Sunday, August 7, 2011

Beginning in Baltimore

I first became interested in teaching while working for the Ameri-corps affiliated program called "Teach Baltimore", which I have learned has now grown to become the National Summer Learning Association. In the program, I had to organize the daily learning activities of a class of Kindergarteners for about ten weeks. We did mostly early childhood literacy in the mornings, and a combination of math, science, and foreign language, music, and art in the afternoon. I did this for two summers, and volunteered others hours in the main office. During both summers, I taught in a school in West Baltimore called Steuart Hill Elementary.

As to be expected in most of West Baltimore, nearly 100% of the children live below the poverty line; and most children live with either an aunt or uncle or grandparent. Many of the children I knew had parents who were either dead, in jail, or living on the streets due to drugs or prostitution. Most of the children I taught witnessed constant violence in their neighborhoods and often times in their homes. Some had already been witnesses to murder by the age of six, and had school mates that had been mistakenly shot down. I got fairly accustomed to walking through drug deals to take children home after school–we weren't supposed to walk them home, but sending them to children services was not a good option. It is true that I always felt safer holding the hand of child, than I did walking back to the school alone. As a side note, the organization of gangs to control corners and evade police observation is really interesting to watch.

Kindergaten in West Baltimore was very different than other schools I had experienced. Where I grew up, most children knew how to read before coming to Kindergarten. In West Baltimore, most children I taught didn't not know all the letters of the alphabet after Kindergaten. Still, children were learning all the time. Every child knew every lyric to every popular rap song.

Brandon and Brandee were twins in my class the first summer I taught. Brandee would bring the teachers flowers almost every morning, which she would pick from alleys on her way to school. Brandon was strong, both physically and mentally. I remember how we always wore the same blue jersey shirt and shorts. They usually came to the school early, before it actually began. I was there at 6:00 am every morning to open the school for food deliveries. We weren't supposed to let them in until 7:30 am, but I would let them in so they could read and have breakfast. Over a few weeks, I learned that Brandon and Brandee lived with their Grandmother who had recently broke her hip and was at bed-rest. It made me think about the fact that they would wake themselves up each morning, dress themselves, and walk to school (6 blocks). It didn't take me long to figure out that the reason they did so was because they were hungry. We served breakfast and lunch, and these meals were the only meals Brandon and Brandee would get all week.

Another child in my class, Anthony, was the only child that I felt ill-prepared for. Anthony was violent. He would grab a handful of someone's hair and proceed to try to rip it out. One time, during lunch, he gently set a cardboard milk carton on someone's head and quickly smashed it so the milk ran all over the poor girl's hair and face. Anthony was certainly the victim of violence at home. At first, when Anthony was really bad, I would call to have him sent home. Anthony didn't like being in school. He didn't like being at home. He didn't like life. Anthony enjoyed creating a situation that would get him sent home, I think because it was how he controlled his life. It was the little bit of control he had. Once I stopped sending him home for behavior, he found new ways to get sent home. He would pee his pants on purpose. That got him home the first two times, but I went out and bought five changes of clothes for Anthony. Anthony was never good, but he got a lot better once I started listening to him. I would carve out time during the day just to sit with him and let him talk. Most of what he said was lies–more like fantasies. He would talk about how he was driving a sports car or how he went to Florida over the weekend. By just listening to him for about 5 minutes a day, his behavior went from violent to extremely difficult. My main concerns with Anthony was protecting others from his violence, carving out time for him to talk and be heard, and making sure he was acknowledged and praised for glimpses of pro-social behavior.

Tical was a boy who never talked in public–maybe once a week you would catch him whispering to his friend Lyric. Tical lived with his Aunt, who was very nice, and would help chaperone during Friday field trips. By all measures accessible to me, Tical was exceptionally smart. Years later, I was in West Baltimore serving thanksgiving meals at a soup kitchen, and I ran into Tical. He was probably 12 at the time. When I walked by, he was talking and laughing with friends, but as soon as he saw me, he completely stopped talking. I still wonder why Tical never talked in public around adults.

Keenan was a boy in my class with some degree of learning disability. Among other things, he had difficulty with fine motor skills, which made him appear less knowledgeable than he was. For example, Keenan could not identify the sound of the letter "p" when he was trying to draw it on a piece of paper, but if Keenan was to trace a large "p" in the air using his whole arm, he could make the sound, "puh".

Most of what I remember from my time with Teach Baltimore is the smiles of the children I taught. This sounds cliche, but it is true. I can imagine each of their faces with large smiles. At some point, that became the goal of everyday–to engage them in some kind of learning that would make them smile, to create a place where they felt safe and capable of being themselves. I also strongly remember the stories we read together, especially the ones that were their favorites that we read again and again. I can't tell you how many times I read the book "Yes! Yo!" to the entire school before an assembly or some other gathering (which was about 100 students in the summer program).

My wife and I have a friend who works and lives in Baltimore. She lives *in* baltimore, working for a church. She works with children and prostitutes in the area. She runs summer camps. When mission group come to help, her favorite thing is to take them on "Murder Walks." They walk around the neighborhood visiting places where members of the community were murdered. She tells about their lives and death. The sheer volume and density of violence is overwhelming. Just in June, a group of ladies from the midwest volunteering were witness to a murder–a new place to visit on her murder walk the following week.

Her backyard is an alleyway that looks into an entire block of abandon homes. A single block of abandon homes isn't that bad. In some areas, entire neighborhoods are boarded up. Although the homes in the alleyway are boarded up, it doesn't take long to figure out which ones are used for stashing drugs. Looking from her balcony into that alleyway is like looking into a third world country. I encourage anyone and everyone to go and visit such places. Depending on where you live, they are probably not far from you.

Anyway, I've written enough. I just wanted to convey some of my beginnings into education.

Life Lessons

Here are some "Life Lessons" I would like my students to learn:
  • They have wonderful ideas and thoughts that are worth sharing
  • They are smart and capable people who can learn anything
  • Learning enriches life in both practical and aesthetic ways
  • Meaningful learning often takes time and typically happens in concert with others
  • They live in communities that are filled with other smart and capable people
  • Responsibility involves acting in ways as to maintain or enhance one's community
How about you? What's your list?

Thursday, August 4, 2011

Why my students should do assignments

I want students to put in significant intellectual effort into assignments outside of class. It would be nice if they choose to do so for one or more of the following reasons:
  • They have come to feel a sense of responsibility to the classroom as a learning community.
  • They have found out that their own personal experience in class is greatly enhanced when they put in work outside of class.
  • They are intrigued, interested, or excited about some substantive aspect of the assignment, the topic, or the class.
  • They have come to trust (based on their experience with me) that what I ask them to do has or will have value, even if that value isn't immediately obvious to them.
  • They have come to value the attention and feedback they will receive from me and how this feedback contributes to their growth as a person
  • They value the learning and awareness of self that comes with doing the work
I want them to be driven by a sense of responsibility to community (not to authority)–one that comes with a sense of excitement (not punishment). I want there to be a willingness to engage based on trust (not fear) and a willingness to persevere because of the promise of growth (not rewards).

Tis the season for classroom planning...


My wife and I adopted a dog when we moved to Tennessee. We have wanted a dog for a while, but our apartment in Maine would not allow them.

Rudi is a three-year-old, German Shephard. He is pretty big--bigger than any other dog my family has owned. He is friendly and playful, and a bit attention-seeking. But if you ignore him for about five seconds, he will usually walk away and lie down. The previous owner had had him for those three years. He was house trained in simple ways, but beyond sit and one trick that was it, and he didn't really know sit.

After a day, we managed to get him to wait for our signal ("It's OK", and a tap to the shoulder) before moving through the doors leading into or out of our house. In about two minutes, we managed to teach him to stay inside any boundary we set for him (in the kitchen when we are eating in the dining room; in the hallway when we are in our bedroom, etc). In about two days, we also got him to be calm when we come home. Rudi was not leashed trained, but we got him to walk on a slack leash in mostly about 2 minutes in our backyard, and then another 5 min outside for a walk around the neighborhood.

