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."

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?

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?

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?

What's the first question that come to mind?

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.

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.

Light and Shadow: The best questions comes from students

Last year, I watched a lot of video of students working through worksheets on topic of light and shadow. Their questions led me to think about this problem:

The worksheets had students think about this situation: a mask with a circular hole, a screen, and a small (i.e., "point source") bulb are arranged like this


Students are supposed to think about "where" the light goes when you raise it. But one group went about thinking about what would happen to the shape and size of the spot of light as you move it from aligned with the hole to farther and farther up or down? Students questions are the best ones.

So, How does the size/shape of the bulb change as you move the bulb up and down? First give your intuitive guess... and then do some work to figure it out and convince someone else.

(I have three very different approaches to answering this. My most elegant came just last night as I was falling asleep.)

The Result of Mistaken Meaning

Thoughts as I was falling asleep last night: The word misconception can be broke down to mean "the result of mistaken meaning". Let's break it down further.

(1) The word 'result' emphasizes that misconceptions are events that happen.

Another way of thinking about it is like this: Students can't have misconceptions; because they simply are not things you can possess. Oddly, enough, the English language allows us to say things like "I'm having a misconception", even though misconceptions aren't possessions. I'm OK with this, because this is said much in the same way you'd say "I'm having a birthday party!"

And just like students want to invite their friends to the birthday party they are having; as a teacher, I want students to invite me into the misconceptions they are having. Dropping the pejorative language of "misconceptions", I might just say, "I want students to invite me in on what's perplexing to them and into their struggle to understand that perplexity"

(2) By using the word 'result', the definition also emphasizes some other causes.

If you perceive yourself (or someone else) to be in the midst of experiencing some misconception, you can't explain that event by saying, "It's because of a misconception." That's a tautology. We could debate what the variety of causes are, but my point here is just to say that a misconception is not a cause. The pursuit to understand causes is important. It's not simply that teachers should come to make sense of students' experience of misconceptions and their causes, but students must come to know their own minds in ways that help them to understand them as well.

(3) "Meaning" is something achieved across individuals as they attempt to carry out some common activity

This is important because it helps bring clarity to the notion of "mistaken meaning". Students don't have "mistaken meaning" by themselves. Students have ways of making meaning which we often don't understand, and we often have ways of making meaning which students don't understand. There is reciprocity in events of misconception, taking place among many participants. Putting it this way helps me: Teachers experience misconceptions when they fail to understand their students' ideas.

I've written about this before, but I have learned a lot of physics by listening to and engaging with students. The reciprocal nature of it all means that we all have something to learn by engaging in each others' perplexity and thinking.

Listing Math Preconceptions: Where to go next?

On twitter, @dcox21 shares a list he was making of math preconceptions. In the list, various preconceptions have been organized by math topics, for example, by fractions, integers, absolute value, rational functions, geometry, etc.

Organizing by math topic has its advantages, but it masks important things about students, because it's not organized by either the nature of the mistakes or by the student thinking that generates those mistakes.

Consider these three items that were listed as preconceptions.




To me, each of these is strongly related, despite the fact that they are listed in the table under the different topics of fractions, distributions, and non-linear functions.

In the first example, the student multiplies by two everywhere they can, which is top and bottom. In the second example, the student multiplies in one place when need to multiply in everywhere. In the third example, they square both terms, but in doing so, they miss the operations of x*y and y*x. Although the topics and grade levels are different, something about nature of the mistake is similar. Building a table of preconceptions solely around topics masks those similarities.

Next, consider these examples:

“You can’t divide smaller numbers by larger numbers.”

“Division always makes a number smaller.”

-10 > -6

1/3 > 1/2 (because 3 > 2)

These preconceptions were listed under the different categories of "integers", "exponents", "fractions" and "inequalities". But to me, all of these are related by the fact that they seem to stem from ideas that students are have around whole numbers and whole number operations. Children build up a lot of intuitions, ideas, reasoning, and procedures around whole numbers, and we are seeing here that students try on and rely on those ideas in a variety of ways as they learn about fractions and integers and exponents.

