe it isn’t true, but it’s a nagging concern. I’d love ideas about how others see themselves helping students toward deliberate practice.
At my school, all students are required to be in an afternoon activity every afternoon for the entire year. Most afternoon activities are sports-related: either participating on a team, helping manage a team, or doing an independent sports workout (crew winter workout, training for a marathon, etc. usually reserved for upperclassmen). Theatre, organic gardening, mock trial, and non-athletic individual projects (usually only seniors) are other options. So why do we demand that most students spend 1.5 to 2 hours each and every day on a sport?
Typical answers include: teaching teamwork, teaching students to be part of something bigger than themselves, teaching character, teaching lifelong fitness skills… you probably know a couple more reasons. All of these are good reasons, and I won’t knock them. Sports are also fun!
But I think that the most important lesson I learned from swimming as a youngster was that I could become good… actually pretty darn good… at something if I really worked hard at it.
How I learned that hard work makes a difference
I was not a “naturally talented swimmer.” As a pre-teen, I was roughly spherical (perhaps foreshadowing my own predilection for creating simplified physical models). I also had terrible eyesight. My myopia was severe and ever-changing. Within a month of getting new glasses, baseballs again appeared as fuzzy white things with totally unpredictable paths. During neighborhood football games (“hey! I can see THAT ball!”), I always heard “Hammond, you hike the ball and go long.” I went long… totally, but futilely, open in the endzone… beyond the endzone, risking my life by crossing the drive into LeBaron Caruther’s front yard (not that LeBaron was a bully… he wasn’t… but Google him and see what he was really good at, and then realize that in high school he used his parent’s front yard for LOTS of deliberate practice).
In the pool, my poor eyesight didn’t bother me. I was also rather floaty at that age (being roughly spherical and all). Yet I was slow. Very slow. There were two boys I swam with who looked, at age 10, like miniature men… washboard abs, bulging arms and thighs… and they were both ranked in the top ten nationally in our age group. They were so-called natural swimmers. Everyone agreed that they had talent. Me, not so much. But I was a good egg, a hard worker, and several wonderful coaches encouraged me anyway. Within a year, in summer league competition, I could beat those neighborhood kids who wouldn’t throw the football my way. Within two years, I was working out with my naturally talented, svelte and muscled acquaintances, and giving them some tough workout competition. In fact, I was a maniac during workouts. I remember Bobbie L., a year my senior and a state record holder, looking back at me in puzzlement asking “how the ___ are you keeping up with me?” Still, in competition, these boys could easily defeat me. It was only after four years that I could compete reasonably with them at championship meets. The vibe was ever positive and I thrived.
What I learned from swimming
My swimming experience had given me a valuable advantage: I was in possession of a growth mindset… at least some of the time. Unfortunately this mindset did not extend to academics until I was in college (frankly it didn’t occur to me until that point that I could transfer my knowledge from the pool to the desk… just ask my high school Latin teacher). As my swimming buddies and I became high schoolers, I started to surpass them… not always, but often enough. They were no longer nationally ranked. They were, as I knew from daily contact in the pool, not working as hard as I was. And their talent, whatever that was, was not enough to see them through to a NCAA Division I experience. I suspect that they felt their talent had been exhausted at some point around 14 years old. They weren’t as good as they had been told. If you’ve reached your potential, why kill yourself trying to improve any further?
Pretty soon in college, I decided the time I was putting into swimming was probably better spent elsewhere (and eventually I settled on intellectual pursuits after a short detour, but we’ll just pretend that didn’t happen). I still swam, but not passionately, and not with the same commitment as before, partly due to a series of injuries, but mostly due to burgeoning intellectual curiosity. But the lessons learned from swimming… that hard work pays off, that you don’t have to be good at something right away, that improvement feels good… stuck with me. These are the lessons that I seek to convey to the athletes with whose education I am charged. The fact that many of our students play three different sports, often being fairly good already at one or two and stinking it up in the other, gives them ample opportunity to see growth and change in their performances.
Nevertheless, I find it strange that it didn’t occur to me that, although my friends’ talent didn’t carry the day, perhaps the whole idea of talent was flawed.
Later on, I’ll write about what I learned about deep practice (deliberate practice) from swimming. Interestingly, my own swimming career involved very little deep practice, but I saw it, it puzzled me and only years later did I figure out what I had been looking at. Later, though.
I was visiting Carnegie Mellon University yesterday with my son, a high school junior. I grabbed a piece of paper titled “Science” from the wall of information in the Admissions Office as he signed in. On the back, there was a series of questions followed by answers. One question was “Can I create a degree that combines science and the fine arts?” This was followed by an answer beginning, “Carnegie Mellon recognizes that there are students who are naturally gifted in both fine arts and the sciences.” My current understanding is that studies designed to find evidence of “natural giftedness” have come up empty-handed.
Absolutely nothing else on that double-sided information sheet indicated that the view that some are just “gifted” is widely accepted at Carnegie Mellon. In fact, the words and phrases “work,” “doing what it takes,” and “providing you with the skills, knowledge and training” occur. Perhaps it is only biologists that paint or physicists who play the violin who are considered by Carnegie Mellon to be “naturally gifted,” but I think instead that a typical mistake was being made. Even people who are trying very hard to readjust their mindset to de-emphasize the assumption of the primacy of innate “talent” make occasional references to innate talent. I have been talking to colleagues about the lack of evidence for inborn talent recently. I have read Carol Dweck’s “Mindset” and am working on “Talent is Overrated” by Geoff Colvin. The messages of these very different books resonates with something I think I learned in the swimming pool as a youth. I’ll write about that later, but what I want to say here is that even my colleagues who believe that hard work is the most important determinant to success still sometimes slip up and use the language of innate, inborn talent (I include myself in that group as well!). The assumption that certain skill sets are hardwired into us at birth is so prevalent in our culture that it is very hard to keep it from popping into your conversations.
This is not a matter of policing our speech for political correctness. It is not that I want to avoid writing student comments that praise a student as “bright,” “talented,” or “smart” for fear of offending the student not labelled so. No, it is nothing like that. Instead, I fear for the student so labelled. First because it ignores the hard work the student has done previously, and, second, it sets them up for failure as soon as they hit a concept with which they must struggle for awhile. The assumption of innate talent also denies the possibility that other students starting out behind the frontrunners can catch up. Finally, such language simply doesn’t appear to be supported by evidence.
Even students who have worked hard sometimes still attribute their success to innate talent. I have one student, who told me she was “just good at Spanish.” Upon questioning her about her background in Spanish, she told me that she had a very rigorous middle school Spanish class. She had worked “very hard.” In fact, she said she worked harder on Spanish than “any other subject in middle school.” Then she noted that only now, a year and a half after arriving at high school, was she finally learning anything new in Spanish. Then I asked her whether it was any surprise, after she had worked very hard for three years and then had spent the last year and a half in relaxed review of Spanish, that she only now felt like her peers were catching up to her in Spanish? She gave me a very far-away look and a long “huuuhh.” This girl had essentially ignored her own hard work (and the pleasant circumstance of having a year and a half review), because society has told her repeatedly that stuff like this just happens… at some point you just find out what you’re good at. The fact that in seventh and eighth grade she was labelled “gifted” in Spanish may, in fact, have led her to deny the reality or the importance of her own hard work.