This is a paragraph from MTSU’s MTeach Website

Are you interested in teaching Physics and Mathematics?  Are you a Physics or Mathematics major with a concentration in Education, and are you interested in certification in both areas?  The Noyce Physics-Mathematics Teacher Scholarship offers up to $10,000 a year for a maximum of two years.  In exchange, the recipient will agree to teach for two years in a high-need Tennessee school for each year of scholarship awarded.

I don’t have data to back this, but almost all of the MTeach students that I know (those focusing in physics) are struggling to do well in their classes. Some of those students are failing my physics class. Others have just let me know personally that they are scraping by in their intermediate / upper-level math and physics couses. These students are surprised and concerned, because they’ve typically always done well.

I think one big reason they are struggling is because they are taking on more math and physics class than they can handle. Taking 2 physics courses and 2 math courses and 1 or 2 education courses sounds like a nightmare. (Aside: I never took more than 4 classes per semester while in college, and I often took just 3 classes). I think the reason they are taking more math and physics classes than they can handle is because it involves $10,000. I’m not positive, but I think the scholarship is now $15,000 dollars to do both math and physics. It’s also possible that students are being strongly advised to do this, and independent of the money, they feel like this is what they are supposed to do. Whatever the reason, students are doing it, and seemingly struggling as a result.

Surely, an environment in which students are scraping by on a bloated academic schedule in order to get a scholarship can’t be the best environment for future teachers. Right? I mean, I’d rather invest $15,000 for a good physics or math teacher than $15,000 for merely an accredited teacher in both areas. There’s a big difference between taking classes and immersing yourself in the content of a class. I worry that that $15,000 is forcing students to take to many classes, for which they superficially learn a lot of things instead of deeply learn a few things.

Let’s face it. These scholarships are really important to many students. One student in my intro physics class works 30-40 hours per week on top of being a full-time student. If this student passes my physics class, they are eligible to apply for the scholarship. If not, they have to wait another year.

Throwing money at problems, especially teaching, can have unintended effects. Overall, the MTeach program is in its infancy; there’s so many program logistics that will get tweaked and changed. Someone over there should look at the hard data to see how out math/physics students are faring. If they aren’t faring well (like I suspect), we’re going to have to figure out why, and ask the question, “Is our scholarship policy incentivizing failure?”

We seem to make a big deal in intro mechanics that x- and y- motions are “independent”. There certainly are in a limited number of cases (constant forces, linear drag forces, and linear restoring forces, for example) in which the force dynamics described among cartesian coordinates are separate. But this condition isn’t true in most situations (gravitational forces, electric forces, magnetic forces, non-linear drag, non-linear restoring forces). Still, in many situations, we can still find a coordinate system in which the forces are separable. For example, all the non-linear restoring forces (gravity, electric, rubberbands) are separable in (r,θ) coordinates, but the magnetic and non-linear drag forces I don’t think are separable, at least not generally so.

I could be wrong, but I think all (or most) force (fields) that can be described by the gradient of a scalar function will have at least one coordinate choice for which the force dynamics separate. This requires some further inspection, but it has to do with curl being zero. Linear drag forces are, of course, non-conservative; but they “nicely” separate due to a cancellation of factors that would otherwise couple them. This nice cancellation doesn’t occur with v² dependent drag forces, so non-linear drag forces are not separable.

I’m not sure, butI think when we teach this notion of “independent motions”, we are confusing independence with orthogonality, or perhaps separability with orthogonality. X and y cartesian coordinates are certainly orthogonal, but motions described using x and y coordinates are only independent (or separable) under circumstances in which they aren’t coupled.

Anybody know the history of teaching “horizontal and vertical forces” are independent? My suspicion is that it is an over-generalization from projectile motion.

Every student who wants to apply to the college of education at MTSU has to be interviewed by a bunch of different people. I’ve been asked by several students to do this. I don’t really know the purpose of the interviews, but every student explains it like this: “You just ask me about why I want to be a teacher and then you fill out a form.”