Placing the difficulties in different categories masks the fact that they seem to have a common origin-students' prior understandings and thinking around whole numbers.

What's the point?

I think there are lots and lots of potential connections and stories to tell by looking across the difficulties and ideas students have. I believe that a list of student difficulties is only useful if we do the work of trying hard to make sense of it by looking for connections and telling stories that help us see links between students' thinking and mathematical thinking.

Often it begins by asking, "Why would a student do this?" or "What does this mistake imply?" I often ask, "What good ideas do they have that would lead them to do this?" or "What could a student be trying to figure out what to do?" This often leads me to ask, "What ideas seem to be in place?" or "What ideas are they missing?" In the process, I often come to see my students and the discipline in a different way.

I'm curious to hear from other, what connections or stories they can see from the list?

Worrying about Misconceptions

Earlier this week, I was making some "whirli-gigs" to be used in a mock lesson intended to involve students in exploring, thinking, and investigating falling objects. The whirli-gigs are made of paper and they have blades which make them spin as they fall, causing variable amounts of drag.

In this middle school science lesson, students begin by freely exploring how they can make the whirligigs fall faster or slower, keeping track of what they notice and what questions arise as they explore. It is expected that students will begin to notice and wonder a variety of things, including how the length of the blades, the shape and angle of the blades, and the mass influence the rate of falling and /or spinning; and that this noticing and questioning will lead to more carefully designed experimenting and measuring in subsequent investigations.

A college instructor who was watching me prepare for this lesson asked, "Aren't you worried that this lesson will reinforce the misconception that faster things fall faster than lighter things?"

Before I share I how I responded, I am interested to hear what others think about this question and how others might respond.

Eleanor Duckworth is a Poet

I read this over and over, and then over and over. It is the first Paragraph from "Teaching as Research" by Eleanor Duckworth in "The having of wonderful ideas"

"What I love to do is to teach teachers. I love to stir up their thoughts about how they learn; about how on earth anyone can help anyone else learn; and about what it means to know something. I love to help them feel that any aspect of human endeavor is accessible to them and that they can make it accessible to any person they teach. I love to try to find ways into a subject that will catch everybody's interest; to find out what people think about things and to find ways to get them talking about what they think; to shake up things they thought they once knew; to get people wrapped up in figuring something out together without needing anything from me; to help build their fascination with what everybody else thinks, and with the light that other people's thinking might shed on their own. I love to see the most productive of questions be born out of laughter, and the most frustrating of brick walls give way to an idea that has been there all along."

Addressing Misconceptions II

In a previous post, I brought up a question from @thinkthankthunk about a common student misconception about gravity:

"How to address this student misconception? Atmosphere is necessary to create gravity"

My gut-response tweeting at the time was this:

"Engage with it: Ask them to elaborate on their idea... ask them draw pictures, to help explain how it works..."

followed by, "There is a meaningful correlation: b/c gravity is pulling, there is a lot more air near the earth. [It's] just not causal."

and

"Oh, and air collectively pushes UP, because it provides a buoyant force. So maybe helping student to see that?"

Now I've had time to digest it a bit more

First, it has been and continues to be a struggle for scientists to understand phenomena that seem to involve actions occurring over a distance. While Newton's framework for gravity proposed a universal law of gravitation that acted instantaneously over a distance, physicists have worked hard not to do so. Physicists invented the concepts of electric and magnetic fields, partially because they function as intermediary objects that span distances. In the field view, the field at a point responds to neighboring points in such a way that disturbances propagate at the speed of light. In a somewhat alternative attempt, physicists invented intermediary particles like photons to function as energy and momentum carriers over those distances. With gravity, general relativity proposes that space itself is a intermediary that changes in response to mass, and those changes, too, propagate at the speed of light. In contemporary quantum physics, physicists and philosophers still don't fully grasp the causal implications of quantum entanglement, because they seem to imply "spooky" actions at a distance.