Most of this was done by gently using our bodies. For defining boundaries, we simply 'backed' Rudi up with our bodies (no hands or arms), and calmly said, "Rudi, Back up". When he would cross the boundary, we would just do it again, until he got the picture. With the door, we would just crack the door open and if he made any movement we would close the door. We gradually opened the door more and more (occasionally asking him to back up), until he knew that the door would not be opened until he remained back. It took no time for him to learn that a friendly, "It's OK" and a tap means that you can cross the boundary or go through the door. For the leash, we just didn't let Rudi decide where he was going. If he pulled forward, we excitedly and happily turned and ran the other way and saying, "Rudi, this way." If he started pulling that way, we change direction again. There was no yelling or telling him not to pull, or yanking the leash in punishment. If he did walk with a lack leash, we would just continue forward. On the first walk, we had to turn around less than a half-a-dozen times. Since then, he has only pulled the leash a little as we are returning back to the house. Finally, Getting Rudi to be calm when we come home was also easy. When he came home, we simply did not say anything or look at him until he was calm, and then he would get our attention.

More recently, we have started to work on "Come" and "Stay". Stay has been easy, because it is part of the "back up". We are just using "stay" to mean, don't move at all, rather than "back up", which is move back and then don't move forward. With "come" we are using treats and praise to get him to come. I think next week, we will work on "Drop it". The only other verbal talk we use with him is "all done" with a crossing hands gesture, when we are all done playing with him or giving him pets. We then put toys away and ignore him until he settles. If he is still excited enough to come up and bother us, we simply pull our hands up, cross them, and turn away from him. He gets the picture really quick.

It is very enjoyable to train a dog without ever having to yell or feel angry. Using your body and a calm voice makes things so efficient, but also pleasurable. The only escalating sound we use is, "Bop bop!" with accompanying claps to get him to "leave something" alone -- like the trash can. But the sound is not used in anger. Rather, it's used in a distraction kind of way. It startles him and directs his attention to the noise and to us. Pretty soon we will work on a "leave it" command.

Anyway, I wanted to write about this because

(1) It's about learning and teaching, and

(2) I want to write another post about how I "learned" to be this way with dogs.

Wednesday, July 27, 2011

Help me think through a "physics praxis prep" course

If you were overseeing an independent study course where the explicit goal was to discuss and learn content that would typically be covered in the praxis exam for physics content knowledge, how would you structure the course? The course meets 2 hours per week and is targeted at physics majors who are in MTSU's physics teaching concentration

Obviously, we want students to be positioned to pass the exam, but I don't want to turn the course into a "test prep" course. Of course, these are physics majors who should know some physics pretty well, but as I see it, the exam covers a lot of content. Much of the content, students will likely have encountered before. Other content, they might have only gotten cursory experiences with or perhaps none at all. Even for content that's been covered, it doesn't mean they know it well.

If you are curious to know what's covered on the Praxis, here is some information on the multiple-choice exam and on the content essays

So where do we focus our efforts?... I think it's hard for me to make blind assumptions about what these students will need. So, I imagine a good way to decide how and where to start is based on a some assessment of their strengths and weaknesses. I could imagine asking students to rank their confidence in various topics, and then administer some assessment along those topics. We could then use their confidence rankings and the assessment as the start of a conversation for where we need to focus our learning efforts.

But what would I have students do? I think, too, that will depend on (1) how many topics areas students are going to need development in, and (2) how many students I have in the course.

Anyway, as I'm thinking this through, I'm curious to get ideas from anyone and everyone.

Reading Recommendation

I'm always amazed at the new meaning we find when we go back to reread something old a new. These past two days, I have been re-reading the following lecture series by David Hammer:

Hammer, D. (2004). The variability of student reasoning, lectures 1-3. In E. Redish & M.
Vicentini (Eds.), Proceedings of the Enrico Fermi Summer School, Course CLVI (pp.
279-340): Italian Physical Society.

Lecture 1: Case Studies of Children's Inquiries

Lecture: 2: Transitions

Lecture 3: Manifold Cognitive Resources

I highly recommend them.

Monday, July 25, 2011

Exposing Ignorance and Fostering Intrique

** I'm writing this post as a way to try to get to the heart of what bothers me about a video I watched. I am fessing up right away that the video bothered me somewhat on an intuitive and emotional level, and that this exploration is an unrefined and exploratory attempt to turn that intuition and emotion into words. Here goes. **

In a prior post, I discussed my views on the common student misconception about the seasons. In that post, I discuss why I prefer my students to have a well-articulated and personal misconception over an impoverished and authoritative correct answer. I also present in that post an alternative question that I have found to be MUCH more generative for learning and much less about exposing ignorance. I turned the question, "What causes the seasons?" into "Why in Maine is sun out for 16 hours in the summer and 8 hours in the winter?" My experience has led me to believe that this first question can set up a classroom dynamic of "expose and shame", while this second question can set up a classroom dynamic of "intrique and pursue". I'm not saying that the question alone does this, but that it helps put either the teacher or the students in a different frame of mind, which I can help sustain.

In a recent series of video (first and second), Veritasium asks passers-by the question, "Why does the earth spin?"

** Now, before you watch the videos, I want you to stop here, and ask yourself the following question: Do you think the above question is more likely to be an "expose and shame" type question or an "intrique and pursue" type question. Why do you think so? After you think about it, feel free to watch the videos if you want, but you don't need to.**

In the video, a common response from passers-by is that there is a force keeping the earth spinning–gravity, centripetal acceleration, something from the core. Veritasium states several times (to the youtube audience) that there is no force keeping the earth spinning. It is only inertia. The earth is spinning because the dust it was made from was simply spinning before hand. Fair enough. Veritasium's is trying to point to the idea that things in motion tend to stay in motion–the earth has been rotating and will keep rotating.

Aside: After seeing the video, Andy Rundquist and I began discussing with Veritasium on twitter why it might make sense to say force is involved in turning the earth. I'll argue that forces are, in fact, involved in TURNING the earth–included in these forces are gravitational forces and inter-molecular forces. Those forces act in concert to generate centripetal forces. While they ARE NOT involved in maintaining the speed of the spin, they ARE definitely involved in maintaining the turn. Each piece of the earth turns, exactly because there are net forces that turn those pieces. So the blanket statement: "There is no force" is kind of well, wrong, at least a little bit. To take this even farther, these inward forces WERE actually involved in how the earth got to its present speed, because as all that dust moved closer (decreasing its potential energy) together each piece increased its kinetic energy. So in some sense, gravity was the cause (not of the spin), but of how the earth got up to its current rate of spinning. Taking this even further, the earth is now SLOWING down. It is slowing down for much of the same reasons that objects on earth start slowing down--the earth interacts with other objects in the universe. Without going into details, the earth is slowing down as the moon moves away from the earth--this is like the opposite of when the dust was collapsing in causing the spinning rate to increase. With the moon moving away, there is an increase in gravitational potentiel energy, associated, in part, by the loss of the earth's rotational kinetic energy.

My point isn't to shame Veritasium on his physics. He is a sharp guy that knows a lot of physics. My physics is probably wrong, incomplete, and misleading in some way. My point, however, is to emphasize how simple-authoritative answers to complex and intriguing phenomena often lead to impoverished understandings in science and of science. My second point is that how we talk with people, including the questions we ask, establish the kind of science we invite them to participate in.

When I see Veritasium's video, I see evidence of people who have been victims of a life time of "impoverished-science-answer-give-a-ways." My evidence being the amount of science jargon being throw out–centripetal forces, law of inertia, equal and opposite forces. At on point, Veritasium micro-shames one person for thinking that inertia is a force. At another point in the video, a student just starts throwing out words, "velocity, rotation, speed, spinning, moving". Veritasium wants the kid to say, "acceleration," and even at one point says to the kid that he is so close. This kind of interaction is no different than what this student probably experienced in school where the teacher had a correct answer in mind and the kid was supposed to guess that answer. Another kid at another time makes the right observation (that forces causes change in speed) and he immediately validates his right answer with a high five as says, "you are nailing this." This is just like science class as well–quickly validate the right answer.

Now, once again, my problem with the question and the video isn't so much that the physics answer is a little big wrong or perhaps incomplete or misleading. My issue is more that the question and the situation is designed to expose ignorance rather than to generate learning or foster intrique or promote inquiry. Now, to be fair, we do see some forms of inquiry going on. People are grabbing this sphere and trying to speed it up or slow it down. People are pondering a bit about how things work. But the interviewer, ultimately keeps steering that inquiry toward a "expose and shame" kind of interaction and steering the conversation toward "say the right words" kinds of interaction. The best inquiry I see happens with the little kids--this is probably not a coincidence. They haven't yet been victims of a lifetime of teachers and scientists talking to them about science in a way that is about "expose and shame" and "say right words to get validated".