I’ve decided that “Why do you want to be a teacher?” is the stupidest question ever. In fact, I can’t hardly imagine a worse question. So I have been thinking about what questions I am going to ask students instead. Here’s my rough draft of possibilities:

• What’s your most meaningful learning experience (// in school // out of school)? Tell me about what you learned and how you learned it. What made that learning experience particularly meaningful?
• What role did other people play in helping to make that learning experience so meaningful? Are there other factors that helped?
• Of all the skills and knowledge that a teacher needs to engage students in such meaningful learning (like the one you described), which skills do you believe are most important  // believe take the deliberate practice to develop?
• What do you think great teachers do throughout their careers to develop these skills? What do you see yourself  doing over your career to ensure that you continually work to develop this set of “hard-to-develop” skill set?
• In the short term, what goals have you set for yourself? Why are these goals important to you? What specifically are you doing to work toward those goals? How will you know if you are or are not making progress toward those goals?
• Tell me about something that you understand well now, but really struggled to understand early on.
• Tell me about your biggest fear / worry in becoming a teacher. Why does this worry you?
• Outside of teaching and school, tell me about three things that you value most about the yourself and the life you lead. Why do you values these things? How did you come to value these things? What impact does this have on others around you?

I’m hoping you all will weigh in and help me figure out what’s best to ask.

Issues that are on my mind today about the intro physics course I teach:

(1) Students don’t get enough individual feedback from me, partially because almost everything in class is done in groups, but their high stakes assessments are done individually. This is not good for students (especially those that are struggling). Plus, for me, it makes assessing and diagnosing individual students difficult. I need to get students doing more individual work for which they can get feedback, even if that’s not part of the model for the class.

(2) What little individual feedback they do get from me (mostly on lab reports) is for things that are borderline irrelevant / on the margins of importance. This makes me spend my time “grading” student ability to write their lap report in the correct format rather than “assessing” their understanding of disciplinary ideas and skills. That, and it gets students really focused on the wrong things—looking for ways to make sure they dont’ lose points in the future rather than learn.

(3) The overall grading system has so much “stuff” with so little substance– reading quizzes, project presentations, project reports, discussion quizzes, clicker participation, checked labs, and graded labs. There is nothing in those parts of the grading system that point them to what is important to learn. Rather, it seems to point them toward what bases are important to have covered to get a good grade or be positioned to get a good grade (if one performs well on tests). Students who struggle to understand (and do poorly on tests) can’t spend time trying to learn and understand because there are too many hula-hoops to jump through in order to guarantee enough fluff points that a good test grade will even matter.

(4) I have growing concerns about differences in performance outcomes among different populations I teach. Without going into details, there are certain combinations of race and gender are faring well and certain combinations that are faring not-so-well. This is probably typical of college physics, but it’s still weighs heavily on my mind.

What we know about stacking transparencies…

Cyan + Magenta = Blue

Cyan + Yellow = Green

Magenta + Yellow = Red

One Theory to Explain this pattern is the following

Cyan filters block out all RED (leaving primarily blue and green) — blue/green looking cyan jives with their intuition

Magenta filters block out all Green (leaving blue and red) — blue/red looking magenta jives with their intuition

Yellow filters block out all Blue (leaving Green and Red) … leaving question why does green/red look yellow? Not-intuitive

This theory is somewhat uncommitted about what happens with oranges, yellows, and violet;

The theory goes:

Cyan (blocks red) + Magenta (blocks Green) = Blue Left Over

Yellow (blocks blue) + Magenta (blocks green) =  Red Left Over

Cyan (blocks red) + Yellow (blocks blue) = Green Left Over

Another Theory Goes like this

Cyan enhances blue and green maybe even yellow and dims other

Magenta enhances blue, red, and violet (and may even yellow/orange) and dims others

Yellow enhances yellow and dims others

The theory goes like this

Cyan + Yellow gives Blue, Green,Yellow enhancements , making an overall Green Appearance … this jives with their intuition

Magenta + Yellow gives Blue, Red, Violet, and Yellow, Orange enhancements … Not sure why this come off just Red?

Cyan + Magenta = Blue (enhanced twice), Green, Red, Violet, Yellow, Orange … why does this come off as just blue?

 

Both theories have gaps and puzzles. However, Caroline invented a theory, which seems to fill in a lot of gaps for both theories.

Caroline’s Extended Theory of Opposition

Blue / Orange are Opposites (…we do find that stacking orange and blue gives a dark appearance)

Violet / Yellow are Opposites (…we didn’t have violet transparencies… but yellow and purple gave a dark red)

Red and Green are Opposites (…we do find that stacking red and green gives dark appearance)

The Theory Goes like this

Since Magenta contains both Blue and Red, it probably blocks out both oranges and greens!

Since Cyan contains both Blue and Green, it probably block out both red and oranges!

Yellow blocks out Violets. Since it must also oppose blue, does this mean that yellow contains orange? 

