Modeling Unit 1

As I noted at the top of my "modeling" page, I'm going to go back and reorganize my blog posts.  I've found that organizing by the day of the workshop isn't very effective.  I plan to try to go back and organize the posts based on the Unit in the modeling cycle.  So, here's Unit 1 (with the preliminary stuff of the workshop added in):

I'm blogging about my experience at the FIU Modeling Workshop.  Much of this is for me, so that I can remember my experience.  However, maybe this will help someone else to come over to the Modeling Method.  I'm not sure if I've mentioned it before, so I might as well state it here, I currently teach Standard, Honors, and AP-B Physics.  I've been using the CPO Program, which is a hands-on program.  To me, it's biggest downfall is that the labs, although well constructed, are cookbook labs.  The students can get caught up in the procedure, and miss the concept.  After joining twitter, I've come across several teachers that use the Modeling Method, and have become more and more interested.  Which brings me back to the point of this post, my experience on the first day.  However, before I get into that, I would make the following claim, if this interests you, please go to the workshop, don't just rely on me.  Even after only one day I can tell that my recount will mean nothing for you without you attending.

Day 1:

We started the day with our leaders introducing themselves (Jon Anderson and Chris Doscher).  They quickly led us through a great introductory activity, that I might very well use with my students.  We each had to come up with 2 truths and 1 lie about our self, and the other people in our small group had to try to determine which is the lie.  After that, each person in the group had to introduce another member from the group to the entire cohort.  To me, it was a fun way to break the ice.

After taking the Force Concept Inventory test, we then got our first taste of whiteboarding.  We were asked to answer the following 3 questions as a group:

1. What are your greatest content-related teaching challenges?
2. What are your greatest instructional teaching challenges?
3. What are your goals for this workshop?

Here are the whiteboards:

Unit 1: Scientific Thinking

After breaking for lunch, we began our first experiment, a Pendulum Experiment.  

In walking us through the experience of the lab, we were given a few questions and comments after we completed the task.  (For the sake of brevity, I'll omit our responses to the questions). 

Jon set up a simple pendulum and then wrote the following questions in succession:

What do you observe?

(side note, Brian W. Frank  recommended asking "what do you notice," rather than "what do you observe." Here's why)

• Jon mentioned to try to not give any comments/facial gestures, just write.
• Ask if you need to rephrase for fewer words

What can you measure?

• Don’t comment until at the end.   
• Do you need to pare down the list, do to lack of equipment?
• Are any measurements redundant, if so discuss with the class.

What can you manipulate to change the time?

• Edit down after complete based on equipment present

State purpose of lab for students:

To determine the mathematical and graphical relationships that exist between time, length, mass, and angle of release of a simple pendulum.

 (Jon told us that the bold part represents the beginning phrase for basically all the lab objectives)

Before assigning the different types of relationships to different groups, Jon told us two important "rules" for labs:

1. Fair Test: manipulate only one variable at a time
2. 8x10 rule: collect at least 8 data points separated by at least a factor of 10

After collecting the data, they then introduced the group to LoggerPro, to analyze the data. We used LoggerPro to analyze our results and then put them on whiteboards to share with the other groups.

During this time, my small group discussed some of the strength and weaknesses with excel vs LoggerPro.  Namely, to us LoggerPro can analyze the data faster, but excel integrates with word docs a little easier.  (We could easily be wrong on this.)

Well, that's basically it.  A good first day, and I'm excited for the second day.

To start of today, we finished up the "Board Meeting" with the groups that studied length vs period.  For physics teachers, this is obviously the group that was able to show an actual correlation.  One of the most interesting parts of the discussion, to me, was when Jon and Chris recommended not worrying about linearization yet.  They told us to now worry about that battle, as it will come up as you move into the next phase of the cycle.  Just let the kids use LoggerPro to get the mathematical relationship.  They did recommend spending some time to discuss whether or not the data should go through the origin.  In the course of that discussion then mentioned what they called the "5% Rule" which basically states that if the y-intercept is less than 5% of the biggest measured value in the data for the y axis, assume that it goes through the origin.

