Simple Problem

This was my attempt today to create a problem that:

(1) Isolates a simple skill (in such a way that it might be useful for SBF)
(2) Tries to connect the reader to the problem in some personal way
(3) Has the potential for even a bit of learning to occur

On the Diversity of Student Thinking

Here is a question that I have been fortunate enough to observe many students pondering over:

"A stone is dropped from a cliff. One second later, an identical stone is dropped from the same height. Describe the distance between the stones as they fall."

The question is a little bit interesting because it has this compelling wrong answer: The two ball's keep the same distance. I have seen this answer arise as simply an intuitive reaction, but I have also seen this intuitive reaction argued for in terms of school knowledge that students can call upon.

"Gravity acts the same on all objects."

"Gravity acts the same and the initial position and velocity are the same"

"Both balls falls with the same speed of 9.8 m/s"

While each of these students has given the same answers, their thinking about the problem is different. The first student I might characterize as over-generalizing from a rule they've learned*. The second student I might characterize as conceptually equation hunting (e.g, "If I plug in all the same stuff, the number that comes out can't be different"). The third student I might characterize as not distinguishing acceleration from velocity.

While students' answers to the question don't tell me much, listening to them explain tells me quite a bit about how they are approaching the problem and what difficulties they might be having.

In general, the diversity of thinking is something that intrigues me. Partially because it is just plain interesting much in same the way that the diversity of life is interesting to biologists. But it also intrigues me because it places serious constraints on the possibility of "carefully sequenced instruction."

The diversity of thinking, of course, is not restricted to wrong thinking. Consider the three following arguments for the correct answer. I've seen each of these arguments in person.

Pulling Away Argument

After one second, the first stone will have picked up 10 m/s of speed. The second stone, however, hasn’t even started moving at all, at least not yet. So it’s speed is still 0 m/s. Since the first stone is moving and the second stone is only about to start moving (but not moving yet), the first stone will pull away from the first stone, making the distance between them greater. This trend of pulling away (and making the distance greater) will continue because the first stone will always be faster than the second stone by 10 m/s.

Shadowing Argument

We can think of the second stone as “shadowing” the first stone—it will be where the first stone was, exactly one second later. Since both the original stone and the shadow stone are falling faster and faster as they fall, the distance that each travels in that one second must be greater and greater as well. Thus the distance that the second stone covers (in order to “shadow” the first stone) becomes greater and greater, showing that the distance between them increases over time.

Parabola Argument

The position vs. time graph for free fall is a parabola. If you pick two points on a parabola that are one second apart near the origin, you will see that there will not be much separation on the y-axis. However, if you pick two points that are one second apart that are also far from the origin, there will be a big separation. This shows that distance increases as time increases.

Just as the wrong answer doesn't tell you much, knowing that a student gets the right answer doesn't tell you much. Each of the above arguments tells you something quite different about the student. The first student is thinking about acceleration as the accumulation of speed and about the consequences of relative velocities. The second student has invented a novel way of thinking about the problem in terms of speed-distance-time comparisons. The third student is bringing graphical tools to this problem in a successful way.

Like I said, I think the issue of diversity in thinking is interesting, but it is also important. So, what does the diversity of thinking imply? I'm going to be exploring this issue over the next week or so in blog posts. I hope to discuss its implications for assessment. It's implications for curriculum design. And it's implications for teacher preparation.

* Footnote: I've heard students use this argument to support all kinds of non-nonsensical answers. Students will say that a ball thrown straight down and a ball thrown straight out will hit the ground at the same time because gravity is the same. Students will also say that a ball thrown a mile into the air will take the same amount of time to reach the peak of its motion as a ball thrown an inch into the air because gravity acts the same. "Gravity acts the same" functions as a blanket statement to cover any problem where a student is asked to compare times. In fact, the only time these students get the question right is when they are asked, "If a bullet is shot from a rifle and another bullet is dropped at the same time from the same height, how will time compare for the two to hit the ground?"

Pseudoteaching on the Guided Inquiry Front

Last year, I spent about a week substitute teaching in a college physics course for pre-service elementary teachers.

For the week I was there, the class was well into learning about bulbs and batteries. In the course, groups of student work through materials in a somewhat self-paced manner. The instructor strolls around and discusses the students' investigations with them. Every once and a while the instructors do a formal "check out" before students can move on to another section.

One group was being "checked out" by me on a section about voltage, and I discussed with them the questions that the instructor had designated that I discuss with them. I don't remember the details. But I remember feeling that they had met some reasonable minimum standards for explaining why they had carried out the investigation, what they had learned, and what the results had to do with concepts they had learned prior.

As I was walking away, I kept listening (as I always do), and overheard them continue to discuss:

"So, is like current the flow of voltage? ...Like, you know what I mean? I'm trying to figure out what voltage is. And I was thinking that maybe voltage is like logs flowing down a river, and current is the flow of water moving those logs along."