How Caroline’s Opposing Theory Fills in Theoretical Gaps

Caroline’s Theory fills in a lot of holes in theory #1, by detailing what happens to Orange, Yellow, and Violet…

It says that Cyan (blocks Red and Orange), leaving not just Blue and Green, but Yellow and Violet

It says that Magenta (blocks oranges and greens), leaving not just Red and Blue, but also Yellow and Violet

It says that Yellow (blocks violet and blue), leaving Red, Orange, Green, and Yellow

Caroline’s Theory also fills in holes of theory #2, because it can explain complicated mess of why Blue and Red end up

Blue + Red + Violet + Yellow + Orange = Red . This is because Blue/Orange and Yellow/Violet are opposing, leaving only red unopposed

Blue (x2) + Green + Red + Violet + Yellow + Orange = Blue. This is because Red/Green Oppose, Yellow/Violet oppose, and One Blue is opposed by an orange, leaving only one blue unopposed.

In my inquiry class, we are sorting through a surplus of observations about what happens when we stack various colored transparencies. I decided to narrow the focus down from all transparencies to just CYM, so that we can try to pin down some things in a certain arena without having to worry about everything all at once.

We have (at least) 3 ideas about how colored transparencies work. Here’s is what I think those theories are:

Theory #1: Transparencies are Color Activating (or Enhancing)

White light has all the rainbow colors available (ROYGBIV), but white light by itself is mostly colorless. It is colorless because none of those colors are activated. When white light hits a yellow transparency and then goes through it, the yellow component of white light becomes activated (or now visible). All the different colors of light get through, but only the yellow light is activated. Transparencies work by activating some portion of the rainbow colors but not all of them.

How this theory explains and accounts for other phenomena:  This theory explains why we see green when we stack Yellow and Cyan transparencies in the following way: After enhancing the yellow light, all the unactivated light continues on where it reaches the cyan filter. The cyan filter activates both Blue and Green. So now, both green, blue, and yellow are activated. Green is obviously present from being activated by by Teal, but the blue and yellow activated light blend to make more green. Thus, yellow, blue, and green give the overall appearance of green. One group says this theory can also explain other CYM combinations, by noting that magenta must enhance much more red more than blue.

Theory #2: Transparencies are Color Changing

Transparencies work by changing the color of light. For example, white light is white. But white light upon a yellow transparency causes the white light to undergo changes which make it yellow. Of course, different colored lights upon the yellow filter will change the color in different ways. For example, the magenta light on yellow the transparency changes the light to be green light. Different colors have different rules.

I’m not sure if hidden in this idea is a “blending” or “averaging” idea–meaning that maybe we could come up with some rules. But it seems like the idea is “colors mix in weird waya” and you just have to go observe every combination to learn each rule. I think what I can appreciate about this idea is that it doesn’t assume that there should be simple rules: Why should we expect a yellow filter to have the same behavior when different colored lights shine through them? Can’t the change it induces be particular to the kind of light we shine on it?

One limitations of this theory (so far) is that it has a difficult time making predictions because it sort of says, “Go out in the world and find out what all the rules, because the rules are different for all the different combinations”. It’s feels almost anti-theoretical.

Theory #3: Transparencies are Color Filters

This idea also focuses on white light having all the rainbow colors.  Transparencies work by blocking some colors and letting other colors through. For example, many groups decided that we know both Magenta and Cyan must let a good amount of blue light through, because Magenta stacked on Cyan make blue. So a lot of blue light must be getting through. Most groups thought that Magenta must let mostly red and blue (and maybe purple, orange and yellow), and that teal must let through mostly blue and green (and maybe purple and yellow). They explain that blue light results from stacking Cyan and Magenta because it’s the only color that doesn’t get filtered out. I’m interested to see what these groups say about yellow as a filter.

The Big Picture: Assessing student theories? Assessing disciplinary knowledge?

Most of the time, we assess student ideas in terms of correctness. Most of you know which of these theories is more closely aligned with current scientific understandings. However, without correctness, how do we assess the “goodness” of a theory or of an explanation. I think the only refuge is to think about how the scientific community assesses scientific theory, because in science we don’t have the answer key to tell us what scientific theories are correct. Surely there are some criteria for judging some theories to be better than others. Surely we must have ways of assessing scientific explanations in light of the current ideas and evidence we have.