I would probably not ask my students the question, "Why does the earth spin?" I might ask instead, "Why doesn't the earth seem to be slowing down in the way that spinning objects on earth seem to?" I might ask, "Do you think the earth has always been spinning at the same rate? What would make it speed up, slow down, or stay the same rate?" I'm not convinced that these questions, in and of themselves, would be much better. But I do think that the question would position me and my students to be more attuned to and expressive of tentative hypotheses and authentic explanations over vocabulary and authoritative handy-downs.

Now, granted, I enjoy watching Veritasium's videos. I will continue to watch them and continue to enjoy them. But if I don't try to uncover the source of my uneasy feeling about them, then I'm not growing from that experience. Here's to growth

Sunday, July 24, 2011

Poynting Vector in a Current Carrying Wire

Steve Kanim, who is a professor and physics education researcher at New Mexico State University, brought this cool puzzle to my attention a few years ago:

If you calculate the poynting vector for a current carrying resistor–considering the E field that drives the current and the B-field generated by the current, you get that the energy flux in the resistor is directed radially inward toward the center of the wire. If you don't believe this, figure out the direction of those fields, and use the right hand rule to calculate the cross product. At first glance, this seems kind of weird. You would think that the EM energy would be directed outward, because, well because a lightbulb is a resistor, and a light bulb emits light, and that light is electromagnetic waves, and that light is certainly traveling away from the light bulb. Of course, there is nothing deeply troubling here, but that doesn't mean it isn't worth thinking through.

I'm curious: How are you making sense of this seemingly odd result? Are there different ways that you might make sense of it?

Thursday, July 21, 2011

Certainty and Vulnerability: Learning and Teaching Science

I expect (and expect with excitement) that I will forever find that I have ideas about how the world works that are problematic in some manner or another. I have no illusion of the final certainty in my own knowledge of the world nor the scientific community's knowledge of the world.
  • I know that I have ideas about how the world works that are at odds with others ideas I have. Sometimes "at odds" means logical inconsistency. Sometimes "at odds" means an ontological inconsistency. Sometimes "at odds" means an emotional incongruence. Some of these I am aware of and have ways of reconciling them. Some of them I am aware of and have not yet reconciled. Others, I am not even aware of.
  • Importantly, I also have ideas that are at odds with some of core ideas that are central to contemporary scientific understandings. And with these, too, some of these I am aware of and some not.
In other words, I am a lot like my students.

Of course, I have fewer inconsistencies than my students–both in terms of internal consistency with myself and external consistency with core scientific knowledge. But the major difference between me and my students is that I know that the nature of the game is to continually work at locating sources of inconsistency and working through them. I know that this is the primary activity of doing and learning science, and I enjoy it.

This growing sense of science has changed me and how I interact with those around me. For the first part, I am much less concerned with maintaining an appearance of being knowledgeable. In fact, I spend a lot more time seeking out people to share the things I don't understand. I also spend more time seeking out people who challenge me and often point out things I don't understand. I am much more interested in exposing my knowledge vulnerabilities than my knowledge certainties.

Of course, there are times where I get roped into caring about my external appearance of being scientifically knowledgeable and acting in ways that are more about exuding knowledge than exposing and sharing my own uncertainty. But those moments are fewer and farther between. I hope to become less and less prone to such moments.

I wrote previously about the damage that school science had on my enjoyment and participation in science. In this way as well, school was not and is probably still not the place for these new habits of mine to be nourished. In fact, school tends to nourish the opposite. School typically pressures students into masking and hiding any and all forms of not understanding. We often take off points for students being "wrong", even when that being wrong comes with a sense of maturity, awareness, and propensity for future learning. We secretly (or not so secretly) cringe whens students exhibit misconceptions, as opposed to celebrating the possibility for exploring and coming to better know current ways of thinking and knowing. We often present ourselves in ways that stress that we are science knowledge experts rather than science learning experts, and students tend to model their own science identities based on this presentation.

In the coming years, I will have more and more opportunities to grow as a science learner, a science teacher, and as a mentor for future science teachers. I hope I can eventually live up to my own growing expectations. What I do know is this–achieving this will involve continually trying to expose my own teaching and mentoring vulnerabilities. It will involve seeking out those individual and communities that challenge me. It will involve locating and pressing through the inconsistencies I exhibit in my own ideas and practices of teaching.

Hopefully, the tenure process will not be the same negative force on my growth as an educator and researcher as school was on my growth as a scientist. I guess, we'll see.

Wednesday, July 20, 2011

Is there a vi hidden in that t?

In a previous post, I asked readers to consider how a student might end up with the following equation to describe a block sliding down a ramp of height h: vf = vi + sqrt(2gh)

I suggested there were two student approaches–both observed two years ago in an algebra-based physics course. The two approaches that were identified in the comments were exactly what I observed in real life:

Scott suggested that a student might have correctly approached the problem using energy principles and then simplified the algebra wrong–turning the square root of a sum of squares into a sum. Sure enough, one student in office hours last year made this mistake.

Chris suggested that a student might have been started thinking from the idea that final velocity is equal the initial velocity plus the change (i.e., vf = vi + dv). Sure enough a different student took this approach: having seen lots of energy problems where vf = dv = sqrt(2gh), he thought it would be reasonable to just add this change to the initial velocity.

I actually like this second mistake.
Why? I think it's a reasonable mistake to make, it reflects underlying practices that are sophisticated, and it provides a generative opportunity for learning. Hear me out on this.

Despite the fact that we'd like students to start from first principles (i.e., energy conservation), many intro physics students simply start problems by following some mindless routines we've taught that mostly involve plugging numbers into equations. This student, however, seemed to be thinking about how the world and the math might work, and he was trying to figure it out without an equation from the textbook. He was going to construct his own equation. More specifically, he was thinking about how quantities change, which is one of the most important things for physics students to think about. He wasn't treating math as stuff to plug numbers into; he was thinking about math as a way to think about and express quantities and how they change.

Second, rather than treating every problem as completely new and different, he was trying to draw on previous results to simplify his approach to a new problem. Now maybe this drives you insane--once again, maybe you want all of your students to start from first principles every time. But the point is, this student was looking for possible connections between different situations and problems, and trying to generalize results. This is something we do all the time and it is quite sophisticated. Sure, when things go wrong, we go back to first principles. But to me, what makes the student approach even more sophisticated is that the student came to office hours, knowing that the equation was wrong. In fact, he had gone back to derive the right equation separately from first principles, but he still couldn't figure out why his first approach didn't work. It made sense to him that the final velocity should equal initial velocity + the change. This student knew the right answer, but wanted to know why a different approach–one he had invented and made sense to him–didn't work.

Where we went from there?

What I ended up telling the student was this: He was right. The final velocity does equal the initial velocity plus the change, but that we had to carefully consider what the change should be. I asked the student to recall what he had learned earlier in the semester.

vf = vi + at.

We discussed what this equation meant in terms of changing quantities, which was easy for him--because he was already in the mindset of thinking of mathematics this way. From this equation, we concluded the more time the ball spent on the ramp, the more the final speed it would have by the time it reached the bottom. So I started asking him how we could get the ball to spend more or less time on the ramp. We discussed several possibilities:

We could make the ramp longer or shorter
We could make the ramp more or less steep.
We could make the ball start with more or less speed

I focused our conversation on this last one, and offered: "That's weird. The equation is vf = vi + at . Vi only appears in one place to represent how much initial speed the ball has, but the time t spent on the ramp is also influenced by the initial velocity vi. "

He pondered over this for a while, looking puzzled before and finally asking, "So is there a hidden vi in the t?"

I loved this question.

I'm not going to go into all the details. But from there we spent a long time discussing and working through various mathematics to show that the reason that dv could not equal sqrt(2gh) is because dv depended on t, which depended on vi, which made vf depend on vi in a weird (non-linear) way. This, I think, was a way better learning opportunity (for both of us) than what might have happened had I simply validated his approach using conservation of energy.

