To Unit or not to Unit?

One of today's discussion centered around the importance of units.  I would really like to take a hard line on this and either say that, "Units are crucial to students' understanding of physics." or "Units are superfluous and not germane to students' understanding."  

Frankly I don't think either is quite right.  Even after 14 years of teaching (12 of which doing it well) I'm undecided on the issue.  I know various physics teachers that would describe themselves as "unit sticklers".  They harp on the students about the importance of units in answers and insist that the students include units in their algebraic expressions.  One (bad) teacher I know used to have students identify the correct unit of a quantity as a multiple choice question on a test.  Ugh.  

The commonality among these teachers is that for the amount of effort and energy they put expressing the importance of units - it seems to make little difference to the kids behavior and even less to their understanding of the concepts!  I have experienced this first hand in talking to these teachers at the end of the school year and hearing comments like, "even this far into the school year the kids still don't know the units for acceleration."  No kidding!  Could it be because they never understood it the first time?

However, blowing off units entirely seems to be even worse!  In using the modeling method we stress the importance of analyzing the slopes of graphs for both numbers and units.  In the first week we ask students to measure the mass and length of dowel rods of various lengths and plot mass vs. length.  The slope ends up with number around 0.40 and units of g/cm.  We ask students to express this in a "for every" sentence; "for every 1 cm of length added the mass would increase by 0.40 grams".  The number 0.40 itself doesn't mean anything. 

Later in the class we ask students to relate the units cm/s to something in their everyday lives like mph.  Without having a good understanding of both cm/s and mph its hard for students to make the right connections.  A couple of years ago there was an embarrassing video of a young woman who didn't have a good sense of what 80 mph meant.  http://www.youtube.com/watch?v=Qhm7-LEBznk  unfortunately for her, her husband took some video of their interaction.  As funny as this may be, analyzing units can be very advantageous in creating a good conceptual understanding.

Let's look at the idea of the Newton for example. What is a Newton? Someone might tell you that it is the "force that would give a mass of one kilogram an acceleration of one meter per second per second." I have no idea what that means - stupid internet - and I know it isn't something that my students would be able to develop, discover or even comprehend! However, there are some teachers that relish in showing students (through some F=ma kind of thing) that N=kg*m/s/s. I do not recommend this as a teaching strategy. In fact, if you get anything from this blog post - please don't do this! Removing the context from the measurement and the unit is not a good way to create a deeper understanding.
So where is the balance?  I know that a really good understanding of units only comes after years of study of physics.  For most of us it only comes after a couple years of teaching physics!  Whatever you choose to do I'd encourage you to attempt to link the units to the context of the situation and if at all possible link it to something physical that they can understand.  Here is an example.

As physics teachers we probably know that the free fall acceleration for an object is close to 10 m/s/s.  A textbook would tell you its 9.8 m/s squared - which is a discussion for another time.  But do kids relate to 10 m/s/s in a way that relates to their everyday experiences?  How would your understanding of 10 m/s/s change if I told you that it was equivalent to 22.5 miles/hour/second?  That would mean that for every 1 second of time that an object falls it speeds up 22.5 mph.  So if you jumped off the building and fell for 1 second you'd hit the ground going 22.5 mph.  Do you want to be hit by a car moving at 22.5 mph?  at two seconds you'd be moving at 45 mph!    

So units?  I think that with all learning and understanding context is important.

The First Rule of Forces

We're on day 10 of our workshop and there is some discussion about how to name forces.  This is necessary because there are a couple of different naming conventions that are popular.  Regardless of the convention I feel like we should all follow the "First Rule of Forces" which states that:

"When naming forces you must name the physical object doing the pushing or the pulling."

I can't remember where I got this rule - probably from my physics teaching mentor, Mark Davids.  He grounded every concept in a physical experience and this has helped me get the students to really examine their own understandings of forces.  By sticking to the FROF kids are forced to think more critically about the forces involved in any situation.

If a student has to name the physical object supplying the force then they can't throw around physics words like, inertia, momentum or gravity as supplying forces because none of them are physical objects.  Too often kids imbue these physics words with special properties.  Popular culture doesn't do us any favors here.  I was watching American Ninja Warrior the other day - which is a game show in which contestants have to complete an elaborate obstacle course - and the commentators couldn't stop themselves from saying, "His momentum kept him swinging..."  I wanted to reach into the TV and throttle someone!