I’d say that right now, I think the “activating color theory” is the best theory… It has the most specificity (details which filters enhance which light), coherence (tells a consistent story for each situation), and has explanatory power (explains all CYM combos).  #2 is almost simply a statement of observations at this point. #3 has some good beginnings, but at this point, it still needs some fleshing out. Yellow in particular is going to represent some serious hurdles. We’ll see where this leads us, and I’m happy to keep all of theories along, pressing upon them in different ways that I think will nudge us all along together.

Of course, to be fair, I also have reason to believe that not everyone has well-distinguished theories. I think many hold some combination of #1, #2, and #3 and they certainly aren’t well articulated or committed theoretical frameworks. So Where do we go now? They have a homework to write about their theory for transparencies (how they work in general for CYM in particular), and how their ideas explain stacked CY, YM, and CM.

Andrew Heckler, a physics education researcher at the Ohio State University, wrote an interesting paper about the consequences of prompting students to draw free-body diagrams. Heckler found that asking novice college students to draw free-body diagrams as part of physics problems has some interesting (negative) consequences for their problem-solving. It’s worth reading yourself, but here are some notes.

One problem involved asking students to simply identify the forces exerted on a basketball rolling across a ‘frictionless’ floor. (correction: the problem states that friction is small enough to be ignored)* Students who were asked to draw and then identify were more likely to identify a “force of motion” than students who were not asked to draw a diagram. Why might this be so? I’d speculate that it’s simply compelling to draw an arrow in the direction of motion as part of a sketch. Then, upon seeing what one has drawn, one is persuaded into thinking that it must be a force. My argument is that it isn’t so much that students have a force of motion misconception, but that there is a dynamic between what one draws, what ones sees, and how one responds. Drawing an arrow in the direction of motion is part of the dynamic by which students engage in thinking that there must be a force in that direction.

Another problem from the study involved students having to figure out the minimum mass needed to get a box initially moving where in the problem the box is being pulled on by both sides with known but different forces and there is friction. Once again, some students were just asked to solve the problem, and other students were first asked to draw a FBD and then solve the problem. With this problem (as with the others), students were more successful in solving the problem when they weren’t asked to draw FBD.

Many of the students who were successful used intuitive approaches that were not taught. One of these approaches Heckler calls the two-step method, in which students first simply subtract the two pulling forces, and then set them equal to the friction force. Some students even went so far to draw 2 different diagrams, one with only the pulling forces opposing each other. And then a new one with the combined pulling forces opposing the friction. In contrast, students are taught to draw 1 FBD that shows all the forces, and then they are taught to write out a complete ΣF statement. The students’ intuitive approach has several benefits. First, it has a divide and conquer strategy–if you can’t figure everything out, start with what you know and work from there. Second, it allows you to figure out the direction of the friction force along the way, instead of having to guess and then adjust at the end if you find you’ve gotten a friction with a negative sign. Third, since the strategy makes sense to the students, they have ways of spotting errors and correcting mistakes along the way. When students take the expert approach, they are more likely to make mistakes and less likely to correct mistakes.

Overall, Heckler found that students did not typically see the FBD as a way to help organize the problem or to check for consistency. Rather, FBDs were more of just something an instructor was asking you to do. In fact, many successful students would draw a wrong FBD, and then proceed to ignore it, so that they could solve the problem correctly using an intuitive approach. And many students who drew incomplete or wrong FBDs often still solved the problem correctly using an intuitive approach. Still, overall, students who weren’t prompted to draw diagrams did better than students who were.

Intuitive Approaches in Energy in my Classroom

Speaking, of intuitive approaches. Last week, I showed students how to draw energy pie charts instead of starting with equations for energy conservation. This led students to use some intuitive approaches that were successful, but quite different than the formal approaches. In one problem, a roller coaster started a height of 85 cm and then goes around a loop with a radius of 17 cm. Students were asked to find the speed at the top of the loop. The formal approach would have students write

PEi + KEi = PEf + KEf

mgH + 0 = mg2R + 1/2 mv²

but several student groups noted that 34 cm was 40% of 85 cm, which meant than the potential energy on the loop was 40% of the original , leaving 60% of the initial energy for Kinetic.

They then wrote this equation

KEf = .6 PEi

1/2 mv² = .6 mgH

I let students go down this path, knowing that this approach might not be easy to implement all the time. Instead  of steering them away from it in the moment, I let them continue. In order to make sure they had an opportunity to make contact with the formal approach they would be expected to use on the exam, I then had them explain their solution to another group, and that other group share their approach, which was more closely aligned with the formal approach.

