Southwest Michigan Modeling Workshop Day 10

Two-thirds of the way through the workshop and I am exhilarated and exhausted!

On day 10 we had some very challenging physics questions to tackle.  The first involved a box on a ramp (what we physics people call an inclined plane problem).  The second involved the Atwood's Machine - and half or modified Atwood's Machine (what we physics people call a two-body-problem).  

The day started with a discussion of the readings from Arons.  The reading was about the common vocabulary of physics with regard to "gravity".  In our modeling class we don't use the word "gravity" at all; in fact I call it the "g-word" and don't let anyone use it!  There are much better ways to refer to things kids usually call "gravity" and Arons goes into detail in this section.
I couldn't agree more with Arons and we talked all about our own conceptions and his observations.

We then embarked on the ramp problems.  After 4 years of leading a workshop (and 15 years of teaching) I still don't have a great way to get students or teachers to discover or construct on their own how to draw a force diagram for a box on a ramp.  It is very frustrating.  So I, instead, wanted to see if I could somehow link what we were doing to this new process.

Earlier in the workshop we had referenced a section of the Arons reading where he suggested a flashlight demo to help students resolve vectors into their component parts.  Take a meter stick to represent a vector and lean it against a wall.  How would you know how long to make the horizontal and vertical components.  Arons says to take a flash light and shine it parallel to the floor and on the wall you'll see the vertical component.  Then take the flash light and shine it perpendicular to the floor and you'll see the horizontal component.

Our participant have really embraced this idea and have even gone to calling the components the "shadow arrows".  

So the question is how does one draw the component vectors for a box on a ramp?  Traditionally we were told to just "rotate the axis" and then break up the weight vector into its component parts.   But this instruction was given without a reason or context.  It was, "just the way you do it".   So I practiced and got good at it but never really knew why.  And I want at least a little more for the participants.

We decided to use the idea of the flashlight demo to link this new problem to something we already understand.  The rule is:

To find the components shine the flash light parallel and then perpendicular to the surface.

This rule gives us a reason to "rotate the axis".  Since the flash light is orientated according to the surface even if we tilt the surface we can still find the shadow arrows!  Moreover, these arrows have to be, themselves, parallel and perpendicular to that surface.

In the end the participants still had to practice.  But I am more comfortable giving them a little more than this is  "just the way you do it".

Unfortunately I had to show them how to do it, which isn't the end of the world.  I don't mind doing an "on the board" demonstration if it is a particular skill I want them to master.  While finishing, one of the participants asked, "how do you convince the students the angle of the ramp is the inside angle of the component triangle?"  

I was like, "I try never to show them anything they can figure out on their own!"  So I asked them to use the method I just described and then measure the two angles and see for themselves.  

The engineering group above used a bit of technology (my favorite app called "clinometer") so measure the two angles.  Other groups used protractors or those giant Plexiglas triangles from geometry class.  The point is, nobody is confused about the fact that those two angles are the same.  No geometry necessary; convincing needed!

Then they practiced.  This basically took all morning.  Ugh.  Learning is so slow when it is meaningful.  

We then moved onto the dreaded Atwood's Machine problems.  These again are tough for almost all physics students.  Why?  It is hard to say.  Probably because you have to think about two objects instead of just one.  But is that really that much harder?

Apparently so.  As teachers we need to practice our RETROGRADE AMNESIA; remembering back to a time when you didn't know or know how to do something.  

Do you remember back to when you didn't know how to tie your shoes? Do you think you could effectively and easily teach that skill to someone without remembering what that feels like? It is the same with these problems!

The issue, again, is traditionally we were told how to do these and just practiced until we got it right.  This involved drawing a force diagram for each object and then writing a sum of the forces statement for each. This would yield two equations and two unknowns. Then from there we do some math-magic (also known as algebra) and solve for something; the tension in the string or the acceleration. Kind of tough for all but the best students (who are probably just following the procedure without thinking too much about it anyway).

Can we do better? What kind of construct can we apply to this problem that is a bridge between what we already know and this new situation?

We decided to go for a system approach for the modified Atwood's Machine. We started by drawing a force diagram for each body and then asking the question, "What is the role of the pulley?" I suggested that it was to turn the force 90 degrees. What would the force diagram look like if we undid the pulley? Can we then smush the force diagrams together to find the unbalanced force?