"I think of it more like a train. Like, current is the train cars moving along, and the voltage is like the engine car, driving the train along."

"And so are the tracks, then, like the wires?"

...

"So what's resistance?"

The conversation went on for a bit like this. I was thinking to myself, "That's the problem with a preplanned checkout." The teacher gets the students to discuss what the teachers (or the curriculum) wants to talk about, but the students don't get to talk about what they really want to discuss.

The section of the curriculum was heavily focused on empirical observations and making sense of those empirical relations in terms of the model that the curriculum would have them develop. But these students wanted to talk about their own models–what is voltage like? Is voltage a thing like a log? Is current like a moving train? Is voltage like a engine car? How do I make sense of resistance?... They weren't intellectually concerned with what the curriculum was dishing out.

Later, at another table, I was doing another "check out". The group explained to me what they did and what they learned, but then I asked the students to explain to me what they had predicted would happen, and if the result had differed in anyway. They kind of shot some guilty glances around at each other, and one finally said, "Well, we stopped doing the predictions." Another one added, "It just confuses us to think about the predictions, especially if we are wrong."

Finally, at another table, I was walking and saw one of the students crossing out stuff from a prior page. I asked, "What are you doing?" The student said that they were erasing their prediction, because it was wrong. I asked them why they would go back and erase a prediction. The student responded that they didn't want to get confused with the wrong answer later when going over her notes or when studying for the test.

What does all of this tell me? Guided curriculum can be dangerous. These students were intended to be doing inquiry, but they we mostly just jumping through inquiry hoops. And I don't blame the students–they learned to do this in class because that's the hidden curriculum that was being taught:

The students in the first example had learned in class not to discuss certain aspects of their own ideas or models. In particular, they had learned not to talk about "What things are like?" This wasn't just because I was there. I actually came back over to this group and we talked about their models for quite a long time, and it was clear to me that they weren't having these kinds of conversations on a regular basis.

The students in my second and third examples had learned that their ideas were worthless (and confusing to think about).

The problem with (some) guided inquiry like this is the illusion of learning. Instructors doing these kinds of "check outs" can convince themselves that students are building powerful scientific models, but really students are just learning not to share any ideas that might be wrong, not to have conversations that they aren't supposed to have, and to hide interesting questions and insights that are outside the bounds of the "guided curriculum".

To me, this is pseudoteaching and pseudolearning at its worst, because students are not not learning. It's quite the opposite. They are learning that their ideas, questions, and curiosities have little to do with science and science learning (except that their ideas are usually wrong).

At the end of the day, if students are learning to avoid taking intellectual risks around the instructor, that instructor doesn't stand a chance of helping those students learn.

"Don't give 'em Components until they Beg"

"Don't give 'em Components until they Beg" ... is a quote from someone's blog I read recently. I can't seem to find it. If this is you, I'll update this post to link and reference you! That post made me reflect back on this story from the frontiers of physics help study:

Update: The original post that inspired me to share this story can be found at Quantum Progress.

Last semester in help study, it was hit-or-miss in terms of attendance. If students were assigned a difficult homework assignment that week, we might have 50 students show up. If it was easy, we might only have a handful. For that reason, we usually assigned 2 helpers to be in help study.

One week, it wasn't particularly busy, and I was watching a group of two students working on a 2d-collision problem with the help of a graduate student. The problem was something like this

A 2kg mass moves east at 2 m/s. Another 2 kg mass is moving 30 degrees south of west at 1m/s. If the two collide and stick together, what will their speed be?

The students and helper were approaching the problem like this:

(a) Set up the conservation of momentum equations in the x and y directions

(b) Find the x- and y-components for the velocity for the mass moving off-axis

(c) Plug in numbers and solve for unknown

(d) Use those unknowns to find the speed and the direction.

Standard solution path, but along the way, they made an error. Can you spot it?

2kg 2m/s + 2kg 1m/s cos (30) = 4kg vx

2 kg 1m/s sin (30) = 4kg vy

The mistake they made was not taking into account the direction of the ball. There should be a minus sign somewhere above to reflect the fact that one ball is moving eastward and the other is moving westward.

Now, neither the students, nor the graduate student, knew what mistake they made. But since the students had the answer at the back of the book, they knew they had made some mistake.

Now, I didn't know what mistake they had made either. They had been working on pieces of paper that kept the details of their work somewhat hidden from me. So I just let them keep working on it, while I went to another board to work out the problem quickly myself.

Here's what I did on the blackboard:

As you can see, my approach was quite different from theirs:

• It emphasizes geometry
• It emphasizes the vector nature of momentum
• It emphasizes that system momentum is the sum of individual particle momentums
• It emphasizes conservation in a simple way (p is both initial and final momentum)
• It emphasizes momentum (as a singular physical quantity) rather than velocity and mass
• It solves the problem through geometrical ideas (here law of cosines, but you could just as easily use a ruler and protractor)

And it does all of this in one diagram and one equation.