After we finished that discussion, we then moved into the next phase of the modeling cycle in which we worked on linearizing data using LoggerPro.  The worksheet had 6 data sets (we had version 3 of this worksheet, I'll add that link if I find it), and we had to plot the data and determine how to manipulate the data to create a linear graph that went through the origin.  Jon and Chris mention that they only used the first four problems (which I think are the 4 in version 2) with their classes as they have found that they are sufficient to get the students acclimated to the process. Jon and Chris did recommend to have the students write the regressed equation rather than the proportion shown (ie: equation with slope and y-intercept, not y is proportional to 1/x).

After we had linearized the data, each group was assigned a different problem to put on a whiteboard to share with the cohort.  Again, we were able to get a greater feel for how the whiteboarding process works, and able to ask questions as to how to moderate, when to step in and when to let the conversation go.

After a brief break, we then moved on to discuss our HW from the previous night.  To do that, each group was assigned a different section of the reading and asked to provide a synopsis on a whiteboard.  To sum up, we had a very lengthy discussion on the discrepancy between what a teacher thinks he/she is teaching and what the student is learning.  I didn't bring it up, but this made me thing of Frank Noschese's blog on Pseudoteaching. In our discussion, we talked about how as we, as teachers, think we are helping our students understand a concept through example problems, our students, for the most part, are fixating on the equations produced.  The problem with that is students mistakenly think they can apply the derived equation to any problem dealing with the same concept.  I alluded to Rhett Allain's post by describing an "ABC Gum Rule."  (I didn't really have a name for this concept until I read Rhett's post, but I would always tell my kids that they had to always start from the basic equations, they could not ever start with derived equations.  Thanks Rhett!)  The rule, as I pointed out, is that you never want to eat Already Been Chewed Gum, rather, you always want a new piece.  Same thing for physics, you should always start a problem from the beginning, not an equation that was made for some other situation (which may or not be the same).

After that, Jon and Chris asked for feedback as to how we thought the first unit went.  It's amazing how well these modeling people all act as I remember Frank Noschese blogging about getting feedback from students more often than just the end of the year (read the post here).

They asked what worked and what didn't?  To the first we said, we liked learning: how to use LoggerPro (especially for linearization), the linearization summary sheet, breaking up the pendulum lab to finish the lab in less time (made groups take more ownership of work since others were depending on them to get it right), and using inductive reasoning to determine relationship instead of the teacher just telling "us" the answer.  What we didn't like: some wanted more explicit explanation of the relationships between independent and dependent variables (hopefully I'm remembering that correctly), and some wanted the workshop to move a little faster (I think she was referring to limiting some of the discussion, but Chris rephrased it as getting started quicker/more punctual coming out of breaks.  I'm not sure which was what she meant).

Buggy Lab

Throughout the day, I've seen and been a part of a great discussion about how to do the Modeling Buggy Lab.  For those not familiar, think classic algebra problem with 2 trains.  After screaming, "I hated that problem!" Ask yourself what did you dislike about it?  Probably the fact that it had no context.  This is where modeling steps in.

Here's the set up, you show the class a motorized car that moves at constant speed.  And, through socratic questioning, lead them to realize that the position and elapsed time are related.  You then ask them to determine the "graphical and mathematical" relationship between position and elapsed time (or clock reading).  You leave it up to the students to figure out how to find those relationships.

If you try this, your students might come up with one of these two solutions, (A) set up fixed distances and measure the time to travel those distances, or (B) place marks at distances for fixed values of time (place a piece of tape where the car is at 1 sec, 2 sec, ...)

This is where are tweebate begins.  Since the "convention" is to plot the independent variable on the horizontal axis, the two different means of collecting data would produce two different plots.  Option A, since the student set up fixed distances, that would be the independent variable.  Thus elapsed time (clock reading) would be on the vertical axis and distance traveled (or more specifically position) on the horizontal.  Option B would yield the opposite.