The Big Picture

I’m pretty convinced that students have a wealth of problem-solving strategies and reasoning skills that go untapped when we teach formal methods to soon. It leaves these formal approaches disconnected from the the good things students have to bring to the table. Of course, I know that students’ intuitive approaches will need to be formalized at some point, and that many intuitive approaches will run into problems later. But I feel that teaching students to use formal approaches without helping them anchor it to their own sensibilities and ideas is much more problematic. I’d rather help them to refine and objectify their own approaches, and introduce formality as authentic need arises.

* Note that many physicists will initially have a problem with this. They’ll say, “Rolling on a frictionless floor? That’s impossible. This question is flawed!” Remind them that students often believe that force is required to maintain motion, and that this is a misconception. Then ask them if they have a similar misconception that rolling (or spinning) objects must be maintained by a torque.

I think when most of us introduce vectors, we mostly focus on the differences between scalars and vectors. I try to convince students that almost everything they know about numbers applies to vectors. I tell them this because there are so many good things they can bring over from numbers, and only a relatively few number of ideas that can go awry. Here are some good things you want your students to bring over from numbers to vectors

The orientation of symbols that represent numbers (or vectors) are important because they tell you about their meaning

For example, 6 and 9 are not the same symbol. Of course, students exploit this property of number symbols all the time to write funny words in calculators.

Symbols that represent numbers (or vectors) can put into new arrangements in order to make it easier to carryout certain procedures with them

For example, 71 + 82  is the same as 71

      +82

When we do this, the meaning of 71, 82, and + don’t change. It simply allows us see how place values compare so that one procedure for adding becomes easier to carry out.

Symbols that refer to “whole” can often be described in terms of “various parts”

987 =  9 x 10² + 8 x 10¹ + 7 x 10°

987 = 900 + 87

987 = 460*2 + 67

This is something students struggle with even with numbers–decomposition and re-composition. So it’s not a surprise it’s hard for students to understand vector components, and odd things like vector components with tilted axes.

Getting back to Vectors

While it’s true that all these properties are also important with vectors, instruction with vectors often makes it seem like these things are special, unique, and weird about vectors. They emphasize how you must carefully move vectors without rotating them. They make a big deal about how you move vectors to carryout procedures of adding them. They make a big deal about how you can write vectors in terms of components.

I’m not saying that students don’t have to learn some new ideas,  procedures, and to learn to distinguish scalars from vectors. I’m just saying let’s not pretend that vectors are all that different than scalars. The difference is subtle, somewhat like the difference between a square and a rectangle. Both squares and rectangles are quadrilaterals. They have a lot more in common than different.

Magnitude and Direction?

Another interesting thing about how we teach vectors comes from something I recently re-read in A. Arons’, “Teaching Introductory Physics”. Arons reminds us that we teach most students that vectors are “magnitude and direction”. Arons points out that vectors commute upon addition, which is something also true for numbers. But Arons reminds us that this is not true for all things with “magnitude and direction”. Everyone familiar with rotations knows that finite angular displacement have both magnitude and direction, but that they don’t generally commute upon successive displacement. Arons points out that “magnitude and direction” is not only a wrong definition for vector. Nor is it just an incomplete definition. He seems to suggest that it is misleading and possibly not generative for later learning. He proposes that it should be emphasized that anything that commutes is a vector. This, of course, make scalars a kind of vector, which is actually how we kind of think about scalars as zeroth order (or rank) tensors. Scalars are a special kind of vector (or tensor) that doesn’t transform under rotation. This makes the analogy about squares, rectangles, and quadrilaterals a little closer to the truth.

I’ve heard a fair amount of these kinds of statements throughout the year in my inquiry course

“I’m not good at science.”

“I don’t think scientifically.”

“I can’t think the way scientists do”

“I don’t like science”

“I’ve never liked science”

So last week, I asked my students to write a blogpost about why a child in their class might say something like, “I hate math. I’m not good at math, and I never will be”. Specifically, I asked them to discuss the experiences this child might have had or be having that would lead them to feel this way about math and themselves. After having wrote their blog posts, they are now reading about Carol Dweck, and the effects of praise and mindset, and I’ve asked them to go back and reread what they and others wrote.

There was a large variety of responses in the blog posts, but the most compelling one’s were from students who identified themselves as that student. Here are some of things they wrote about. Bolded areas not in original, but were added for emphasis:

“I went through early elementary doing well in math. It wasn’t until those darn multiplication tables in 3rd grade that I made my first ever C on my report card. Ever since that experience, I’ve had a bad feeling toward math.”

“I was too intimidated to ask for help because I thought my teachers and peers would think I was an idiot for asking something that maybe everyone else understood.”