I think the students' approach does this:

• It emphasizes equations and algebra
• It hides vector nature of momentum (in signs), also where students make their mistake
• It distributes the concept of conservation across many terms and many equations (masking the fundamental principle from the exercise)
• It emphasizes mass and velocity, not momentum (which is king!)
• It solves the problem through too many unnecessary steps: break into components only to have to combine them back again.

I'm not saying students shouldn't ever learn to solve problems by using components. I'm just saying that "jumping the gun" by teaching components first can't be a good thing.

I suggest (as others have) doing it this way, if at all possible:

(a) Start with protractors and rulers–make 'em do it the old fashioned way

(b) Then, maybe introduce law of cosines and law of sines–give 'em a trick or two

(c) Then, then maybe, think about introducing components

We ended up finding the error in their work (together), and discussed a little bit about the solution I took. They were really interested in what I had done, because it looked like less work. But the graduate student stuck around even longer to discuss this solution, because he was intrigued by the fact that he had never learned to think about momentum problems this way.

Learning to Teach

Quote from UMaineprofessor (quoting someone else):

"The first time you teach a course, you teach yourself. Then second time you teach a course, you teach the course. And (maybe) the third time you teach a course, you teach the students."

My Frustration over Pseudo-"Something" Problems

I organize and volunteer for a physics help study at my university. We get a range of students, including those just looking for quick answers and help on homework, those really looking for meaningful help in learning physics, and even those who love just hanging out to talk physics.

I don't mind that some students are there to only "get' quick help and aren't in it for some deep understanding. Most of the courses aren't structured in a way to help them learn. I am happy to guide them a long a little bit, and make them a little less frustrated by the crap they have to put up with. By helping them out (sometimes a little bit too much), I gain their trust and they actually get to learn something meaningful from time to time. Never underestimate trust.

This week, it seems, students have been learning about electric potential. They are assigned a lot of "exercises". I refuse to call them problems, because there is nothing problematic about them. Take for example, this problem, for which several students called me over to discuss.

The question just asked students to find the potential at a point in space due to three charges. The students had to do a bit of geometry to find some unknown lengths, but otherwise it was a simple straightforward calculation. Each of the student I met had correctly done the calculation. They had called me over because they had gotten the right answer that v= 0. These students must have been surprised by the answer, because they each called me over to discuss, "Does this make sense?"

OK. Stop. Hold the phones. Students spontaneously calling me over to talk about whether an answers makes sense. NOT, "do I have right answer?" NOT, "how do I do this?" They wanted to talk about whether or not an answer made sense.

And this is where I had to sigh. Because saying that the v =0 doesn't mean much. Really, you have to know what the potential is at nearby points to say anything. Because knowing differences in potential tells you something about electric fields and/or where charges are likely to move. Sure, sure, maybe you can make some argument about how it tells you that the potential there is the same as the potential at infinity. And then we can talk about how much net work it would take to bring in a particular from infinity. Sure, sure, sure. But what does v =0 mean? Not much.

So, here these students are, and they have been asked to do this "exercise" by performing some rote calculation using the formula k*q/r. They do it well. And they are puzzled? And I have to be the one to tell them that answer is meaningless, pretty much anyway. Not that their answers is meaningless, but that any answers would be meaningless. (Note: We did talk about why it was meaningless; and what else you would need to know for it be meaningful. But I digress)

Here's why I am so frustrated. We complain so much about students not stopping at the end of the problem to ask, 'Does this make sense?' But I'm the one who has to look them in the face and say, well, your professor has assigned you a problem that isn't about making sense of anything. He just wanted you to do some push-ups. I have to say that the best we can do is to check your work and make sure you calculated it correctly, and maybe to offer a mathematical explanation for why it seems plausible (based on geometry) that it could work out to zero. But I can't offer them an answer to the question, "Does it make sense?" from a physical sense without really twisting things around and bringing in a lot of baggage about potential energy, work, infinity, etc.

Am I wrong? Can I make meaning out of this stupid calculation students have been asked to do?

On the Perils of Pushing for Correctness

Last semester, I gave intro physics students a series of easy, commonsense questions about force and motion. Before instruction, students were doing between 80% and 95% correct on the questions. After instruction, students were doing fairly bad, between 25 and 50% correct. It seemed from the data that students had learned to ignore their productive intuitions, and were simply trying to apply rules that made no sense to them. While we may have eradicated their misconceptions (they no longer say a truck exerts more force on a car than vice versa), we eradicated any sensibility toward the world as well.

It reminded me of an excerpt described below:

Eleanor Duckworth (1996) describes an experiment in which children were taught about density as an explanation for sinking and floating (in a "cognitive acceleration" experiment):

"Among the rules Englemann taught the children, the principle on was : 'An object floats because it is lighter than a piece of water the same size; An objects sinks because it is heavier than a piece of water the same size. Kamii and Derman describe fascinating instances of conflicts between the rules children were taught and their own intuitions–their common sense." In addition to the rules they often gave other explanations, typical of school children their age: 'because it's heavy', 'because it's little', 'because it has cracks in it', 'because I pushed it'; or simply, 'I don't know why.'

