Wednesday, July 10, 2013

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.  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.


Ben Lampe said...

I don't disagree with anything you have said, but I will continue to be a unit hound. I have not had the experience that students do not know their units by the end of the year. If I am a stickler about it, make a big deal about it, and am hard on myself about it, they all follow suit. It usually takes my kids about 1 test to realize that I am serious. From that point on, it is a non-issue. In terms of the 1 N causes a 1 kg mass to accelerate with an acceleration of 1 (m/s)/s. I don't see the issue. Get a 1 kg cart, apply a 1 N mass and measure the acceleration of the cart with a motion detector. I am curious why you are so opposed to this discussion. I think that units only add to a student's understanding, as long as they "get" units in the first place. I have found that after a month of harping on units, most students, when required, can determine the appropriate units with the appropriate reasoning. To be fair, I would accept any unit for acceleration that had the appropriate dimensions. So, my pain in the butt kids will usually do some unit conversion to get an answer in (cm/hr)/microsecond or something like that. I am cool with that because it makes it so clear that they know what they are doing, and they are having their own version of fun with it. Perhaps I am not a unit hound, but rather a dimension hound. I do think that fluency with units is evidence of the students better/different kind of understanding. To sum up, I don't think focusing on units hurts them at all, but failing to focus on units might cause them difficulty later on, when they have learned the bad habit.

Kamala said...

You've never heard of the Millennium Falcon?... It's the ship that made the Kessel Run in less than twelve parsecs...