Tuesday, July 19, 2011

Children Are Born Investigators

A paragraph from "A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas" Copyright © National Academy of Sciences. All rights reserved. PREPUBLICATION COPY---Uncorrected Proofs

"The research summarized in Taking Science to School [1] revealed that children entering kindergarten have surprisingly sophisticated ways of thinking about the world, based on in part on their direct experiences with the physical environment, such as watching objects fall or collide and observing plants and animals [11, 12, 13, 14, 15, 16]. They also learn about the world through everyday activities, such as talking with their families, pursuing hobbies, watching television, and playing with friends [3]. As children try to understand and influence the world around them, they develop ideas about their role in that world and how it works [17, 18, 19]. In
fact, the capacity of young children—from all backgrounds and socioeconomic levels—to reason in sophisticated ways is much greater than has long been assumed [1]. Although they may lack deep knowledge and extensive experience, they often engage in a wide range of subtle and complex reasoning about the world [20, 21, 22, 23]. Thus, before they even enter school, children have developed their own ideas about the physical, biological, and social worlds and how they work. By listening to and taking these ideas seriously, educators can build on what children already know and can do. Such initial ideas may be more or less cohesive and sometimes may be incorrect. However, some of children’s early intuitions about the world can be used as a foundation to build remarkable understanding, even in the earliest grades. Indeed, both building on and refining prior conceptions (which can include misconceptions) is important in teaching science at any grade level. The implication of these findings for the framework is that building progressively more sophisticated explanations of natural phenomena is central throughout K-5, as opposed to focusing only on description in the early grades and leaving explanation to the later grades. Similarly, students can engage in scientific and engineering practices beginning in the early grades."

Monday, July 18, 2011

Office Hours: Anticipating Student Thinking

Teaching Situation

A student comes into office hours and wants to know why the final velocity of a block sliding down a frictionless ramp of height h is not equal to vfinal = vinitial + Sqrt(2gh)

Your Homework:

Describe two different lines of thinking that could have led a student to honestly arrive at this question.

Describe how your discussion with the students would likely need to differ depending on which line of thinking the student had taken.

* Note: I actually observed this situation–two times in fact.

Sunday, July 17, 2011

Jumping through Reasoning Hoops with The Spinning Hulahoop

This is a situation that I've been sharing and discussing with colleagues over the past few months:

Imagine you and friend are holding a hula hoop. Your friend grasps one part of the hula hoop in his hand (not so tight that it won't move through his hand), and you start spinning the hula hoop around until it seems to reach a constant rate of rotation. At this point, I just want to consider what's going on while the hula hoop is and continues to rotate at a seeming constant rate.

Now, based on my description, the hula hoop system can be described as having a constant influx of energy (from you pushing). That rate of energy in to the hula hoops is equal to the rate of energy being lost into your friend's hands. The equality of inflow and outflow rates seems consistent with the idea that the hulahoop is moving with a constant speed, and thus has a constant kinetic energy.

Consideration #1
Energy would seem to flow into system at your hand, and flows out at your friends hand. But your hand and your friend's hand are spatially separated. This leads us to question one: How would you explain how energy gets from one side of the hula hoop to the other?

Consideration #2
Once again, energy is being lost at your friend's hand. But the speed of the hoop seems to be the same everywhere. More specifically, the speed of hula hoop pieces would seem to be the same on both sides of the hand. This leads us to question two: How would you explain how energy is lost at your friend's hand, while, at the same time, the kinetic energy remains the same throughout the process of moving through the hand?

Insight #1
The hula hoop is not a rigid object. Every time you pass the hula past you, you compress a piece of the hula hoop. With your friends hand pushing back, one side of the hula hoop is actually in compression. (We'll ignore for the moment whether or not the other side is in tension or not)

Insight #2
The compressed pieces of the hula hoop act as a energy storage mechanism. Your hand does work on pieces of hula hoop and that work goes into increasing the potential energy stored in the hula hoop. Alternatively, as pieces of hula hoop move across your friends hand, this potential energy is released as those pieces decompress. Thus, the energy lost at the hand is not the kinetic energy of hula hoop; rather it is the potential energy that was stored in the compressed parts of the hula hoop.

Consideration #3
The compressed pieces of the hula hoop are necessarily more dense than the pieces that are uncompressed (i.e., the compression forces the atoms closer together). Since the mass of the hula hoop must be conserved at each point in the circle, this requires that the less dense pieces move faster than the dense pieces (which move slower). This leads us to this questions: If your friend's hand is pushing back on the hula hoop pieces that move through it, how would you explain how the hula hoop pieces end up moving faster on the other side?

Insight #3
The piece of hula hoop right in your friend's hand is actually sandwiched between two different regions with distinct mass densities. Behind your friend's hand, the hula hoop is squished up like a spring. This "spring" creates a force which accelerates the hula hoop piece through your friend's hand, leaving it with a faster speed than before. This faster speed is consistent with the fact that the atoms are more spaced out. The faster speed allows it to get further away from the pieces behind it, which are still moving at the slower speed.

Oddity #1
Intuitively, your friend's hand would seem to the agent slowing things down. On the other hand, as defined by the original problem, the hula hoop seemed to be moving at a constant speed through out the whole process. Through the reasoning we've walked through, we're concluded that pieces of the hula hoop actually speed up through this region.

Loose ends and questions:

#1: It only really makes sense to describe the hula hoop as having a single rotation rate if it is a rigid body. Given that we've concluded it can't be a rigid body, is there a single quantity which describes the flow rate. Is it momentum? Is it kinetic energy? Is it mass current? Does this necessitate a change to the chain of reasoning anywhere?

#2: Is the other side of the hula hoop in tension? Is there any reason to think the hula hoop arc length is longer than, shorter than, or the same as it's resting arc length?

#3: How quickly does energy propagate from your hand to your friend's hand? How does this compare to the rate at which hula hoop pieces make the same journey?

#4: What's going on during the initiation stage before and as the hulahoop reaches steady state? Is this consistent with our stead state solution?

#5: What does this have to do with an electric circuit with a bulb, battery, and wire?

#6: Could you explore the validity of my story experimentally? How would you do it? Could you explore the validity of my story with a simulation? How would you do it? With either, what assumptions or approximations would you need to make?

#7: What parts of my story seem wrong? What assumptions have I made? Are they reasonable assumptions? What aspects of the situation am I ignoring? Is it reasonable? Overall, is this a viable model? How could you tweek it or refine it?

#8: Typically, we use energy to tell stories about initial and final states. Have we gained anything by trying to tell a spatially and temporally continuous energy story? Why is it so hard to tell such stories?

Saturday, July 16, 2011

Two views of Science

Quite a few months ago, I was engaged in a somewhat heated discussion with a visitor about the nature of science, and physics in particular. The debate tended to orbit around the issue of whether or not one could be engaged in learning or doing physics without mathematics. Of course one's answer depends on what one mean by mathematics and what one mean by physics, so there was much to discuss.

If you know me, I tend to espouse a view of physics (and science) in which explanation and argumentation are central to its practice. This visitor espoused a view in which mathematics was central to physics. In the abstract, of course, these two commitments are not contradictory, but it can help to discuss specific examples, because we disagreed on much.

At some point, I introduced an example. I asked him to imagine that two friends are walking out in a field and find that the grass seemed taller on one end then the other. Both friends decide to investigate.

One friend starts by wondering what causes this to happen: Does it have to do with sunlight? Does it have to do with water? Did someone cut it this way? Do animals graze on one side more than the other? So, he walks around the field, feeling the soil for moisture or color difference. He examines the grass to see if it's been bitten or cut. He tries see if there are different species of grass. He tries to imagine how the sun traverses over the sky, and wonder if the trees on the fields edge would shade one side more than the other. He tries as best he can to determine if the field is slanted one way or the other, thinking that water would flow differently. He goes to the edges of the field to look for any creeks or other water sources. He looks for evidence of animal tracks or tracks from a machine.

The other friend wonders if there's a discernible pattern in how the grass height varies: Does it really vary? Does it vary linearly? How quickly is the grass height changing across the field? So he gets out his ruler and starts measuring the heights. He carefully lays out a grid of measurements that spans the field and begins tabulating the data, making sure to get track of his uncertainties. He uses the table to generate various plots showing height of grass vs. various positions. He uses the graphs to draw in trend lines, and then starts modeling the data with various mathematical functions. He goes on to determine values (and bounds) for the parameters in his mathematical models, and even estimates the goodness of his fit.

Now granted, both kinds of activities have value in science: (1) exploring plausible causal mechanisms and looking for qualitative evidence to help define the possible space of explanations; and (2) carefully using measurement tools to quantify aspects of phenomena in order to look for mathematical structure and relations. Let's call the first kind of activity: "the pursuit of causal explanation" Let's call the second kind of activity: "the pursuit of quantitative structure"

Of course, as I mentioned above, these two need not be disjointed activities. Looking at mathematical structure can lead one to ask new and different questions requiring explanation. Seeking evidence to support or refute an explanation may require that one collect evidence that is quantitative in nature. But the visitor saw little value in the first activity. He likened it to the kind of science that took place with aristotle–loosey goosey ideas about how the world works with no mathematical structure. He also saw immense value in this second kind of activity–he likened it to how mathematical structure is used in quantum physics.