"In other instances, the rules seemed to come between the children and their intuitions in ways that led to nonsense not normally encountered in children their age. One child hefted a large candle in one hand and a birthday candle in the other, but having seen that the both floated, maintained, 'they weigh the same.' Another child said that a tiny piece of aluminum that sank weighed more than a large sheet that floated on the surface. Clearly these children were trying to apply rules rather than coming to terms with objects. A typical 6-year-old's reaction to the aluminum foil, for example, might be to say that the tiny piece sank because it was too tiny, and the large piece floated because it was flat.

"In another part of the Kamii and Derman assessment, no longer dealing with sinking and floating, the children were asked why the water level rose in a glass when an object was immersed in it. Two of the four replied, 'Because it is heavier than a piece of water the same size.' The other two children, who tended generally to remain true to their intuitions, answered that the object pushed the water out of the way."

Duckworth (1996) On the Having of Wonderful Ideas.

Englemann (1971). Does the Piagetian approach imply instruction? In Green, Ford, & Flamer (Eds.) Measurement and Piaget. New York: Macgraw Hill

Kamii and Derman (1971) Comments in Englemann's paper. In Green, Ford, & Flamer (Eds.) Measurement and Piaget. New York: Macgraw Hill

Word List

I think my heart and mind has already left this place. I am most excited for my body to join the rest of me, because I cannot use any of the following words to describe the place I am right now:

Nurturing, caring, empathetic, sympathetic, meaningful, collaborative, exciting, curious, wondrous, inspiring, symbiotic, hopeful, loving, embedded, joyous, purposeful, tender, introspective, impassioned, uplifting, welcoming, embracing, inclusive, empowering, fulfilling, aware, creative,

...I certainly could go on...

...And I don't need all these things...

Preparing Physics Teachers in Tennessee

In July, my wife and I are moving from Old Town, Maine to Murfreesboro, TN. I have accepted a faculty position at Middle Tennessee State University in the Department of Physics and Astronomy.

The department has recently become a PhysTEC site, which means they are dedicating time, people, and others resources to preparing physics teachers. The university has also become a UTeach replication site, called MTeach. Both of these programs come with lots of support and expectations. I am very excited about the job, the programs, and my new colleagues.

In the department, I will be teaching a variety of physics and physical science courses, including some specialized content and pedagogy courses just for future physics teachers, working to further our goal of preparing more and better qualified physics teachers, and carrying out research in physics education.

I am most excited about a couple of things:

Their algebra-based physics course is structured with 5 hours of problem-solving labs and 1.5 hours of lecture per week.

• In the "lab", students do a quick "reading" quiz. Because their is little lecture time, students are expected to read some background material online before studio time.
  
• Students then typically get in groups to work on a series of conceptual questions at a computer. The questions are "FCI"-like and provide students with immediate feedback.
  
• The instructor then introduces a problem (often a goal-less problem). The instructor may model for the students how to approach the problem and then assign a new one, or he may send the students off to work right away.
  
• The students collaboratively work on the problem. They then share their solutions with the class a la whiteboards.
  
• At the end of the period, students typically work on a lab.
  
• The entire class time (2.5 hours) revolves around one big idea: From the reading quiz, to the conceptual questions, to the instructor modeled example, to the problem solving, to the lab. The course has a very "modeling" feel to it.
• In many of the classes, their is an undergraduate teaching assistant to help facilitate, because all physics majors are required to take a course called physics teaching practicum.
  

In their calculus-based course, they are switching to using Matter and Interactions. Since the school has no engineering department, this class is small (about thirty). This provides many opportunities to innovate. I'm hoping to push for some SBG.

They offer two physical science courses that are taken by pre-service elementary school teachers. I'll most likely be teaching one of those in the fall. I need to know more, but I imagine I'll be running this class similar to Student-generated Scientific Inquiry.

All undergraduate students are expected to do research and complete a thesis. Students in the physics teaching concentration will most likely be working with me.

A Master Teacher is working with the MTeach program as a teacher-in-residence.

A new interdisciplinary program in Mathematics and Science Education has been launched.

Misconceptions Misconceived: The example of current

A common misconception about electricity

If you've ever been in a physics classroom or read a paper in physics education research, you probably have heard students saying that current is "used up" in a circuit.

For example, in a one-bulb-one-battery circuit, a student might think that current is provided from the battery and transported to the bulb, where some of it is used up. Students often say that some of that current is returned to the battery to repeat the cycle, which is evidenced by the fact that you need a return wire. In thinking more specifically about measures of current, a student might say that there is more current before the bulb and less current after, because some of the current was used up. Based on this idea, once all the current is used up, the battery is dead, which explains why batteries die.

