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!