Anyway, below are some of the conventions you may see for naming forces.  Consider the gravitational force supplied by the earth on a block.
1. Agent Object - in this the force is named with an F and the subscripts list what is doing the pushing or the pulling, the word "on" and then the object on which the force is acting.  For example, Fearth on block.
2. Object Agent - in this the force is name with an F and the subscripts list the object on which the force is acting, the word "by" and then what is doing the pushing or the pulling.  For example, Fblock by earth.
3. Physical Object - in this the force is named by the physical object doing the pushing or the pulling.  For example, "earth".
4. Nickname - in this the force is named by its "nickname".  For example, "weight".
5. F notation -  in this the force is named with an F and the subscript is the nickname. For example Fg.
6. Formula - in this the force is named as a formula.  For example, "mg".

There may even be more!  My opinion?

Not all of these are created equal!   

Soapbox time; there are a couple of these that really are better than some others.  Agent Object and Object Agent are both good.  They allow us to follow the FROF.  I also like #3 in that it is the most basic.  But other than those three - I really have a hard time getting on board.  

Let's talk about nicknames: weight, friction, tension, normal...these are all force nicknames well known to physics teachers - but not necessarily to physics students.  When do we introduce these to our students?  Earlier this year I had a student come up to me and ask, "when are we going to start calling it the normal force?"  First of all, I have no idea how he knows we call it the normal force.  Secondly, what is his hurry?  So I told him this story.  

Last weekend Mrs. Pata and I went out with some of her friends and their significant others.  One of her friends has a new boyfriend and this was our first time meeting him.  I have a nickname; my close friends and family call me DP.  When I introduced myself to this guy I said, "Hi. my name is Don its nice to meet you."  He responded with, "DP great to see you!"  I'm like, um...what?  In my head I'm thinking, dude - you don't even know me!  

It is not appropriate to use people's nicknames if you don't know them.  It is just an inappropriate in a physics class to use the nicknames of forces if we don't know them.  Textbooks throw around these nicknames like "tension" all willy-nilly.  No students can gain the right context from a textbook definition.  This idea is manifested by numbers 4 and 5 that remove the context of the force and require that students have an understanding of these ideas already.  #6 removes the context of the force and asks students to relate it to an even more abstract idea and equation!  

    

Regardless of the convention that you choose classroom vocabulary can/should only be used when the class has been involved in the making of the definition or if 100% of the class in on board with its adoption.  I urge you to be aware of these problems ahead of time and make the choices that are best for the conceptual development of your students.

I love the first rule of forces and the kids always want to know what the other rules of forces are.  I haven't come up with any yet; but its early!  

Modeling Workshop Day 1

It was quite the day.

First of all the content level of this group of physics teachers is very high!  We have many teachers who have been teaching for lots of years and those who haven't were engineers in the past.  So content is not going to be an issue.  The actual issue in the past has been that there has been a mismatch is content expertise between the participants.  There were some that already knew the physics and some who were, let's just call them "novice".  That made it difficult for we as leaders to know where everyone was given a particular moment.  But that is a very good analog to what happens in the physics classroom!

Another difference between this and last year is that there are no outright skeptics.  Sure, there are plenty of participants that question what we're trying to do and why we're doing it.  But no one who thinks that I'm full of shit and is just waiting to point it out.  For that I'm thankful.  It is difficult to get in touch with a group when you as the facilitator constantly feels that you have to justify what you know to be good teaching.

We did have one "ah ha moment!" and that was pretty cool.  The group had completed and white boarded what we call the variation and measurement labs.  These aren't labs in the modeling materials but what we use to establish the relationships that we want the participants to know and be able to use in the future.  Once they have them on white boards we circled up and started to discuss the boards.  I was facilitating the conversation and having a dialogue with one of the participants.  I was asking, "Let's say you had a tile and you added 1 square cm to its area...what would happen to its mass?"  He referenced his "for every statement" and said that, "the mass would go up by 0.71 grams."  I said, "What would happen if you increased the area by 10 square centimeters?"  He said, "It would go up 7.1 grams."  Then I said, "and what would be the mass of tile whose area was 100 square centimeters?"  He looked at me, looked at his board and saw that one of his data points was a tile whose area was 100 square centimeters and the mass was very close to the 710 grams he was about to say.  He looked back at me then back at the board and threw his hands up in the air!

I said to the group, "I think something important just happened there!"  and we all laughed and cheered.  Seldom do we get to see that kind of moment happen so vividly.  It was awesome!

That is the power of the workshop though - it can be that trans-formative; even on the first day.