It is easy to focus on what's wrong about this:

• The current in a single-bulb-single-battery circuit is the same everywhere, not different. There are different ways to make sense of this, but a physicist often thinks of this in terms of the continuity equation– if charge isn't building up anywhere, the flow must be steady.
• The battery is also not a source of current. It provides the conditions for maintaining a difference in voltage, which provide further conditions for current to flow. For that reasons, batteries don't die when they run out of current; they die when they can no longer maintain a voltage difference. This voltage difference cannot maintained once the battery disassociates all of the ionic compounds inside (which is where the energy in the battery is stored as chemical-potential energy)
  
• Bulbs also don't use current, and current is not lost there. Current isn't "stuff" you can lose, because it's a process (the flow of stuff). But energy does "leave" the circuit system here in the form or radiated light and heat.
  

What's so Right about this Misconception?

In order to talk about what's so great about this misconception, I want to engage you with this gem. The excerpt below is from a student enrolled my science teaching and learning seminar. This particular student has never taken any physics. They were asked to read a paper about children's mental models of electricity and pick one of the mental models to write about:

"I want to talk about Model C (the current consumed model) , since that is the model I am currently stuck on. I really have no knowledge of how a circuit works and what the circuit does to provide or result in electricity. But to me, it would seem that “energy” would be coming into the light made from the light bulb, and thus the energy leaving the bulb in the form of light would result in less energy leaving the bulb in the wire going back to the battery. Also, batteries die, so one would think that its ability to provide current to the system is lost in that process. It must have gone somewhere, right?

"So Model C (which I suppose must be wrong) is reinforced by the simple ideas that we deal with regularly concerning electricity. We are told to unplug unused electronics to reduce the use of electricity… (but is that really what we are doing?) And how does this make sense: If current travels through a circuit and none is “used up”, why are our electricity bills so high? If we don’t actually use it up, why do we have to keep buying more? Model C just makes the most sense."

OK. What has this student done:

• First he identifies a puzzle: If energy is being lost at the bulb, shouldn't less of something being going in than going out?
  
• Second he identifies a bad solution to that puzzle: Asserting that the current must be the same doesn't resolve the puzzle.
  
• Third he identifies questions: Why do batteries die? Why do we pay for electricity?
  
• Fourth he is committed to sensibility (not authority): Despite knowing he is wrong, he is for all for Model C.

You should be impressed. Because this student owns his thinking. He is aware of his ideas, his questions, and his puzzles. He is articulate about why Model C makes sense to him.

His misconception makes more sense than most students' acceptance of the right answer.

Addressing Misconceptions

I have seen (to good effect) instructors and curriculum use some combination of these approaches toward "fixing" this current-used up misconception:

• Engaging students with thinking about empirical evidence that support the idea the current is the same on both sides of bulb.
  
• Engaging students with arguments for why current cannot be different. (e.g., if it were different, you'd get a traffic jam or build up of charge; or by appealing to the of matter, charge, etc.)
• Engaging students with what current "is" - it is not a "thing" or substance that is used up, it is a flow of charge (a process);
  
• Engage student in learning about and applying Kirchoff's Laws.

These approaches can be done together in a variety of ways that are effective, and they each embody something important about science and science learning:

1. Empirical evidence - what data could I collect to help address this question?
   
2. Argumentation - In light of evidence, what claims can I support?
   
3. Ontology - what is the nature of this concept or quantity?
   
4. Scientific Knowledge - how do scientists represent, talk about, and use these concepts?
   

For that reason, Kudos to us for engaging students with important aspects of science as they learn something that is hard to learn.

But where do these strategies miss the mark?

They are all built around the idea that students' thinking has more to do with current, than the questions, puzzles, and the desires for explanation from which those ideas emerged.

From my experience, the students I encounter are not really trying to explain anything about current. They are trying to make sense of how bulbs and batteries work: They have ideas about what aspects of the situation are in need of explanation. They also have questions about how it works. They are capable of recognizing puzzles and inconsistencies. And they have some ideas about how they might explain and address those questions. The above excerpt has more ideas about "energy" than about current, and I'm impressed.

But I shouldn't be that impressed. Why? Because the excerpt above is fairly characteristic of the students I encounter in the real world when I talk to them about bulbs and batteries. Of course, if I hand them a multiple choice pretest about current, they look like they have a misconception about current. But when I talk to them away from worksheets and multiple-choice instruments–when they know that I care about what they think and that they will have to put some care and effort into expressing their ideas to me– they talk about evidence, and ideas, and inconsistencies, and questions. And sometimes they bring up ideas like energy, current, voltage, and sometimes they use those words in ways that I wouldn't. But is that a misconception? I'm not so sure.

The questions and ideas that arise in those conversations are way more interesting to me than this question:

Is the current at point C greater than, less than, or equal to the current at point D?