We asserted that Newton's 2nd Law applied to systems as well:

a(sys) = Funbal(sys) / m(sys)

Once we had the unbalanced force and mass for the system we could then find the acceleration of the system. This procedure allows us to simplify the large problem into something manageable. The participants, however, had to make that cognitive leap in order to get on board with this idea.

Not too many had a problem and we made sure to work with them and that they had enough practice.

The day ended with a practicum challenge.  They were given a Modified Atwood's Machine and asked to release it and a buggy at the same time so that the little mass on the end of the string landed in the buggy.  The group that was the closest landed it on the hood.

I didn't assign any homework because it was the 4th of July weekend.

Mass - do we even know what it is?

Today in class we talked about a reading from chapter 3 in the Arons book.  He asked the differences between gravitational mass and inertial mass.  The participants were like, "Forget the differences, what ARE gravitational and inertial mass?"  I was like, "forget gravitational and inertial, WHAT IS MASS?"  Do we have an operational definition for mass?

No, really, do we have an operational definition for mass?  In all of the years that I've been teaching I never have come up with anything that made sense.  We have an idea of mass (at least we can say if an object has more mass than another) and even measure it in kilograms.  But what it is?

I've had to rely on the circular reasoning argument that "all matter is made of atoms and has mass" and then "mass is the amount of matter contained in an object".   These statements, unfortunately, make so sense at all!  We still don't have a good definition of mass.  WTF!

To make matters worse it turns out that we have no way to directly measure the mass of an object!  I asked in class and they suggested a balance - but that is a comparison between an already known mass based on a gravitational force; how did you establish the first mass?  Then they suggested the "inertial balance" which puts you in a position to measure the frequency of a vibrating mass and inferring the value for the mass.  Someone suggested we just push with a force and measure the acceleration; again inferring the mass.

We don't have a way to measure the mass of an object!  I am not sure that the participants have thought that deeply about mass as a concept before but we still have a long way to go with it.

I am thinking about an operation definition that allows us to use the mass but doesn't hinge on a origin.  How about this:

mass is the measurement of an object's resistance to change in motion

We know that the natural tendency of an object is to resist changes in its motion; an object at rest will tend to stay at rest and an object in motion will tend to stay in motion (in a straight line at a constant speed).  But which will resist changes more, a basketball or a bowling ball?  Obviously the bowling ball, but do we know why?  It is not because it weighs more - we're not trying to pick it up.    Its because it has more mass!  

The more mass the more resistant to changes in its motion.  We measure this in kilograms which is quite arbitrary but we've decided to go with it.  

I can't wait to see how the participants respond to this idea.

Southwest Michigan Modeling Workshop Day 9

Started the day with white boards from acceleration, mass and force lab which is ostensibly the Newton's 2nd Law lab.  Yesterday they had made white boards where each group varied two quantities of the four:
1.  Pulling force
2.  Mass of the cart
3.  Angle of the pull
4.  Angle of the ramp

We looked at the boards and found out that there was a linear relationship between pulling force and acceleration.  In addition there was an inverse relationship between mass and acceleration.  These were the two expected results and they came out quite good despite the trepidation of the groups about the wonky lab procedures.  They didn't think that pushing or pulling the cart with a spring scale would give good enough data to model the actual physical laws.

But the data came out great - WHAT'S UP NOW!  To be honest, this isn't my first rodeo!  This was enough to move on to generate the law, but we still had two more situations to examine.

Next came the pull angle.  We looked at their data and my question was - if you break up the pulling force into it's "shadow arrows" the component forces, which one is responsible for the acceleration.  AND which one is the unbalanced force?  We looked at a couple of the situations and it turned out that the horizontal component was the unbalanced force and responsible for the acceleration.  In addition, it changes with the angle.  So we looked at a couple of situations (30 and 60 degrees) and asked the questions how does the unbalanced force change and how does the acceleration change?

I was very specific here to make note of the unbalanced force which I called the Funbal.  The participants immediately started calling it the FunBall; which I love!  This is WAY better than Fnet or Sum of the Forces because it ground the understanding in the language.

I decided to ignore the angle of the ramp.  Mostly because we didn't yet have any context in which to analyze the forces of a cart on a hill.  More on that tomorrow.