“In my experience I had several other students in my classes in 3rd and 4th grade that I remember as being pretty advanced and fairly fast when it came to learning math and science but especially math. I would find myself frustrated at not being as fast as some others and that frustration only added difficulty to my ability to understand math. Plus I just had hard time comprehending some of the more difficult concepts and I didn’t want to embarrass myself in front of others.”

“For my brother, he hated math because he made B’s and C’s whereas I would make A’s and B’s and he felt like he didn’t understand it as easily as I did so he wouldn’t want to try.”

Saying I hated math covered up for answers I may have gotten wrong. “Well, I hate math so it was expected that I missed those.” This may be the way students hide that they do not understand. They may feel embarrassed or not as smart as their peers for getting the wrong answers.

I can definitely relate to this student because I was this student at one time, and sometimes still think of myself in this way now…. A students begins getting lower grades in math than desired, and might even start to compare his or herself to the rest of his or her classmates…

I hated math too… maybe the student is comparing their ability to someone else’s and they are upset because they do not think they are as good as their friend.

My 6th grade algebra teacher told my mom “Jane Doe is a good girl and I never have any trouble out of her but she is just not good in math and I don’t have time to work extra with her”.  I remember her saying this to my mom with me standing right beside her.  I knew I didn’t catch on to math at the same speed or in the same way as some of my peers but up to that point I had not thought that I was really bad at math.  From that day on I thought I stunk at math…my teacher said so…..this was just my lot.

What are you noticing? Here are some of the things I notice

• I see the impact that our current grading systems have on students’ feelings of self-worth
• I see how children use shifts in (math) identity as a mechanisms for maintaining self-worth.
• I see how school reinforces a view in which your worth as human being can be mapped to your place in a linear hierarchy
• I see how school reinforces the view that intelligence and smarts are fixed attributes
• I see how one of the primary activities of school children is to avoid looking stupid and to maintain one’s standing in the hiearchy

Today I watched group of people with none to little to some to a good bit of background in education research try to write a education proposal. Many of those people were scientists, and here are some thoughts from the day.

When a scientists thinks of a physical system, they think of its parts and how those parts are organized in that system. They think of the relevant properties of those parts and the system, and how those properties might be measured and what roles they play. They think of how those parts interact with each other and the rules for how those interactions play out (which are often dictated by properties). They think about the surroundings of that system, and how interactions with that system either introduce new parts, change  properties of certain parts, or change how those parts are organized. They think about how those changes act together to bring about functional changes to the system as a whole. All of this might be understood as physicists “modeling” that system in order to understand how it works. They think about systems in terms of models. They develop models, deploy models, think about the implications of models, reflect on the parts of model that aren’t flesh out. They use model to ask questions. They use models to make predictions. They use models to inform them about designing experiments and what might be measured. All of this modeling is informed by theory.

Despite the fact that scientists do all of this with physical systems, they struggle to play this same game when thinking about educational systems. They don’t know what the relevant entities are. They don’t know how to draw boundaries between systems and surroundings. They don’t know about the properties of the entities or know what properties are relevant. They don’t know how those entities arrange themselves and how those properties and arrangements lead to different functional states of the system. They don’t know how those entities interact with each or respond to external interactions. But even worse is that they also don’t even know that they don’t know these things. Mostly, they don’t even think that should be thinking in terms of models (or theories), so they don’t even try to think in terms of models. Rather, they just go on instinct. They go on things they feel, things they’ve heard, things they’ve experienced. What they do is no informed at all by theory. In many ways, they are novices in all the ways that new physics students are.

Aside: If you’ve ever entertained the thought that general “critical thinking” skills is something that exists, this is evidence that there is no such thing. People who can think critically in one context do not typically spontaneously think critically in other contexts. Critical thinking requires rich knowledge base from which to think.

The good thing about this group of people is this: They have some really good ideas. They are learning. They are growing. They are well-intentioned. They have some good experiences to draw from. Part of the problem is that they are missing lots of knowledge. Part of the problem is that they don’t know the game they should be trying to play.

I feel the same way about my physics students. They have some really good ideas. They are learning. They are growing. They are well-intentioned. They have experiences in the world to draw from. Part of the problem is that they are missing lots of knowledge. Part of the problem is that they don’t know the game they should be trying to play.

The best I can do with my students and these proposal writers is to enter into a dialogue that nudges their thinking along–provide them with some impetus to learn some new knowledge or rethink the game they are trying to play.