--> Who asks these questions anyway? No one in the real world asks questions like that. My students are way more interesting and critical with their own questions.

So here's the problem:

The four strategies to eradicate students' misconceptions do not address any of the questions or issues that perplex students.

By focusing on immediately on current, we are simply trying to correct a detail of their thinking that we are unhappy about. In doing so, we stamp "current must be the same" over the students' interesting questions and insights. And, sure, maybe we even do this in an intellectually honest way so that they really understand deeply why current must be the same. But I fear that along the way we've lost their interest, curiosity, and sense of access to the phenomena. Or we've replaced with a false sense of interest–an interest in superficial understandings.

How I Reconcieve Misconceptions

I will say, in most classes I have experienced, I see instructors spending way too much time trying to eradicate misconceptions. I, instead, try to choose to pursue and explore the questions and puzzles students identify. Along the way, misconceptions seem to corrects themselves through the honest pursuit of students' ideas and questions, because we've been exploring and refining those ideas along the way. And while I may want to monitor misconceptions, I shouldn't be fixated on them or apply too much press on them. The truth is, the more pressure I apply to this misconception, the quicker students learn that I am there to correct them. Once that happens, game over.

So when my students say that current must be different, I don't hear a misconception. I hear an ingenious way of trying to answer the question, "Why do batteries eventually die?" and a good explanation for how bulbs can be a sink for energy.

When a student balks at the idea that "current is conserved", I think, "Great, it doesn't make sense, does it?" When students don't want to accept that answer, I see them as being committed to sensibility (not to authority).

I'm MORE worried about the students who quickly accept the "right" answers. I really am.

And then end of the day, I'm not interested in stamping out misconceptions and replacing them with impoverished ideas, nor am I interested in having students ignore perplexity in the world.

SBG: Transparency, student involvement, temporal patience, and diagnostic precision

OK. I am enamored with all that is going on with standards-based grading:

Here's four reasons why:

• I love that the skills and concepts that are to be assessed are made transparent. They are made transparent to students. But the work a teacher has to put into to making them transparent is an important means toward clarifying norms, expectations, and outcomes for oneself, for one's classrooms, and in one's community.
  
• I love that students are involved in self-assessment. Students get to keep track of what they are learning. They know what they know, and know how to improve.
  
• I love that assessments make learning a priority, and this is done by exhibiting temporal patience. It doesn't matter when you learn, only if you learn. Assessment reach into the past, present, and future, but they are largely about the present.
  
• I love that assessments are diagnostic. The (attempted) isolation of skills makes the diagnostic element of teaching much easier.
  

So here's the thing. If what I love is transparency, student involvement, temporal patience, and diagnostic precision, is standards-based grading the only way to go? I don't think so. But it's been a great entry into my re-thinking about assessment.

What do you think? What other assessment systems meet these criteria? What important features of assessment am I missing?

The Setup

When I first started teaching in "somewhat-reform-minded" college physics courses, I remember learning that I wasn't supposed to give students the answers. I was also never supposed to "lecture" or tell students if they did something right (or wrong). The implicit philosophy was that somehow this was supposed to make me a better teacher and that it would make students learn more. "Students have to do it themselves" was the takeaway message.

Now, I understand that physics is not a spectator sport (students DO have to do it themselves with guidance, encouragement, and support), but I also know this

What we do TAs in preparing them for "reform" courses is a set-up:

• First, it is a setup to take away from students something that has for so long been valued (answers) without replacing it with something else that can be valued (equally or more than answer)
  
• Second, it is a setup to take away TAs' easiest and most natural way to praise students (for getting right answer) without replacing it with tangible ways to praise students in other ways
  
• Third, it is a setup that we fail to give TAs any reasonable tools for interacting with students in ways that tacitly change the value-system in the classroom

As I see it, we often blame students (for just wanting answers) and blame TAs (for not being good reform teachers). Often the blame game involves identifying the bad "beliefs" and "attitudes" that students or TAs have about learning. This, I tell you, is part of the setup. We put TAs and students in a fundamentally "bad" situation, and blame them for the "bad" things they do.

The way I see it– we have designed a systems in which classroom discourse with and over worksheets dominates the classroom environment. And here's the problem. Worksheets can only really do two things: make statements and ask questions. And those questions tacitly send the message that answers are what matter.

Think about all the things that worksheets can't do? Worksheets can't value questions, or creativity, or having a sense of curiosity or wonder, or individuality. They can't value patient problem solving. They can't smile or get excited with you. They can't value persistence through confusion.

Once again, this is part of the setup. We tell TAs not to value (or give) answers, but we pit these TAs against a system in which all the material structures around implicitly value answers. Questions on worksheets demand answers. But if TAs or students seek out answers, we blame them for not having sophisticated beliefs.

We have put TAs in the garden of "answers" and have told them not to let anyone bite.

So what would I do differently with TAs?