Second, it seems relevant to think of air molecules as carriers of momentum and energy, and thus could be considered force carriers. For example, air is the medium responsible for drag and buoyant forces. The interesting thing about the student idea that air causes gravity is that, in their idea, somehow the air causes a downward force. Perhaps they are focusing on how air pressure pushes down? Well it does push down, it just happens to also push up, and to the side, and every which way. In our mind, objects experience an upward buoyant force due to air as a result of all that pushing. What do students think? We can only know if we ask and engage.

This is a bit of why I tweeted, "Engage with it". If I don't know why my students think atmosphere is necessary for gravity, I don't know enough about their idea to know what to do next. If my students don't know why they think atmosphere is necessary, than it's probably worth while asking them to elaborate and make drawings. They have to come to know their mind.

In my mind, given that (1) gravity seems to exist where there is atmosphere, and (2) gravity seems to have no visible causal mechanism, it seems perfectly natural for a person to infer that air plays a causal role in the effect of gravity. In students doing so, it's possible we are just seeing their commitments to empirical regularity and to causal mechanism, both very important pieces of doing science. If students are struggling to see spooky action at a distance, then perhaps they are being equally as skeptical as scientists have been for hundreds of years. Certainly we may think that students are crazy for thinking atmosphere creates gravity, but isn't it weirder to propose massless particle called "gravitons" or curved spacetime

In fact, it was without the weird notions of fields, gravitons, or curving space-time, that Newton had little choice but to give in to empirical and mathematical coherence of the universal law of gravitation. His law fit the data. But, keep in mind, that Newton could only do so when more empirically precise data of moving planets was made available by better optical instruments and calculus was available to understand better how that data could be made sense of in terms of the rate of rates of change. While causal mechanism was abandoned at the time, it was reintroduced later when new concepts and mathematics allowed for it.

What's the point?

It's tempting to think that students' wrong ideas can be simply described as misconceptions concerning an isolated topic X. I am always skeptical of that position.

In this case of atmosphere causing gravity, students' ideas are entangled in a large web, including the notions of action at a distance, causal mechanism, empirical precision, astronomy, rates of change, buoyancy, air pressure, spacetime, particles as force carriers, etc. In that web, they are entangled with the historical and contemporary puzzles in physics that have not fully been resolved. Certainly they are just beginning to make contact with those puzzles, but I believe it is our job to help students make meaningful contact with puzzles that arise in the web. It is our job to help them become better navigators of that web.

All and all, I think I would be tempted in a class to pursue these ideas (which seem to be about gravity) through buoyancy. Overtime, by helping students come to see air as providing an upward force, student have a genuine puzzle to resolve on their own terms: if air pushes up, what's pulling down? If not that route, I would simply "engage with it", by saying, "That's a good idea. How would that work, air causing gravity?"

Light and Water: Post Ten

In this photo, you can see the water in an alpine pond acting as a mirror and a window, superimposed on each other. This phenomenon is fairly common in everyday life when looking at glass windows–depending how you focus your eyes, you can either see a reflection or see through the window. This is also true for laptop and TV screens, where you can often see both your reflection or what's on the screen. By focusing your gaze differently, you'll see one aspect more than the other.


This is cool is because, up until now, I have been focusing on factors mostly external to the viewer--the angle of light, the angle of the object, the wind, the particulates in the water, the intensity of light, etc. But here is where we can begin to think about properties of the eye, the camera, and the brain.

In the picture above, you can clearly see BOTH the mirror and the window behavior of the water. However, when I was standing there, I could "flip" my perception back and forth between seemingly just seeing the reflection and just seeing the bottom of the lake. The question is, "Is this something my brain is doing?" or "Is it something my eye is doing?" Is this a filtering process or a focusing process? Or is it a bit of both? My hunch is that it's more of an focusing phenomenon, because my eye actually gets tired trying to maintain certain foci, but I wouldn't be surprised if there were also a bit of my brain doing some selective-attentioning process.

Anyway, my goal is to find a similar situation and then manually adjust the focus in my camera to see if I can make a photo switch from mirror to window just by adjusting the focus, and not any of the external factors.