Once we got to the point of seeing that the the pull force and the mass were the only real factors that affected the acceleration we used the mathematical structure of those relationships to create one equation that related all three variables:

a = (coefficient)Funbal/mass

The participants then set up their stations to solve for the coefficient.  With the exception of one group (who ti think had faulty equipment) each group found a coefficient very close to 1.0 and we settled on that and wrote the law.  

From there we talked about what the Funbal meant in a few different situations and I set them on unit 5 worksheet 1 the elevator problems.  They worked on these but had significantly more difficulty that I thought they would.  That, however, is very positive.  It means that they were either in a very good "student mode" or that they need the content help.  Both work for me.

This is kind of where the wheels fell off the cart. One of the questions asks what would happen if the elevator cable broke.  At that moment I realized that we never measured a free fall acceleration.  This is because in my class I don't do things in the prescriptive modeling order and I would have done free fall before this.  But I forgot!  So we went back and talked about what happened to the acceleration of the cart when you increased the angle of the ramp.  And it its max angle do we know the acceleration?

They set up the situation and measured the free acceleration of various objects, a book, a ball, anything they could drop.  Asked them to get the acceleration after a drop AND after an object was thrown upward a little bit.  They found and white boarded this data and we agreed upon a free acceleration of 10 m/s/s.

Then I asked them to ride the elevator and find the 4 accelerations.  One group used a bathroom scale, one group put a 5 N mass on a spring scale.  Two groups used data taken with LabQuests.

We then asked them to find the acceleration of the elevator using their actual data.
This was a little challenging but worth the effort.

I then asked then to relate the force diagrams, the acceleration of the rider to how you feel (heavy light or normal).

The point of the discussion is that:

Our bodies are not speedometers - they are accelerometers!

When they finished that activity we decided to finally talk about the readings.  The first reading was from Hake and was on the SDI labs that he ran at IU.  The participants liked the dialogue and felt that it well reflected what Laura and I are trying to do in the class.  I tried to emphasize that we are not promoting the SDI labs but highlighting the importance of the Socratic Dialogue in the classroom.

I have an idea that in order to create the constructivist science classroom you need two aspects:
1.  Inquiry lab experiences
2.  Socratic Dialogues

Neither one by itself will lead to the promised land, but together they can be very powerful!

The second reading we talked about was from Arons.  He asked the differences between gravitational mass and inertial mass.  The participants were like, "Forget the differences, what ARE gravitational and inertial mass?"  I was like, "forget gravitational and inertial, WHAT IS MASS?"  Do we have an operational definition for mass?

No, really, do we have an operational definition for mass?  In all of the years that I've been teaching I never have come up with anything that made sense.  We have an idea of mass (at least we can say if an object has more mass than another) and even measure it in kilograms.  But what it is?

I've had to rely on the circular reasoning argument that "all matter is made of atoms and has mass" and then "mass is the amount of matter contained in an object".   These statements, unfortunately, make so sense at all!  We still don't have a good definition of mass.  WTF!



To make matters worse it turns out that we have no way to directly measure the mass of an object!  I asked in class and they suggested a balance - but that is a comparison between an already known mass based on a gravitational force; how did you establish the first mass?  Then they suggested the "inertial balance" which puts you in a position to measure the frequency of a vibrating mass and inferring the value for the mass.  Someone suggested we just push with a force and measure the acceleration; again inferring the mass.

We don't have a way to measure the mass of an object!  I am not sure that the participants have thought that deeply about mass as a concept before but we still have a long way to go with it.

System Schemas

I have been practicing the Modeling Method for 14 years now with varying degrees of success. I have been leading modeling workshops now for 4 years (this summer is actually my 5th year) and I learn so much in my time.

This year I am running the workshop in Muskegon, Michigan.  Since I am not in Detroit, I am working with a new co-faclitator. Her name is Laura Sloma and she is AWESOME!  She teaches at East Kent Wood High School just outside of Grand Rapids and is a seasoned practitioner of the Modeling Method.  I love working with her and it is great that we gotten to share our ideas.  I've already learned so much from our interactions.

The biggest addition to my knowledge and procedure has been the introduction of SYSTEM SCHEMA to the force unit.

I never got this.  I have read it in some Hestenes literature namely, "Modeling Methodology for Physics Teachers" but it was decontextualized and too abstract for me to see how it would apply in actual practice.  A couple of years ago a teacher that I work a lot with in the Detroit area brought these to my attention. I didn't see how they could enhance student understanding and I thought they would actually work against me in that they seemed more abstract than the force diagrams themselves.  