Man that's tough. But the answer has to involve thinking of TAs as capable of being good teachers and of students not inherently seeking answers. We have to think of simple skills that we can have TAs practice that will help them grow and that will help establish different classroom conditions. Conditions in which TAs and students aren't constantly having to avoid doing "bad" things.

One thing that I'd have all my TAs practice:

I'd have my TAs practice listening to what people say and writing it at the board in real time.

For many of my colleagues, the blackboard is sacred place where only correct science ideas can be written. Think about this: How comfortable do you feel writing WRONG ideas on the board. This is something I had to get over, but it's not hard with practice. I want TAs to practice writing what their students say (right or wrong) in such a public space. I want the blackboard to become ingrained a sacred place where student ideas get written.

Why do this?

• First, writing requires listening and interpreting. Paraphrasing what students say requires a different kind of listening than purely evaluating does.

• Second, writing gives TAs a more tangible job to focus on rather than what is mostly automatic (i.e, responding to the correctness of ideas). Telling TAs to write down student ideas is WAY better advice than telling them "don't give away answers", and is more easily carried out than more sophisticated "talk moves".

• Third, writing at the board means that TAs are not constantly facing their students for appreciable amounts of time as students express ideas. This may sound silly, but this takes away a lot of the pressure of TAs to respond. It naturally builds in wait time, which is something I want my TAs to practice. Writing at the board protects me from getting into I-R-E patterns of discourse. With the face hidden more of the time, my poker face becomes less important.

• Fourth, it is hard for new teachers to verbally value students' wrong ideas in authentic ways with out lots of practice. But writing ideas down concretely values those ideas by making them public and durable. This helps to build the culture of "not valuing only answers" in a way that TAs can do.

On the Virtues of Knowing the Virtues of not Knowing

This post over the Physics! Blog! got me thinking about how important it has been for the students in my science teaching and learning seminar to have read an essay called, "The virtues of not knowing".

The essay from Eleanor Duckworth can be found in an amazing book called, "The Having of Wonderful Ideas" . I would recommend this book to anyone interested in science, science teaching, or research in science education research.


Here are several passages from that essay:

"Of all the virtues related to intellectual functioning, the most passive virtue is of knowing the right answer. Knowing the right answer requires no decisions, carries no risks, and makes no demands. It is automatic. It is thoughtless.

"In most classrooms, it is the quick right answer that is appreciated. Knowledge of the answer ahead of time is, on the whole, more valued than ways of figuring it out.

"... The virtues involved in not knowing are the ones that really count in the long run. What you do about what you don't know is, in the final analysis, what determines what you ultimately know.

"It is, moreover, possible to help children develop these virtues. Providing occasions such as those describe here , accepting surprise, puzzlement, patience, caution, honest attempts, and wrong outcomes as legitimate and important elements of learning, easily leads to further development. And helping children to honestly come to terms with their own ideas is not difficult to do.

"The only difficulty is that teachers are rarely encouraged to do that... Teachers are encouraged to go for right answers, as soon and as often as possible....

"It would make a significant difference to the cause of intelligent though in general, if teachers were encouraged to focus on the virtues of not knowing, so that those virtues would get as much attention in classrooms from day to day as virtue of knowing the answer."

One reason why this reading has been so important in our class is "The virtues of not knowing" has become both a catch phrase for calling attention to moments of puzzlement, curiosity, questioning and a lens through which to see ourselves in a positive light. We not only exhibit the virtues of not knowing, the phrase lets us call attention to and celebrate it.

How do you celebrate the virtues of not knowing in your classroom?

Part of a group, but still an Individual

Yesterday in my science teaching seminar, we had an hour long discussion about, "Are all the colors in the rainbow?" My students were very engaged with the discussion and we also had a lot of fun. There were lots of good questions and ideas that you can read about here.

Afterward, we talked about what makes a science conversation interesting, and I have been deeply moved by something profound that one of my learning assistants said:

"I liked feeling like I was part of a group, but at the same time, I was still an individual."

All I can say is wow.

Who are we kidding? Apparently not my LAs

Here's an example of the kind of worksheets students are doing in college physics courses around the country and also here at my university. I have no doubt that students working through these worksheets (especially in groups) is better than having them silently watch a graduate TA work out problems at the blackboard. But who are we kidding with this stuff?


Apparently not my LAs:

On the heels of a reading about the difference being "univocal" discourse and "dialogic" discourse, this is what one LA had to say about the class she teaches in that uses these worksheets:



I love how this LA feels that this worksheet is a trap for both the teacher– "The teacher is limited to this because of worksheets..."– and for the students, "You must realize the exact answer it is asking you for"

This LA also realizes that what appears to be open questions about science are really closed questions, "Questions could have more than one answer... however, you realize that it was asking for a particular answer."

And how this LA connects the worksheet structure to how students behave: Students are asking questions like,"What are they looking for here?"