Our debate was whether or not we should let this happen.  Also discussed was the above was ok, but to just tell them to all plot time on the horizontal axis.

So here's my two cents:
What I love about the modeling curriculum is that we (teachers) are trying to foster discussion, which in the end should induce critical thinking skills.  So to me, let the students measure it how they think they should.  Let them graph it how they think they should.  As they all come together in the "Board Meeting," where they share their results, as the teacher try to help them draw out the important conclusion.  Did the two methods produce different results?  Did both methods produce a straight line?  What does that say about the relationship between position and time for the buggy?  Assuming the buggies go at the same speed, how do the slopes compare? If some have a slope that has units of m/s and some have s/m, lead them to generate the algebraic equation for the line.  Have one group rearrange their equation

$y=mx+b$

$\large x=\frac{y-b}{m}$

Discussing the "10% rule" which helps them figure out if the y-intercept is significant, can also come into play here.  If $b$ is 0, then:

$\large x=\left(\frac{1}{m}\right)y$

Thus, how do the slopes compare.  Again if the cars all travel at the same approximate speed, won't this be a great aha moment?  To me it's worth the time, rather than the teacher merely saying, "Don't worry about the convention you learned in middle school, just plot it this way."  In no way am I trying to demean those that do this, I just think it's worth the 10 minutes to let the discussion play out.  

If you have the time, you can also bring in the discussion of slope recommended by Arons, the "bible" of physics teachers (personally, I think it's an amazing book, but it's still no Bible, sorry Arons).  He recommends discussing the meaning of slope.  What does the slope of position vs time mean?  Most students will probably respond "change in y over change in x," which would confirm what Arons suggests. He writes that most students don't understand slope, they just know how to calculate it.  This is where you can take another 10 minutes and lead the students to realize that option A will produce a graph the measures how fast the buggy is moving while group B will produce a graph that measures how slow it is moving.  This is now a great time to lead them to see why the convention of independent variables on the horizontal and dependent on the vertical is not a convention that is always used.  Rather think ahead of the relationship you want to show, then set up the axes to show that relationship.

I know I'm new at this, so I would love to hear where, other than possibly time, we wouldn't want to have these discussions.

PS - for those wondering where the train problem comes in - take away the first buggy and now give them a second buggy (which travels at a different constant speed).  While the students turn in that buggy, have them graph (and find equation for the slope) the data for the second buggy.  Now, without the buggies in hand, have them predict where the collision will occur if you start them at opposite ends (meter stick, room, table, etc).  Viola, the train problem will come to life.  I did this with my AP kids and they were so excited when they say that their calculation was "right"  (read within error predicted by a monte carlo analysis, which I say a big thank you to Andy and the rest of the crew in the Global Physics Dept).

Oh no you didn't!

So I was relaxing, watching tv, and basically minding my own business.  Then it happened!  I saw the most offensive commercial I've ever seen.  I'm not going to give the company the time of day (I'm well aware the power my blog carries in the world) by naming them.  Needless to say, it was a company trying to entice people to receive help from IRS past taxes.

Here's the kicker, a few seconds into the commercial, the spokesman (a cartoon of a classic nerd as the host) begins to explain how their company will lower your tax payments to the IRS.  Here's what he writes on the whiteboard for someone that owes $20,000:

$5 / 2*3.14$

then:

$A \times b/C + 8^2$

followed by:

$x2+u2\,(40\%)+pi^4$

which magically makes the $20,000 become $1600!

I'm not sure which is worse, the fact that this company thinks that a "nerd" would write the above gibberish or that people will think this "magical" equations are the way for them to fix their problems.  I'm hoping Dan Meyer's head is erupting right now!  (I say that knowing he probably won't read this, and may, with his Jedi mind for math, just sense this atrocity of mathematics!) 

Sorry to vent, thanks for making it this far, just had to get that off my chest.

The Atlantic-Pacific Rule

In preparation for this weeks Global Physics Department meeting, Andy has set up a online corkboard for people to begin sharing how they teach error propagation/analysis.  After briefly posting how I teach it, I thought it might be worthwhile to share in greater detail.