Categorizing my Feedback

In a previous post, I shared a sample of the kind of feedback I gave to students this year. Here, I try to put them into categories...

Reflecting Back only (10)

You have brought up a lot of...
It sounds like you are trying to...
It sounds like you are trying to think of ways to...
It sounds like one your strategies is....
It sounds like you... And you are concerned that...
I can see how your were trying to...
I hear what you are saying about...
It sounds like you are saying...
Others have also expressed your concern, which seems to be... Is that right?
It seems like two things: ... and... Do I have that right?

Reflecting Back then asking for a question (11)

I hear what you are saying about... do you think...?
You wrote...Do you think...?
You seem to be making an important distinction about...Why do you think...?
You mentioned something... Was it...?
You mention this... By that do you mean...?
The last thing you write here about... is an interesting problem. What made you think about that?
You mention... What experiences have you had with...?
In your reflection, you highlight...How are those things going...?
You pointed out that...Why do you think...?
It's very clear that... What do you think...?

Praising and Reflecting Back

Thank for you being honest about...
It's great that you are thinking about...
I love how you have earnestly you have tried to...
I like how thoughtful you were about... I wonder...
You have written very thoughtfully about... it sounds like...
It is nice to see you having an emotional and intellectual connection to...
I appreciate how you’ve...
It is clear that you thought deeply about this, especially your idea about...
You wrote clearly and thoughtfully about...
What I like about what you've done here is...

Praising and Reflecting, but in an Epistemological Way (10)

Thank you for... It really helps me to understand...
I appreciate how much...This helps me to concretely understand...
I also like how you...this shows me that you are...
I like how you...This is a great thing to keep doing because...
I really like your idea about... This shows you are really thinking about...
I especially like how you made connections to...
I like how you have written a rich description of... In explaining the ideas, you’ve included...and...

I like how you are looking for connections here... This is something expert learners do all the time...
It's clear that you tried to think why... But you also included how... which helped me to understand that...
You have done a nice job relating...This shows me that...

Encouraging in order to Nudge (2)

Keep up with..., and I hope to hear more about...
I think you did a nice job of initially describing...I'm wondering what else you might include to help me understand...

Commenting (4)

You seemed very concerned about... the empathy you express here is...
This indeed sounds like a complex problem....
I agree it can be hard to know...
It sounds like you... Two things that stand out about it are...

Reflecting back then Commenting

I hear you saying that you'd like... and also that...I can certainly relate to...One suggestion is that...

Other

I'm wondering how you...
How do you think this is different...?
I like your goal to...I have also...Let me know how it goes.

Addressing Misconceptions

Today, @thinkthankthunk tweeted this: "How to address this student misconception? Atmosphere is necessary to create gravity"

Responses to this tweet were the following:

• [Ask] ,"What keeps the moon going around the earth?"
• [Show] Bell jar or some sort of vacuum chamber I'd say.
• [Show] Videos of things falling in a vacuum. Or in your own bell jar?
• Show vids of astronauts walking on the Moon.

I'm wondering how the responses would have been different if the tweet had been this:

"In my class, several of my students were debating whether or not air is needed for gravity to work. As the conversation went on, more and more students were beginning to be persuaded that air is definitely necessary. What should I do to help keep the debate alive?"

Then I'm wondering how the responses would have different if the tweet had been this:

"In my class, several of my students were debating whether or not air is needed for gravity to work. As the conversation went on, more and more students were beginning to be persuaded that air is definitely not necessary. What should I do to help keep the debate alive? I'm not convinced they have compelling arguments on either side?"

A glimpse into the nature of the feedback I give to students

I went through the first four weeks of feedback I gave to students this semester, and this is what I found.

Impressions? Feedback on my feedback? What does yours look and feel like?