He went on to argue that the mathematical model for the grass was an explanation and that it could be a good explanation if it could predict with some degree of reliability the height of grass anywhere in the field. To him, it didn't matter whether the grass was cut by a lawn mower or whether it was a matter of water source. Of course, someone might care, but caring about those questions is not science but of agriculture. To him, science was about laying down the quantitative structure and coordinating that structure with quantitative data in increasingly precise and accurate ways. I felt like all the mathematics wasn't an explanation, but that it might serve the point of helping to better define the space of possible explanations or to point to new questions or inquiries about the phenomenon.

Our conversation went on for quite sometime, and it was never quite resolved. Afterwards, I came to think that the root of our different views of science were actually in much deeper differences in worldview. The visitor was a professor of physics from a developing country, and I am a physics education researcher who grew up in a US middle class home. Based on much more conversation with him, I have come to see that his views are much more rooted in pragmatic needs for technical training and economic development, while my views are much more rooted in some idealistic notions of the enlightenment. We are both a product of our personal, cultural, and nationalistic histories. I have tried for sometime to write up more about this difference, and how our views of science are embedded with deep issues of culture and history. It's something I need to think about more and write up carefully, so I'm going to get to it eventually. But for now I wanted to just write about the back story of our science conversation and foreshadow that later blog post.

Thursday, July 14, 2011

I don't believe in physics

When I first met my wife, and she learned that I was studying to be a physicist, she said, "Oh. I don't believe in physics." I replied, "That's fine. I don't really believe in physics either." We both laughed.

While I do value and enjoy physics as a set of cultural activities to take part in , it's not something I believe in. I'm not sure I know what would it mean to believe in it. For example: I'm fine saying I believe that objects fall toward the earth. And I really like learning about how ideas about falling objects have changed over centuries: from it being about the natural tendencies of objects, to it being about forces acting between massive objects at a distance, to it being gravitational fields propagating through space and time, to it being about how energy curves space-time manifolds, to it being about graviton exchanges, etc.

But do I believe in forces? Do I believe in fields? Do I believe in space-time manifolds? Do I believe gravitons? No, not really. Do I think there is value in humans learning, thinking about, and exploring those ideas? Absolutely. Do I think that playing such physics games requires taking on stances of realism from time to time? Probably. Do I think one has to believe in the ontologies we create to model the world? Not really.

Over the years, I have told lots of people that my wife doesn't believe in physics. That usually gets some laughs as well. Just before we left Maine, a friend of mine trapped my wife into a public display of participating in physics. My wife was explaining to my physics friend something about cooking–how some eggs float and some eggs sink, and how that has something to do with whether the eggs have gone bad. My physics friendly slyly asked the question, "Why does that happen?" And my wife went on explain why... and not long after she was trapped. She was doing physics, explaining sinking and floating in terms of densities. My physics friend called her on it, and she was shamed into believing in physics, at least for a moment. We all laughed.

Monday, June 27, 2011

Three Things about Physics

Thoughts about physics, mostly stolen or adapted from others:

(1) The ideas of physics are relatively simple; but they are also quite subtle, especially in how they make contact with the real world, which is (undoubtedly) messy and complex. Understanding how simple ideas interface with the complex real world lies at the heart of understanding physics.

(2) Physics is not quite the study of natural phenomena nor the study of philosophy; rather physics lives in and around the boundaries of the real and the ideal. Physics, thus, flirts with the notion that our most complex experiences are quite simple and that our simplest experiences are quite complex.

(3) Physics begs us to problematize that which is not intuitively or initially problematic, and then to wonder whether and if our approaches to the unproblematic will be useful somewhere entirely different. For this reason, the world is both the source and target of our ideas, but the distances those ideas must traverse can be staggering.

Saturday, June 25, 2011

Recapturing a Sense of Science Away from School

I have recently been thinking a lot about how school distorted my own sense of doing science–one that I am only now recapturing in my post-school life. In school, a part of my own "hidden curriculum," especially in undergraduate and graduate physics, was learning that science (especially physics) was something to be done at academic institutions with academic people–in classes, in laboratories, in dedicated office spaces, at conferences, through grants, etc. School supported a view of science that science was done by people who had scientific knowledge–knowledge that was sanctioned by scientific authorities. It tacitly taught that science was done by scientists and that scientists had the right to decide what was and what was not science, as well, as who and who was not doing science.

I think the biggest impact that this had on me was when and where I felt like I was doing science
and with whom I felt like I could do science. I felt like I was doing science when I was around other physics majors (or physics-major like people), or working on physics problems alone, or tinkering in the lab, or sitting in physics classes, or reading physics articles. Of course, I talked with "other" people about physics and science, but it was not so much to do some science with them, as it was to tell them about some physics or science that I knew (that most likely they didn't). In that sense, I was modelling my interactions with them much in the way I had been interacted with. The sense was something like this: "There are people who have scientific knowledge and there are people who don't. It is the responsibility of those who have this knowledge to impart some of that knowledge to people who don't." Without doing this deliberately, I turned my interactions regarding science with other people into miniature versions of school. Perhaps I knew something cool, fun, or perplexing about quantum mechanics or relativity, and I would proceed to dole of this puzzling and fun knowledge to anyone willing to listen.

Now, I am turning back to a sense of doing science that I had two decades ago. I don't see the world through the lens of opportunities to teach science knowledge. I see the world as opportunities to do science with others, anywhere, anytime. I love walking through the woods, just noticing, and inviting others to notice and tell me about their noticing. I love wondering about how things change, and inviting others to tell stories with me about change, I enjoy trying to coordinate stories of change with evidence we might collect. I love sharing my own ideas, much more so than the ideas from books and lectures. I love listening to the ideas that people have, and how they've come to know those ideas. I love the feeling of doing science with others, and I love the learning that happens when I do this.

Whereas before I interacted with the tacit assumption that people needed scientific knowledge from some scientific authority; I now interact with the assumption that everyone is doing science all the time, and that I can uncover and make visible the science that others are doing by interacting with them a sense of mutual wonder. I find that by making all of my science and their science more visible, we can together sustain our doing of science more deeply and for longer periods of time. The spark of "Huh, I wonder how that happens?" becomes a conversation, which becomes a scurry to collect evidence, which becomes more conversation, which becomes the building of a contraption, and so on. My view of who does science is much more expansive. I'd say that now I do a lot science with friends, children, and my wife than I do with academic scientists. I do a lot more science by myself, as well, and I share that doing of science not to teach people what I have learned; but to invite them into my science in the hopes that it will become our science.

I am excited to continue to recapture this sense of science away from school, away from sanctioned authority. I hope to get better at inviting others into the science I am doing and better at encouraging others to invite me into their science. I hope to continue to expand upon boundaries of the people and places where I see opportunities for science to occur.

Friday, June 24, 2011

Worrying about Misconceptions II

I was at a conference yesterday, where there was lots of talk and questions about misconceptions, mostly from the audience and less-so by the speakers. This isn't an exact quote but it's close:

"I'm worried that if we leave students to talk by themselves, they will develop misconceptions. I mean, where do misconceptions come from? They come from students. I'm worried that those misconceptions will crystallize and form stronger if we let them talk too long away from the guidance of an instructor."

OK. Yes, I cringed a little when I heard this. So, I want to to try to rephrase what this person said in a way that won't make me cringe, and may help me to empathize with this statement.

"I'm worried that if we leave students to talk by themselves, they won't always make adequate progress through their ideas. Where does ideas come from? They come from students. I'm worried that much of the progress they could make by working through their ideas will peter out or fall short if we let them loose too long without any guiding structures."

Tuesday, June 21, 2011

Kinetic Energy and Temperature

A long-standing discussion among colleagues has concerned the understanding of temperature. Central to our discussions has been the heuristic, which is often taught, that temperature is a measure of kinetic energy or average kinetic energy (per something).

There are many touchstone examples we have discussed that have drawn our attention to critical features of not only the concepts and their connections, but what it means to understand them.

Included in these touchstone examples are
  1. An ideal gas in an external gravitational field. How do we think about the kinetic energy and temperature varying with height? Theoretically, intuitively, and empirically.
  2. The free expansion of a non-ideal gas. How do kinetic and inter-molecular potential energies change? How does temperature change? Why? How are these changes related?
  3. A gaseous systems composed of boson and fermions in near classical regime. How do kinetic energies compare?
From these discussion, we have enriched our understanding of all the ways we might think about temperature, how it is related but distinct from average kinetic energy, what it has to do with heating and entropy, how the theoretical construct relates to the ways in which we attempt to access it through measurement, and importantly when it suffices to associate temperature with energy per particle or mode.