As an engineering major, I had my fair share of error anaylsis.  I think many of us High School teachers would agree that to get our students proficient in proper error analysis and propagation is not likely.  Although I feel the engineering way is a better method (ie: $4.2 \pm 0.3\, cm$), from my experience, HS students get lost in the numbers and miss the point.  Getting them to then use something like this is basically impossible:

$\large \sigma_f = \sqrt{\left(\frac{\delta f}{\delta a}\sigma_a)\right)^2+\left(\frac{\delta f}{\delta b}\sigma_b)\right)^2}$

Moreover, I don't think a HS physics student needs that level of sophistication for their error analysis.  A practicing engineer, with lives in his or her hands, absolutely, but a student just being introduced to the idea, I don't think so. 
 
So instead, I build off what my school's chemistry teachers do.  One of their fundamental aspects is the beginnings of error analysis and propagation: writing the measured value with the correct significant figures (SigFigs), and knowing how to determine the number written by others. For this, instead of the traditional rules for reporting numbers with SigFigs, they use the Atlantic-Pacific Rules, which goes something like this:

Imagine the measured number is written such that the outline of the United States is surrounding the number:

You then ask yourself a series of questions:
1. Is the decimal point Present or Absent?
     - If the decimal point is Present, start from the Pacific side; if it is Absent start from the Atlantic side.
2. Once you have identified from what "side" of the number you start,
     - begin by counting the first non-zero number.  Count that number and every number that follows it.
3. The right-most SigFig is the uncertain digit that was estimated.

For the number above, since the decimal is Present, start from the Pacific side and count left to right.  The first non-zero number is "1" and if you follow through, there are 4 significant digits with the 0 (to the right of the 7) as the estimated digit.

For the number "$549,030,000" the Atlantic-Pacific Rule would tell you that there are 5 SigFigs with the 3 being the uncertain digit (decimal point absent, so you begin from the Atlantic Ocean side and count from right to left).

From my experience, this Rule gives all the same results of the typical rules found in most texts.  However, I find that students can remember this much easier, many liking the visual aspect of the rule.  If you've never seen this before, maybe give this a try.

Parent Letter - First Draft

After talking with some in my admin, we decided it might be a good idea to send a letter the parents of my new students to prepare them for a guided inquiry based class.  My hope is to not make it full of teacher talk, but a quick, concise preview to prevent the complaint, "He doesn't teach anything."  Any feedback would be greatly appreciated:

Dear Parents and Guardians,
    I would like to take this opportunity to welcome your son or daughter to my physics class. Physics is a challenging subject, that unfortunately, brings negative perceptions for many people. I wish this was not the case, as physics is a fascinating class and the foundation for all of science and engineering. Over the last several years, I have continually asked myself, “How can I better teach this course?” Luckily, many other Physics teachers have asked this very same question, and they have actively researched the answer. What the research is showing is that physics teachers need to stop talking about  physics, and start helping their students do physics.

One quirky way I’ve seen this transition described is the teacher needs to change from being a “Sage on the Stage” to a “Guide on the Side.” What I mean by that, is research shows students need to be actively engaged in deductive reasoning to determine the laws of physics from experiment rather than passively listening to a teacher describe those laws. In the process of helping students do physics, those students learn better problem solving skills, critical thinking skills, and communication skills. Unfortunately, most students haven’t been exposed to learning through guided inquiry, so many students feel uncomfortable early on. For most students, this discomfort eases part way through the first quarter. If your son or daughter feels lost at any point, please have them come and see me, and I will be happy to do what I can to help them.

In the end, my hope is to create an interesting and enjoyable way for your son or daughter to learn physics. I continue to try to find better ways to try to do that. Along the way, I hope your child will learn skills essential for college and their future job, even if he or she has no interest directly in the subject of physics. Who knows, maybe your son or daughter will decide that pursuing a career in physics is for them too!