It sounds like you... Two things that stand out about it are...
You seem to be making an important distinction about...Why do you think...?
Thank you for... It really helps me to understand...
It's great that you are thinking about...
You have brought up a lot of...
I love how you have earnestly you have tried to...
What I like about what you've done here is...
I also like how you...this shows me that you are...
You wrote...Do you think...?
I appreciate how much...This helps me to concretely understand...
I'm wondering how you...
It sounds like you are trying to...
Thank for you being honest about...
Keep up with..., and I hope to hear more about...
It sounds like one your strategies is....
How do you think this is different...?
It is nice to see you having an emotional and intellectual connection to...
It sounds like you are trying to think of ways to...
I like how thoughtful you were about... I wonder...
You mentioned something... Was it...?
You mention this... By that do you mean...?
You have written very thoughtfully about... it sounds like...
You seem very aware of...
I agree it can be hard to know...
I appreciate how you’ve...
I hear what you are saying about... do you think...?
I like how you...This is a great thing to keep doing because...
Others have also expressed your concern, which seems to be... Is that right?
I can see how your were trying to...
I really like your idea about... This shows you are really thinking about...
I especially like how you made connections to...
It seems like two things: ... and... Do I have that right?
It is clear that you thought deeply about this, especially your idea about...
I like how you have written a rich description of... In explaining the ideas, you’ve included...and...
You mention... What experiences have you had with...?
I like how you are looking for connections here... This is something expert learners do all the time...
It sounds like you... And you are concerned that...
This indeed sounds like a complex problem....
I like your goal to...I have also...Let me know how it goes
It's clear that you tried to think why... But you also included how... which helped me to understand that...
In your reflection, you highlight...How are those things going...?
You have done a nice job relating...This shows me that...
You seemed very concerned about... the empathy you express here is...
I think you did a nice job of initially describing...I'm wondering what else you might include to help me understand...
You pointed out that...Why do you think...?
It's very clear that... What do you think...?
You wrote clearly and thoughtfully about...
I hear you saying that you'd like... and also that...I can certainly relate to...One suggestion is that...
The last thing you write here about... is an interesting problem. What made you think about that?
I hear what you are saying about...
It sounds like you are saying...

A powerful question

A powerful question I have learned to ask students is, "What do you notice?"

One of the reasons why this question is so powerful is because students can't be wrong. Only a student can know what they notice.

I first picked up this question in an education talk about poetry. The speaker asked us "What do you notice about the poem?" NOT "What do you think the poem means?" Collectively, we noticed rhymes. We noticed rhythms. We noticed themes. We noticed alliteration. We noticed contrasting words. We noticed metaphor. We noticed allusion. We noticed a shift in mood across stanzas. We noticed repetition. We noticed imagery...

Out of our noticing, meaning of the poem emerged.

And so, too, I have learned to ask this question in science. Present students with phenomena and ask what they notice... not to predict what will happen. Not ask them to explain. Not solve for a number. Simply ask them to notice and ponder and let questions and meaning emerge.

Pointing to Learner's Excitement with Science

This semester I learned how important it can be to point out to people when they are having fun learning and doing science.

Learning, learning science, especially science class isn't always going to be fun. Sometimes it's going to be frustrating, either for students or for teachers or both, for a variety of reasons. Inquiry, especially, comes in fits and starts. Conversations, debates, presentations are probably going to go on, at times, too long, causing tedium or frustration. There are days that people just seem less excited to talk and to share, and to "dive right in" to science. Hopefully those days aren't too often, but they do happen. Even in a given day, you can hit some slumps or even walls, from which the class may or may not rebound from.

It even varies with students and classes over the years. Some students will be excited about science often. Some students will be excited about science rarely. Some years, there are classes that just click together with their science learning better than others. But with any class and any set of students, there are moments where a whole class becomes excited together about some science thing–a conversation, a puzzle, a phenomena, an experiment, a question, whatever. In these moments, even those students who are rarely excited get wrapped up in the excitement.

I am convinced that pointing out these good times pays big dividends, simply by saying, "I want you to remember this feeling you are having, the feeling you are having talking about science and learning together."

Now, I don't think you should point it out too early, like while the excitement is still building–that might disrupt the "flow" and the "excitement." But I do think it's worth pointing out before the excitement has died down completely, while the feeling of excitement is still palatable. Pointing it out, I think, helps buffer the bad times, because people remember that good times. I think it also helps to build students' identities around science and science learning, because you are pointing to their own emotional capacity to feel good and to get excited about doing and learning science.