After working with Laura, my co-facilitator, who has been using them for years (since 1998) I realize the value.  The system schema area a precursor to a force diagram!  The students list the physical objects in the interactions and construct the force diagrams from there!  So as a student, even if you don't get the whole "dot and arrow" thing the system schema gives you a place to start to analyze any situation.  

In addition to jump starting a force diagram, the system schema help us to understand the N3LFP!  Every line connecting the circles on a schema is an interactive force pair!   And the number of lines drawn to each circle is the number of forces on that object.

One aspect that the participants haven't really noticed yet is the fact that if every line is an interactive force pair then even the lines drawn from the "Entire Earth" to an object must also be a force pair.  What does that mean; that if the Earth pulls a box down the box pulls the Earth up with the same force?  I can't wait until they notice!

These are a revelation!  I have never used them with my students but I'm going to this year.  I can see what a positive impact they have had on the participants and I am excited to see  

Southwest Michigan Modeling Workshop Day 8

So we are halfway through this roller coaster we call a workshop!  Halfway already?  Part of me feels like we have been doing this forever; and part feels like we just started.

Everyone came back bright-eyed and bushy tailed this morning, myself included.  

We started the day with a discussion of the lone reading from the weekend, the foundational article by Hestenes and Wells about the Modeling Method.  The participants were really focused on Malcolm Wells as an individual.  They wanted to know all about him, were so impressed with his genius and with his passion for teaching.  In all of the years I've done this (5) the participants never focused on him so much. 

What is different about this year, or this year's group that put them in that position?

We talked for a while about the 10 year rule for mastery and I talked about chess and Hestenes and then for a while about Malcolm Gladwell.  I think they were a little disappointed to hear that it would take them 10 years to become a master.  I tried to reassure them that each of them could get huge gains in even their first  years, which helped a ton, but realistically to is going to take between 5 and 10 years of directed practice to get good at this.  Frankly it takes about 4 years to just get comfortable with the content!

I word about me.

I am pretty good at this; the Modeling Method.  But that is because I took my first modeling workshop in 2000.  The next summer I took a related (but not modeling specific) workshop in Portland, OR.  In 2002, 2003 and 2005 I went to ASU to take  advanced Modeling courses.  Between my own practice and my advanced training I got good.  But I worked my ass off at it!

So in 2010 when I was asked to lead a workshop I was ready - at least I thought I was ready.  I learned more running that workshop than I had in the previous 3 years of teaching combined!  It takes time, and work and directed practice but you can get good.  

Do not, however, let that discourage you.  Bad modeling isn't any worse that bad lecturing.  At least you 'll be having fun!

We then did some review of the concepts from later Friday.  They did a lab activity on Friday where the conclusion was that no matter how the carts interacted the forces that they exerted on each other were exactly the same; constant speed, constant acceleration, collisions, different masses the interaction forces were always the same.  What does this mean?

The only conclusion we can draw - without evidence to the contrary is that the interaction forces is equal!  This is not a small deal, however, seemed logical to all of the groups because that is exactly what they saw in the lab.  So we went with it.  I constructed two situations where this was the outcome but seemed different (a 2N block on top of a 4N block AND THEN a 4N block on top of  a 2N block) and asked which pushed more 2 on 4 or 4 on 2 for each situations.  Each group drew the schema and the force diagrams and we compared them.  

We got the same equal relationship in the force diagrams.  

Then I told the "Confrontational Stu" story.

After that I asked them to teach me how to walk (we started wtih jumping)

Tomorrow we'll start with a block on the table and see if the weight and the normal forces are N3LFP.

The friction lab was after that and we did a pretty standard modeling treatment for that.

Then we jumped into the Newton's 2nd Law lab.  I set up the track, pulled the cart and watched it accelerate.  The questions was, "What could you change that might affect the acceleration of the cart?"  The participants (acting like students) suggested the mass of the cart, the strength of the pulling force, the angle of the pulling force and the angle of the track.  The first three of these I'm on board with but I didn't really understand the angle of the ramp.