FCI: I didn't know what I didn't know

My first year of teaching was the 1999-2000 school year.  I felt so good about the year.  I connected with the students, I had a ton of fun and I really thought that I taught some good physics!

I great teacher that I knew sent me an email and asked me how my year went.  I don't like to toot my own horn but I told him that I thought it went great.  So he said to me, "Well, I have this little test that you can give to your students to kind of see how you did in your teaching."  I said, "Send it over!"

The next day I received a copy of the FCI.  Attached was a note that said, "Good luck and make sure you take it before you give it to your students."

Keep in mind that this was 2000 and the internet pretty much sucked at this point.  If I put FCI into Yahoo I'm sure that nothing of import would have come up.  I didn't really know what a big deal this thing really was.

I looked at it and saw that it was a physics test.  So I decided to jump right in.  I read number 1 and kind of knew the answer; I mean I knew the answer but wasn't overly confident in my concepts.  So I didn't answer it and moved on to number 2.  Same result.  Lucking it came with the answers!  So I checked, just to make sure that I was right (seriously).  I went on to the next couple just checking to make sure I was right again.

Let's face it, I had no clue if I was right or wrong.  I still have a hard time admitting that to myself, let alone you!

So I gave it to my students - in denial about the fact that if I didn't know what I was doing then they might not have the same experience.  I scored them and the students scored an average of 13.5 out of 30.  Is that bad?  Yep.  The teacher who gave me the FCI contacted me later in the week and asked how the kids did.  I lied!  Well not lied exactly I fibbed.  I said that they didn't do as well as I would have liked.  He told me that if I was interested in improving my teaching he was teaching a workshop for physics teachers that summer.  That is how I got into my first modeling instruction class.

I learned through the literature that the pretest scores on the FCI are barely over 8 and 13.5 is the score that an average traditional physics teacher's students score.  I was completely average.  My kids knew less than 50% of the correct answers!
I have now been giving the FCI for 10 years and it allows me to see how the changes that I make each year in instruction and assessment affect the students learning.  I don't know of another tool that has impacted my teaching so much.

I didn't realize that I didn't know anything about conceptual development or student misconceptions or the importance of qualitative knowledge.  Nor did I know how important these are.  Thank you FCI!

The Hard Boiled Egg: A Metaphor

Every Monday morning before school starts I meet with my PLC which is the best part of my week!  This is a group of smart, highly motivated, committed and talented educators.  And conversation are amazing!

We call ourselves the "Constructivism PLC" because our goal is to implement constructivist lessons in our classroom, record them on video and then watch (and critique) them as a group.

I spend a good deal of my week thinking about what I want us to talk about during the next PLC.  I usually get inspired by something I read or experience.  This week I was listening to an NPR show that I like called, "The Splendid Table".  The host was talking about talking about cooking and mentioned eggs - specifically hard boiled eggs.  That started thinking me about how I boil eggs.  I use the method my grandmother taught me; put the eggs in a pan, cover with water, put the pan on the stove on high, when the water boils, set the timer to 12 minutes, drain and let cool, peel and eat.  This is a far cry from the Julia Child method.

I thought to my self, I wonder how other people boil eggs; I bet there are other methods.  So when everyone started coming into the meeting I asked.  It turns out that NO ONE boils eggs in the same way!  There was even some controversy as to whether adding salt to the water will prevent cracking.  Here is the thing - my suspicion was that there would have been different methods and that everyone would be comfortable with their own method.  This is the key for me - every teacher has their own methods with which they are comfortable.  But we rarely ask, "Is there a better way to boil an egg?"

I was ready to roll with the metaphor.  But when it came time for me to roll it out, I thought, "This is so contrived...there is no way these English teachers are going to let me get away from this."  I paused and then bailed... I BAILED ON MY OWN METAPHOR!  It was awkward to say the least.  I can't believe that I had a crisis of confidence.  Sometimes I suck at life!

But then a very interesting thing happened.  Another teachers said, "Wait, what is the metaphor?"  I was like, "Um...um...uh..." and then Geoffery jumped in.  He picked up my fumble and ran with it.  He linked the egg metaphor to two ideas - working with students who couldn't care less about boiling eggs and to working teachers who already think they are egg boiling masters and aren't interested in hearing about how anyone else boils eggs.  Every comment from there was linked to this egg metaphor and it grounded the conversation.

It turned out that this mornings conversation was really about motivation.  How do we motivate our students (at all levels) and how do we, when interested in real professional development, motivate our peers?  These are not questions with easy answers but by sharing our ideas in a safe and open environment we feel like we are part of a community.  I cherish that feeling.  Thank you PLC.