Ralph Baierlein in "Thermal Physics" writes the following in a section called "Temperature recapitulated" in a subsection called, "Temperature is deeper than average kinetic energy":

"The misconception that introduces this subsection is propagated with the best of intentions: to make temperature easier to understand. The root of the conceptual error lies in this: a belief that the purpose of absolute temperature is to tell us about a physical system's amount of energy. That is not the purpose of the temperature notion. Rather, temperature is intended to tell us about a system's hotness, its tendency to transfer energy (by heating). All physical systems are capable of heating or cooling others. The purpose of temperature is to rank the systems with respect to their ability to heat one another."

Monday, June 20, 2011

I would never let my students within ten feet of...

At the Foundations and Frontiers of Physics Education Research, I can be quoted as saying something like the following: "I would never let my students within ten feet of those worksheet."

I didn't say this in a public talk, but I did say this in public during lunch to a handful of people. I believe the entire quote was something more like, "I love Tutorials as a resource for myself for thinking about activities, questions, and bits of sequencing in instruction, but I would never let my students within ten feet of those worksheets". As it happened, and by means of conference nearest-neighbor interactions, my comment was propagated through space and time and eventually found its way to some of individuals who created those very worksheets and whom were likely positioned to take offense at my suggestion that those worksheets should be kept in careful isolation from students.

I want to make it clear that I do stand by my statement. But that statement requires a bit of elaboration on my part to be full stood by.

First, the statement is truly meant to be about my students (with the emphasis on ME). I don't mind so much that others would use such worksheets as an orienting artifact for discourse management. In fact, I actively support instructors who choose to use tutorials and similar well-structured, research-based curriculum materials, and am committed to helping those instructors to implement chosen curricular materials in ways that maximize their productivity for students and instructors. For me, however, the set of things I want my students to experience and learn, I have personally found difficult to achieve with worksheets. I want to emphasize that it is not impossible to achieve them, but it is difficult. I must confess that have never felt extremely competent as a tutorial instructor, partially because of the feeling that, in such an environment, I am forced to co-teach with someone (i.e. a worksheet) that often undermines much of the productive patterns of listening, discourse, and engagement that I actively work to promote. Co-teaching can be an amazing experience, but it need not be, and I don't find that a worksheet is the kind of co-worker I want around, at least not very much.

Second, I learned a lot about student thinking and learning by being an instructor in tutorial environments where a highly-regimented, worksheet-driven discourse mediates much the classroom talk. By not having to mediate all of the discourse all the time, I was given the opportunity to listen without worrying about where we were going next. I didn't have to worry, because the worksheet remembered where we were going and what we would do next to get there. As a novice instructor, with all of this to worry about, I could allocate more of my resources to trying to make sense of what students were doing, what they were thinking. I believe that structured environments in which artifacts do much of the remembering can be fertile grounds for novice instructors to develop skills they might not develop without such structures. I have benefited from being a tutorial TA, and I expect that others can benefit from them as well. Do I think they are the most optimal place for novice instructors to be? Probably not, but they are certainly not the worst. On a side note, I think the Modelling Curriculum does much of this for teachers as well. It remembers what models you are supposed to help students make contact with, and some ideas for experiments and activities that will get them there.

Third, I have two concerns with highly-guided worksheet-based curriculum. First, students are intended to learn by engaging with worksheets; but they have been habituated to treat worksheets as opportunities to drill and practice what is already known. Because of this, we are always fighting the tendency to 'put down answers' and/or 'get through as quickly as possible'. There are certainly ways to mitigate this: Being explicit about your expectations for tutorial activity, providing common writing spaces like whiteboard, only giving students one page at a time, engaging with students in kinds of discourse the undermines the worksheet-driven discourse (instead of allowing it to undermine you). But that's a fight I don't want to fight, if I don't have to. Second, I find the word 'guided' curriculum problematic for me and my students. My experience is that students can quickly learn the boundaries of that curriculum–the one set forth by worksheet and the instructors who teach around it. When students sense that their ideas do not comprise a significant part of the curriculum, I believe they start to shut down. They start to think within the boundaries of the curriculum instead of the boundaries where their thinking and their inquiries lie. Sure, a good curriculum should have boundaries that overlap with students boundaries, but the reality is that they rarely do because individuals and classrooms are idiosyncratic and variable. Students don't make contact with ideas exactly when they are supposed to.

Other have said this better than I can, so I cede the remaining space here to another. The following excerpts are from David Hammer's "Discovery Learning and Discovery Teaching" published in Cognition and Instruction in 1997.

“Students do sometimes see and invent what they are intended to see and invent, and well-designed materials can improve the chances of that happening...On a traditional view of teaching and curriculum, one might expect these worksheets to succeed in guiding the flow of student learning through the predetermined sequence of ideas and observations. Thereby, one would see shortcomings in [them] for not anticipating the various aspects of students' knowledge and reasoning. The teacher's role in that view is peripheral, to help keep the students on the planned path, and the most successful materials should obviate teacher intervention."

"On the view of teaching and curriculum that I am promoting, a curriculum succeeds, not by guiding the flow of learning and instruction, but by helping to establish an arena of activity rich with opportunities for student and teacher discovery. Within that arena, the substance of the course, the curriculum, emerges. This is a view of teaching that is more flexible with respect to pace and substance, but it is also more dependent on teacher awareness and judgment. Presuming uncertainty, the teacher does not expect students to arrive at given insights at given moments; rather, it is the teacher's responsibility to recognize when and if they arrive at those insights or others, to discover their progress, and diagnose their difficulties. The teacher's role is not simply to keep students on the right path; it is to find out what paths there are, to scout
ahead to see where they may lead, and to make judgments about which ones to follow."

Tuesday, June 14, 2011

PER Summer School

At FFPER, I am in a working group that is supposed to make plans for a Physics Education Research summer school. Three overall models have been proposed and are being discussed.

The first would be somewhat like a peer-review workshop, where researchers would be invited to bring their work to be presented, examined, and critiqued.

The second would be more like a formal PER school setting, where classes would be held to learn a particular research methodology (e.g., video analysis, item response theory).

The third is a research institute, where a different institution of education research would invite a dozen or so persons to come each summer for an intensive immersion in research on the local educational context.

Curious to see where this goes. Our goals are to make some decisions and make progress of funding plan.

Thursday, June 9, 2011

Feedback on Workshop Abstract

I have to run a workshop for secondary math and science teachers at a conference in two weeks, and have to turn in the abstract/title tomorrow. I'm looking to do something new I haven't done before, and this is something that has been stuck in my brain these past 6 months.

The session will be one of five parallel sessions, with around 20 teachers each. This is what I drafted this morning. I'm looking for feedback. What do you think? Would you got to this session?

You are your own guide post: Fostering our own sense of inquiry

There are many calls for engaging students in scientific inquiry, and there are equally as many definitions of what constitutes inquiry. This workshop is based on the premise that we can better position ourselves to know and to teach inquiry when we cultivate our own inclinations to inquire as part of our everyday lives. We'll explore the following four strategies aimed at re-invigorating and sustaining everyday engagement in inquiry: capturing spontaneous wonder in multimedia, drawing others in to wonder with you, tinkering and exploring in the everyday world, and exercising one's authority to know and learn. In this workshop, we'll do a bit inquiring together, explore each strategy with concrete examples, and discuss connections to classroom inquiry.

Monday, June 6, 2011

Exploring and then Naming in Upper-Level Physics

Corrinne Manogue at OSU is the source of this one:

You teach upper-level physics. Say, you want to teach your students about eigenvectors. You could

(A) Introduce the word "eigenvector" before or at the beginning of lecture, explaining what the term means and where it comes from. And then lecture on how to solve for eigenvectors, and then have students practice.


(B) Put students in groups: give each group a different (carefully chosen, of course) matrix and ask them to see if they can find any vectors that don't change direction when you multiply it by the matrix. Let them explore, remember how to perform matrix multiplication, encourage them to draw (not just do algebra), watch them develop an intuition for what each matrix is doing, and try guess and check, encourage them to use geometrical insight to rule out or hone in on solutions, let them struggle with whether there can be more than one solution. Then let them share their solutions with their peers. Point out important similarities and differences across problems and solutions strategies. Point out important things you'll need to bring up later. Then, then introduce the word "eigenvectors". Draw on the insights they have (and haven't) made and present the formal method for finding eigenvalues.