This should disturb us–not about our students, but about our worksheets. What are we doing to them? These students aren't asking about the physics, they are asking about what they are supposed to put down on a piece of paper. Seriously, don't get me started on a conversation about who is "they", anyway.

But here's the question:

If my LAs aren't duped by worksheets after reading just one paper about the nature of discourse in math and science classrooms, why are so many of my colleagues?

Why I am doing more science with my LAs

OK. So here's the thing. This semester, I am teaching a one-credit "science teaching and learning" seminar for undergraduate learning assistants (LAs).

I have ten undergraduate science students for a little over an hour per week. Each of them helps to facilitate some classroom learning activities in a course they did well in previously. Four of them teach in introductory chemistry in what is called "Peer Led Team Learning". Six of them teach in introductory physics using "Tutorial in Introductory Physics"

My class is supposed to help them be successful in their classroom teaching experience by giving them tools for questioning, listening, and promoting productive group work. A secondary goal is to expose them to variety of issues in teaching and learning with the hopes that they will take an interest in teaching, and decide to become certified to teach in secondary science.

When I first started teaching this class, I was closely following the model of the Colorado Course. They are doing great things over there, and they have over a hundred LAs per semester distributed across many departments and colleges. I visited last October for their LA workshop and got to experience firsthand what they are doing.

For me, their course structure and guide was a great starting place, until I realized something:

My LAs don't necessarily value conceptual understanding, inquiry, or deep-engagement in science.

Sure, they have moments where they do. Somewhere we all realize the importance of deep learning and the deep shallowness of school to engage most with deep learning. But those moments are tempered by the realities of their (mostly bad) college science courses, where they are required to memorize a million things and perform well on high-stakes tests. My LAs value doing well in school, and I don't blame them. They want to go to med school. They want to get good engineering jobs. In the worlds they live in right now, GPA is currency.

So where does my course fit in? C'mon. Let's face it. Do I really think my students are going to come around to valuing inquiry and conceptual understanding by reading some papers about teaching and learning? Do I really think my students are going to value inquiry and conceptual understanding just because they are teaching in classrooms where students work in groups? The courses they teach in are "band-aids" at best. There is lots of pseudo-teaching going on. Students sit in groups and are dragged by the teeth through some reasoning that a worksheet demands of them.

I don't want the papers we read or "pseudo-reform" teaching to be the thing we hang our hats on. Sure, I want us to draw on various papers to inform our discussion and to challenge our own thinking. Sure, I want them to reflect on and critique the teaching they are engaged with.

So what did I do? Most importantly, I have committed the class to doing more science and doing that science together. If we a read paper about problem solving, I engage them in problem solving. If we read a paper about formative assessment, I run a science lesson in which I model formative assessment. If we read about conceptual vs. algorithmic problems, you bet we're going to be doing both of those and discussing the difference.

After we've done some science (and have a shared common experience around doing some science), then we can talk about teaching and learning through the lens of the paper we've read.

I am certainly still struggling to do a good job with this course, but at least I think I've nudged in the right direction. One of my persistent concerns is that I have made too many "one shot wonder lessons". They are getting to experience some good one day lessons that are perhaps fun, engaging, and involve the beginnings of deep learning with content; but teaching is also about the coherence of those lessons over time and sustained engagement. In what ways am I misrepresenting the profession? Could I do any differently with a little over an hour each week? I think I could if I made sure I was teaching the same science topic each week. But that would require some serious planning, and not just mid-semester adjustments.

What could you do with this?

Here are photos of the sunrise taken from my balcony. One is from August. The other is from January. What question could I ask students? What questions could my students ask? What could I ask them to do with this?

A Conversation I Try to Avoid

What kinds of conversations about teaching or learning do you avoid having?

There are two kinds of conversations I have learned to avoid having with most people:

• Conversations about what students can't do
• Conversations about the misconceptions students have

And I want to be clear that these conversations are distinctly different from similar conversations I enjoy and find immensely productive:

• Conversations about what is hard for students to learn?
• Conversations about why those things are hard to learn?
  

What's the difference? The first conversation is about students as objects - they are filled with inabilities and misconceptions. It is about students being hopeless.

The second conversation is about students, classrooms, and content; and the potentialities for learning that exist if we get it right.

So here's the hard thing. There are a lot of people who want to rope me into the first conversation- about hopeless students filled with negative things. This happens to me at conferences. It happens to me in the hallway. It happens in papers, in books, and in proceedings.

But, now, here's the harder thing. My first instinct is to enter into that conversation with the hopes of changing that person's mind about their students and the conversation. I have often tried to coyly change the conversation into this one:

• A conversation about what students can do (or might be able to do soon)
• A conversation about what ideas students might have that serve as productive beginnings
  

And while I think this third conversation would be great to have, it never turns into that conversation. Because that person wants to talk about what students can't do. So, now with most people who want to have that first conversaton, I simply say, "I don't want to have a conversation about that." And I walk away.