Next year, I am going to more deliberately do this. We'll see how it goes.

Facilitating Discussion with Peer Instruction

Here are two trappings I've seen recently:

#1: Validating the right answer the moment you hear it, thereby short-circuiting any dialogue about the problem.

Recently, I heard a college instructor say, "I agree with you," anytime a student said something correct, and "Are there any other ideas?" anytime a student said something incorrect. My sense was that the phrases "I agree with you," and "Are there any other ideas?" were honest attempts by the instructor NOT to say "That's correct" and "That's incorrect". I caught on to this pattern of talk quickly, and I imagined students would catch on within a few days or weeks.

#2: Requesting that a nearly correct student "say more" in a manner that implies, "Could you please restate what you said using the correct terminology?" rather than, "I'm really interested in your idea, please say more about that?"

This can be subtle, as it often has to do with tone of voice, body language, and subtle phrasings. When an instructor does this, however it really gums up the dialogue. Because students pick up on the fact that it's not about their ideas, this kind talk quickly descends into a game of "the teacher is thinking of a number between 0 and 100." Students either start opting out or just trying to guess what the instructor wants them to say.

The Big Picture

Facilitating discussions is hard work. In my mind, the number one priority is getting students to invite me in to their learning through their talk. Largely, this means that they are sharing their ideas and thinking, not trying to guess what's in my mind or avoid being wrong. When I see instructors falling into these kinds of traps, I see this priority being undermined.

Some people might think the solution to trap #1 is to have a better poker face–don't have any "tells" that give away the right answer. I think that approach is flawed because it's trying to stop the symptom, but not the cause. I don't need a poker face if I am not listening to student ideas primarily through a lens of correct and incorrect.

Some people might think the solution to trap #2 is to not care about terminology. While that's possible, I don't think it's realistic. I think the solution is to distinguish the activities of "shopping for ideas" and "connecting with disciplinary formalism". The problem is in trying to do both at the same time and in the same way.

I certainly enjoy watching other people teach, because it gives me an opportunity to reflect on my own teaching. There are times when I "gum up the dialogue" and focus on correctness when I shouldn't. Sometimes by watching others, I understand better why we all fall into these traps and what impact it can have on students.

Light and Water: Post Nine

I went hiking today and couldn't help but take this photo of water acting like a mirror and a window.

In the picture, I am standing on a wooden platform looking down into a vernal pool. Where the sun shines directly onto the water, you mostly see all leaves at the bottom, but where I block the sun, you mostly see the reflection of the trees above.



In this photo, the wooden platform creates its own a shadow (as well as a shady tree to the left), and we see the same effect.

Sorting out Inconsistencies

This quote has stuck with me since I read it.

"I don’t trust myself to be an effective inquiry-based teacher if I’m not living an inquiry-based life. I don’t trust either of us." Dan Meyer

On that theme, I have recently been sharing a series of posts about my own inquiry into light and water, which began with a simple juxtaposition of two photos. This inquiry has led me to seek out and further juxtapose a range of natural and contrived phenomena. It has also led me to try to sort through various pieces of explanation, which have arisen through contemplation and conversation with peers.

In this post, I want to share another piece of inquiry that I think is important and important to infuse into one's inquiry life: seeking coherence and spotting inconsistency. This puzzle has stuck with me as fun and engaging.

The puzzle:

If we (a) approximate a shallow chunk of water (near earth) as being incompressible
and (b) we assume that piece of water is in thermal equilibrium
and (c) that piece of water is in a constant gravitational field

then (d) macroscopically, we can show that the pressure increases linearly with depth.

but (e) microscopically, the particle density and kinetic energy would appear to be the same be, via our starting assumptions (a) and (b);

so (f) how can the pressure be different, if the particles have the same kinetic energy and particle density?

You have a couple of options here to approach trying to sort this out, and I encourage you to explore this a bit before you settle on a quick answer. Any takers?