I should have done what I do with my students and steered them away from it, but I though it would be cool do "chew" on it a little bit.  It turns out that it was quite a debacle!  The two groups who chose to examine that didn't have a good concept of how it was even done, let alone an idea of how it should come out.  So a lab that should have taken at best 35 minutes lasted past an hour.  

Bad decision making by me?  Maybe.  But there was a point when I wanted to pull the plug, call it quits and just have them do the ones that really matter in this context.  However, it occurred to me that maybe this might be a good transition into forces on ramps.  So I let it ride.  That and it was a lot for them to chew on.  

I can't wait to see the results tomorrow.

Fsubscript more like WTFsubscript

This was mentioned in a blog post and I can't stop thinking about it!

In a blog post one of the participants queried as to why I didn't use standard notations like Fg, Fn, etc.  I almost fell off my chair!

I can't believe that after working so closely with me for two weeks anyone would not see that I'm all about the most basic conceptual understanding for the students.

The only reason I listed the nicknames of the forces was to:
1. Show anyone who doesn't have fully developed content knowledge where the text book names come from and
2.  Help the still traditional teachers in the workshop feel better about the names of the forces.

Apparently this backfired because there is still an idea that Fn and Fg are appropriate in any way.  To be clear:

THEY ARE NOT!

The first rule of forces says that all forces must be exerted by physical objects that are made out of matter.  That is why we never say, "gravity pulls objects down" because "gravity" is not a physical object, it can't exert a force, it is not even a thing!  Can I hit you with a gravity?  Can you buy a gravity on the way home at the gravity store?  NO!  Then why would I ever roll up with Fg - the force from gravity?  I can barely even type it, my hand are shaking!

To list the forces as Fsubscript horribly confuses the students.  Writing the names of the agents next to the forces is the least abstract.  Writing forces and Fagent object is a little more abstract but still acceptable.  But Fg and Fn - come on!  You can do better.

I have seen too many traditional student struggle with naming.  Two common issues arise.  The first is with Fg.  So many traditional teacher tell the kids the Fg =  mg.  Do you see why this might be a problem?  If the notation isn't crystal clear to kid (without context) they just think that F = m (because the gs cancel).  Or even worse, the force of gravity = milligrams!

The other arises from Fn.  For years I heard traditional students ask about the "natural force".  I was like, "what in the hell is the natural force?"  It turns out that the teacher was saying "normal force" but without any context to know what "normal" meant they were reverting to this idea that Fn meant natural.  I assert that this is because in their math classes ln means natural log (something else they don't understand) and they thought the notation was the same.  Who could blame them?

So maybe it was my fault for having introduced the nicknames before we all got to know each other well enough.  Maybe I should have stayed with the names that made the most sense (perpendicular surface force, force of the entire Earth, etc).  If so, I'll do better in the future.

Sum of the Forces - what's a sigma?

My co-facilitator and I were having a conversation on Thursday about how we wanted to attach the forces unit on Friday.  I asked her where she went with her own students from here and she described the 5 step problem solving process.  I asked her to describe it for me and she told me this:
1. Draw the system schema
2. Draw the force diagram
3. Resolve any diagonal forces into the components
4. Write the sum of the forces statements (with a sigma)
5. Solve the problem

I thought about this all Thursday night and was very conflicted.  

I love 4 out of the 5 steps...but couldn't get on board with sum of the forces statements.  

Why?

My thought is this - if we have the participants write sigma F statements it looks WAY too much like something that they have already done or something you'd find in a text book.

I want this (the modeling method) to look vastly different to the participants so that they aren't relying on some traditional mode of instruction.

I am afraid that some participants will take this and think it is an addition to what they already do.  Like, "when I teach the students about normal forces I'll make sure to do these worksheets."  This method is not something you do in addition to your lectures!  

In addition, when our procedures are different it puts the participants in a place to question why they have done things the way they were doing them before.  Is it the way you were taught and/or the way you've always done it.  

The real question is, how do you get students to develop their own process and procedures?  

Telling them to write sigma F statements won't really help.  So I suggested to Laura that we just take it out and see what happens.  To my delight there seemed not to be a real problem.  In fact, the participants were writing mathematical statements that were very grounded in their force diagrams.  They were setting forces equal to each other based on the diagram and solving from there.

I was elated.

So I love the 4 steps - and I'll be bringing it to my students in the future.  And I am so glad we thought deeply about the sigma F statements and were able to make modifications that are positive for the participants.