The argument for doing A could be this: "Students don't have any intuitions about eigenvectors and linear algebra. It's a weird word that's distracting. If I introduce the word before lecture, it will help them focus on the mathematical structure and methods I want to teach, rather than on the weird vocabulary."

The argument for doing B is this: "By drawing on what students do know and can do, you can quickly build up a set of intuitions that orient students to the concept of eigenvectors. Since, they are not likely to formally develop all the methods on their own, I can capitalize on what they end up doing to anchor the formal instruction to their own ideas and methods."

Anyway, what do you guys think?

Vocabulary and Jargon

If you taught physics before, you've likely heard something like this from a student: "The ball's energy force went into powering all the momentum of the collision vector."

Many of us cringe when we hear sentences like this, but maybe not for the same reasons. Some of us may cringe because students are mis-using a lot of vocabulary. Others may cringe because it seems such an unproductive way to approach talking and making sense of the world with other human beings.

Perhaps, all this jargon from students really signifies nonsense--the student is just grasping at whatever vocabulary they can, hoping that with a shotgun of terms, something will sound right. Or, perhaps, the student was thinking something more like, "The ball was moving fast, and so it had a really big influence in the collision," and they were trying to communicate this idea using terms they thought they were supposed to. I tend to think it can be one, either, both, or something in between. My inclination is to gently encourage students to stop doing this, and I try to help them express their ideas using familiar words, pictures, etc. In the PER community, there have been and continue to be lively debates about whether this kind of jargon-infused talk can be productive for learning.

Jargon-infused talk is not limited to physics. As an education researcher, I've heard new PER graduate students say things like this: "The framing was made of and led to symbolic forms and p-prims resource schema activation, but not a coordination class." I sort of cringe when I hear students say these sorts of things, too. If I listen really hard, I can imagine maybe they are trying to say, "The students seem to be engaged in the activity with a mish-mash of ideas that are both mathematical and physical". Like the physics students, I encourage them to articulate, elaborate, clarify, and refine their ideas in their own words, and not worry (yet) about technical vocabulary.

The role of vocabulary in learning is a tricky thing, because it's not all the same. Learning that the french word "pomme" means "apple" is easy, because we already have the concept of apple. We have likely felt apples, tasted apples, smelled apples, seen apples. You've probably had apple juice, apple sauce, apple pie. You've head phrases like, "the apple of my eye". You've distinguished apples from other fruits like pears or plums. You probably know that apples come from trees, and not from the ground (like the pomme de terre). You know of different kinds of apples. With this rich network of ideas, distinctions, and experiences, it's easy to just add on "pomme".

With scientific terminology however, it's not always as simple, because we aren't likely to have all the (right) conceptual anchors in place to hook those words to. The question of when and how to introduce vocabulary is an interesting one. Recently, I was discussing two different approaches to managing vocabulary in the physics classroom:

(1) Frontload the introduction of vocabulary, so that students can better make sense of ideas discussed during class. This will help reduce students' cognitive load, and students can spend mental effort on understanding ideas and not just getting lost in a sea of vocabulary.

(2) Backload the introduction of vocabulary, after you've had a chance to introduce ideas in class. This will provide students with some conceptual "hooks" to anchor the vocabulary to.

I want to talk about this more, but I want to pause with the following questions:

What are some situations in which you think #1 would be better than #2? Why?

What are some situations in which you think #2 would be better than #1? Why?

Sunday, June 5, 2011

Engineers vs Construction Workers

In the car with the 3.5 year old that my wife watches. He says, "Engineers are smart, and construction workers are not very smart."

Sigh. We get to hear a lot of the dumb things parents say through their children.

Friday, June 3, 2011

Flow into the Rainbow

I've been having conversations with a graduate student here about student engagement. In particular, we've been discussing the concept of flow. Flow is a psychological construct that is meant to capture the feeling of being fully immersed, focused, and engaged in what one is doing.

There are many aspects to flow, but some that stand out for me are the following:
  • loss of self-consciousness
  • high levels of concentration
  • intrinsically rewarding
  • absorption into the activity
  • distorted sense of time
This graduate student is interested in investigating how it is that college physics students experience flow (in various instructional environments), and what that might have to do with learning, persistence, and attitudes toward science.

This past semester, students enrolled in my seminar on "science teaching and learning" seemed to have had one collective flow experience that has really stuck with (many of) them, and consequently, it has stuck with me. It was a discussion around the question, "Is every color in the rainbow?" If you are curious, this activity has a facilitators guide written by Leslie Atkins and Irene Salter over at SGSI.

Certainly, from my perspective the lesson seemed very fun and engaging. But it was also engaging enough that, apparently, several random groups of people walking by the classroom stopped to watch for some period of time. Of course, we were so engaged in our own discussion that we didn't notice, but in the following days, several faculty in the department commented about it or asked what that class was about. The students in my class also spontaneously wrote about it in their weekly reflections; brought it up in the course feedback; and talked about it in exit interviews at the end of the semester (with a 3rd person).

That same day, after the Rainbow discussion, we had a discussion about what makes for a good science conversation. And this is what they came up with:
  • having relevant everyday experiences to draw on
  • having a diversity of opinions and people
  • having a culture of trust (already established)
  • having fun and laughing
  • being challenged
  • making progress, getting somewhere
  • feeling like part of a group but also an individual
  • listening and sharing, not just waiting to talk
It is certainly a very interesting list. I love that they have included having fun and even laughing as important to a good science discussion. Apparently, the balance between "being challenged" and "making progress" has a lot to do with flow, at least according to what I've read. It's also interesting to think about how much they valued each other: "feeling like part of a group", "having a culture of trust", "listening and sharing", "having a diversity of opinions and people". It makes me think that they were not just immersed into the activity, but they were immersed into each other, because each of them were so integral to the activity. Lastly, the idea that "everyday experience" makes for a good science discussion would make many of colleagues smile.

I'm interested to know what everyone thinks their students would say to the question, "What makes for a good science conversation?"

Thursday, June 2, 2011

Images of Teaching

I was reading a recent book chapter by Russ, Sherin, and Sherin. In the chapter they discuss, among other things, four images of expertise in (mathematics) teaching:

Teacher as diagnostician

"Examining the mathematical thinking of students, looking for symptoms, and diagnosing their underlying causes"

Teacher as conductor

"Directing and shaping the classroom discourse... to orchestrate whole-class discussions in ways that advance the mathematical learning of the whole class"

Teacher as architect

"Selecting and implementing curriculum materials...choosing tasks to use with student as well as deciding how those tasks should be carried out"

Teacher as river guide

"To be flexible in the moment...responding quickly and effectively...responsive to the context, to students, and to what occurs in the moment."


I like this breakdown, both for thinking about research on teaching and how we conceptualize teaching, but also for thinking about my own teaching. How do I imagine myself as a teacher? In which of these images do I feel competent? In which do I feel more novice?

I will say that my weakest area is as architect- especially thinking about the design of a whole course. I haven't had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other three areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability. I have become more aware this year of my needs to mature as an architect, and have taken some steps to reflect on and enact some novice architect moves. One professor here at UMaine has been helpful in nudging me in this direction.

I'd say conducting is where I am strongest. Of course, I still need a lot of improvement, but I feel pretty comfortable and confident navigating whole-class discussion. This is a lot based on my experience in teaching as a summer kindergarten "teacher" in an Americorps program, as a tutorial TA and instructor at UMD, and even more recently as an instructor and PD facilitator at UMaine. But I also had the opportunity to watch a lot of good conductors. In particular, during my second year at Maryland, I watched David Hammer lecture everyday. A few times I even got to substitute teach for him, and try it out. Having role models helped a lot, but it helped even more that these role models were often the same persons coming in to observe me and give me feedback. Now that I think about it, I also got a lot of good feedback from my mentor teacher in the Americorps program. Mrs. Patterson was always nudging us to make sure that children had opportunities to learn from mistakes, and to not let them feel bad OR to let those mistakes just pass by.

As a diagnostician, it shouldn't be surprising that I feel adequate in some ways and less adequate in others. This is because I feel more confident as a conductor than as architect. I am good at diagnosing when I am conducting, but I need to improve my skills at designing more and better opportunities for diagnosing.

I think the river guide image is the hardest for me to assess. I feel like I am almost always playing river guide, largely because I fail to play architect well enough, but that doesn't mean I am good at being the river guide. I suspect my expertise is patchy. There are certain rivers I feel very competent reacting to rapids and obstacles; but there are other rivers where I would be lost and tumble over ungraciously. Being the river guide means you both know the terrain have all the skills down, but that you can perceive and react quickly and appropriately. It'll be interesting after my first year at MTSU to revisit this list.