So here is the question; are we as professional educators, ready to admit that there is more out there to learn?  This is the point of our group.  Is one method to boil an egg better than another?  Can I get over myself and try new techniques?  Is the fact that I've been boiling eggs the same way for years a reason to keep doing it?  Is just getting the egg boiled good enough?  Are there really better ways to do it?

And does salt really keep an egg from cracking?

Stumbling Upon Good Teaching: Building Projects and PBL

So often in my teaching I do stuff - or have the students do stuff - without a really good pedagogical justification in mind before we do it.  Sometimes it goes badly but more often it turns out awesome!  This is a tale of the awesome.

A couple of weeks ago I assigned the kids a building project called the Marshmallow Catapult.  The task is to build a catapult (usually out of wood) that can shoot a marshmallow 5 meters into a bucket.  It has to have a triggering mechanism (they can't just pull it back and let it go).  But pretty much, that's it.  This seems pretty open to interpretation and it really is.  The kids really have to figure out, how to build a catapult, how to get it to go 5 meters and how to make it adjustable enough so that if they are too short or too long they can make changes during the shooting.  

I don't really have examples around and I don't give them much in the way of instruction.  And we don't talk too much about what's important.  They are really on their own.  But they know the expectation and its up to them to make it happen.

In past years I've assigned this AFTER we studied projectile motion which meant that kids would have a working knowledge about the relationships between launch angle, launch speed and horizontal range.  But this year I assigned it BEFORE in the hopes that they would discover some of these things on their own; kind of an organic discovery process.  This shift is new for me and it part of my goal to incorporate some PBL into my teaching.

The kids' catapults were awesome!  

The shooting was so FUN!  The kids had a great time and really celebrated their success and the hard work that lead to it.  We were able to talk so much about projectiles and now that they had an experiential sense of it I think our discussions will be so much more fruitful.

In three of my physics classes there were 54 catapults (for about 95 kids).  They could work in groups up to three.  Of the 54 catapults 30 shot the marshmallow into the bucket, 9 hit the rim 8 at least shot the marshmallow around 5 meters and there were some that sucked!  

The best part for me and for the kids is that any group that didn't meet their own expectations can re-tool or re-build their catapults and try again next week (this time after school).  You always have a chance to meet the expectation. 

I know that building projects can be a great addition to the classroom and even though I may not have the best pedagogical justification for it I know that the kids got so much out of it that I'll continue to do it in the future! 

The Power of Telling Stories in the Classroom

At the high school we were recently treated to a couple of lessons on "real talk" by one of our own teachers.  Real Talk describes his practice of communicating with his students in way that is meaningful for both parties.  Thinking of the way that we talk to our students forces us to ask a couple of tough questions like; what are the do the words we use matter and are there shared experiences we can draw upon to resolve conflicts.

To give us a sense of his methodology the teacher Geoffrey told us a couple of stories from his experiences; one was from an experience he had in college and two were experiences from his classroom.  Each of these stories had all of us on the edges of our seats!

Geoffrey has the reputation of being an excellent classroom teacher.  I know him a bit personally and find him to be delightful and engaging.  But I've never been in his classroom so I don't really know that much about his practice.  However, when he started telling us (the whole faculty which is around 80 teachers) stories from his experiences I had an immediate sense of the power of his teaching.  

Now, I fancy myself something of a story teller.  I love to tell stories to my classes that highlight certain physics principles.  The kids love them, remember them, and often site them during class discussions and even on tests!  

This got me wondering; what is it about Geoffrey's story telling (and story telling in general) that makes it so (anecdotal-ly) effective in the classroom.  In reflecting on Geoffrey's stories I realized that he opened up to us and shared part of his history with us; he let us into his world.  By connecting us to his past he's allowing us to share an experience with him.  By providing that context he is creating a bridge for us to move forward together in shared understanding.  

Stories allow us to give a part of ourselves to the kids - which allows them to give a part of themselves to us.

One of my favorite movies is a 1987 Joe Mantegna film called "House of Games".  It's a con man flick.  To me the most interesting part occurs when Mantegna's character is explaining the origin of the term "con man".  According to the movie the term comes from "confidence man".  He says that the key to gaining someone's confidence (in order to dupe them) is to give them your confidence first; to put your trust in them.  

Not that I'm saying teaching is a con game, but if you expect kids to be themselves with you, being yourself (open and honest) with them is a good start and telling stories is a great way to do this.