Anyway, where do you all feel more or less competent as a teacher?

Wednesday, June 1, 2011

College Instruction: Dollars and Sense

Yesterday I realized that the the University of Maine, in-state students pay about $20 an hour for instruction. In a lecture, where there are 150 students, this means that students collectively throw out $3000 every time they sit down and listen to a lecture.

I was wondering how students would feel if every time they walked into lecture they had to fill a bucket with $3000 dollars before the lecturer began. How would students feel differently about their investment? Would they perceive the value of instruction differently? What might they demand in return? What do they deserve in return for that money?

A colleague of mine helped to put this in a different perspective: an adjunct faculty at UMaine only gets about $3000 dollars to teach an introductory physics course. This, of course, means that an instructor who teaches all semester long only gets to keep one of those buckets, the rest goes to paying TAs, administration, maintaining libraries, computer labs, paying electricity and heating bills, providing labs, paying support staff, and so on and so on and so on.

But it makes me wonder again: How would an instructor feel if they had to teach all semester long watching those buckets fill with money, knowing that they only got to keep the last one? How would they feel differently about students' investment and their own compensation? Would they perceive the value of the university infrastructure differently?

Tuesday, May 31, 2011

You know you might need SBG when...

A professor gives the following directions to graduate teaching assistants on how to grade physics labs: "If they do everything, give them an 85. If they wow you, you can make it higher."

Sunday, May 29, 2011

Rock Skin

One of the kids my wife takes care of called the outside part of the mineral its "skin". I think that is a really cool way to see that rock. Plus, I think it potentially tells us a lot about perception, language-learning, and even perhaps naive understanding of topology. It made me wonder what she thought the skin was for: Would she think is was to protect the crystal?

Friday, May 27, 2011

Light and Water: Post Eleven

Here's another example of a surface acting like a mirror, made particularly interesting by the fact that some objects are behind the table, and some objects are on the table.

Question of the Day: Why does Joe Biden's hand look so much closer to the other guy's chin in the reflection than it does in reality?

Tuesday, May 24, 2011

Shock, Curiosity, and Empathy

My office mate told a story today about a friend who is a teacher. This teacher shared with him a story about the children in her class who thought that the wind was created by trees shaking their branches and limbs.

Here are a series of three questions I think are worth thinking through:

Shock: What's shocking to you about this idea? Why is it shocking? (i.e., how is this different from what you know?)

Curiosity: What's intriguing about the fact that children have this idea? What questions do you have about it?

Empathy: Why does the idea make sense? What are all the experiences or though-processes you can come up that make this idea wonderful for someone to have?

Sunday, May 22, 2011

WCYDWT: Rought Sketch of Possibilities

There has been an explosion of dandelions in Maine, and I think it has something to do with how wet this spring has been. Today was the first bit of blue sky we've seen in two weeks. Walking around today, my wife and I were very curious about the sequence of dandelions transition and the mechanisms by which these transformations take place. Here is a photo of some collecting we did today.

Our inquiry, the evolving stories we told, and the evidence we collected and coordinated with those stories made me wonder what kids would do if you drew attention to it, asked them what they thought, and helped them to wonder, collect evidence, and tell stories.

Tuesday, May 17, 2011

Any Questions, WCYDWT, and the Rainbow Question

The #anyqs hashtag has led to much exploration and conversation about using images and video to foster convergent classroom interest around spontaneous questions and wondering.

In this post, I want to throw out some ideas about the intricate balancing act between the "diversity" of ideas and the "coherence" of inquiry pursuits. I want to do this in the context of a lesson I've taught several times recently.

Leslie Atkins and Irene Salter developed this amazing lesson around the question, "Are all the colors in the rainbow?" I have run this lesson now three times as part of professional development for secondary science teachers and college science instructors.

The last time I ran this lesson, I did a good job of managing the balance between the exciting diversity of ideas/questions with the comforting coherence of common pursuit. Here is how it started:
  • 5 minute silent free write about question, "Are all the colors in the rainbow?"
  • 5 minute discussion with neighbor (prompt, learn what your neighbor is thinking)
  • Whole class discussion where I write down everything on the board
Here is what got written on the board during the discussion last time I ran it with college undergrads in my science teaching and learning seminar.
  • What do we mean by color? - primary colors, crayon colors, secondary colors?
  • Where is brown? Is it there? Isn't brown from mixing colors?
  • If white light has all colors, why don't we experience seeing all the colors when we see white light?
  • Is this question being asked to like a scientist or like an artist? It seems like that would matter
  • What about black? Is black a color? It seems like its the absence of color? But then again, there are black crayons.
  • What about neon colors? Are they in the rainbow? What makes something neon?
  • Doesn't a rainbow have all the light colors, because it breaks it up like a prism.
  • Isn't purelight ROYGBIV?
  • In ROYGBIV, Yellow + Blue = Green, and that makes sense because green is between yellow and blue. But Blue + Red = Purple doesn't make sense because violet is on the end, not in between red and blue.
  • What about a blind person? Would they just see the rainbow in grays? Does that mean gray is in the rainbow?
  • Can you be underneath a rainbow? Can you see a rainbow from above? Yes, I've seen rainbows from above
  • What about double rainbows? How does that work?
  • When people look at a rainbow from different angles, can they all see it? If so, do they all see the same rainbow?
  • When you mix paint colors you get poopy brown, but when you mix all the light you get white light. Why?
  • Absorbance vs transmission? Doesn't that matter?
  • How do we see? Do we see what's reflected or what's absorbed?
  • What's a shade? Are shades in the rainbow? Can rainbows come in different shades? Would the rainbow be a lighter shade on a sunnier day? Would pollution effect the color of the rainbow? Isn't a shade like when you add white to it.
  • What is the wave length of brown? If we know that, we would know where it goes in the rainbow
  • Since rainbow is the diffraction of light through water? Does the color of the rainbow depend upon properties of water?
  • Is pink in the rainbow?
  • Don't we see color because we had rods in our eyes?
  • How does the brain interpret color?
  • Can a color blind person use 3D glasses?
  • How do 3d glasses work? Old vs New ones?
  • How does turning a color photo into a black-and-white photo work? How does black and white TV decide to make colors into different shades of gray?
  • How does gray work? If white is all the colors, and black is no colors? What why does having less of "everything" look gray?
  • Does needing glasses to see influence the experience of seeing color?
  • Does my "anti-glare" glasses that look blue-ish change my experience of color? Like more blue? Or does my brain correct for that over time? We've heard that when you wearupside down glasses you're brain corrects for the flip. Would it correct for color, too?
  • Can you create colors that don't exist yet?
  • Turquoise - it seems like it should be a mix of blue and green, and therefore be in between blue and green. But it doesn't look like right. It looks like a lighter shade. Which raises the question again of "are shades in the rainbow?"
  • Red-violet seems like it can't be in the rainbow because red and violet aren't next to each other. But we can see red violet. What if we could bend the rainbow in a circle? Would we get red-violet?
  • Red-violet is like the color of a plum. So it must be a color, because it exists. If it exists, does it have to be in the rainbow?
  • It seems like white and black aren't in the rainbow, and therefore gray can't be in the rainbow.
  • If brown has a frequency it's in the rainbow, if not then it's not in the rainbow.
That's a HUGE amount of divergence. But students were overflowing with excitement. I could barely stop them from sharing and talking, nearly too fast to write it all down. While the diversity and free exchange of exciting ideas and questions generated that excitement, I think that same diversity was going to soon get overwhelming and incoherent if I didn't bring it in.

The question is this: How could I capitalize on that excitement and personal investment in rainbow question while still bringing everyone to a more focused and shared inquiry?

Answer: Pass out a pack of crayola crayons to each pair. Tell them to put each crayon in one of three categories: Definitely in the rainbow; definitely not in the rainbow; unsure. Tell 'em they have to have reasons and arguments. For the colors they say are in the rainbow, ask everyone to put those colors in rainbow order. Let the excitement and motivation pay off.

What's the point?

The point of Dan Meyer's #anyqns is to create an image or video that stimulates interest around a common question. I'm wondering however, what's the best route to common interest. It may be that you want to start right out of the gates with a common question. Alternatively, it may be that you want to generate an overflow of divergent interest, and let that interest bleed

We do need to foster students' interest in the collective pursuit of some sort of coherent inquiry, but it may be that the diversity of ideas (across stakeholders) is exactly what builds interest in a common goal. That said, I believe it is the timely convergence of collective inquiry that brings comfort to the vastness of escalating divergence.