Human Dimensional Analysis

This week I decided to #BeBrave and try something I had never done before.

 The whole idea came about on a random Wednesday, when, by 4th hour, I was decidedly grumpy.  I knew I was grumpy, and I didn't want to be grumpy.

 We have been talking a lot about controlled experiments and variables in my class, so I shared with my class my hypothesis: If I stand on the lab desks, then I will be less grumpy.

 And, I jumped on the table top, pencil skirt and all.

There were a ton of variables in my experiment, and it wasn't exactly controlled, but the kids loved it. I taught all hour from on top of their tables, freaking them out when I stepped too close to the edge and making them giggle as I attempted to hop from one table to another in my dress clothes.

Despite the lack of control in the experiment, however, I have to admit that my mood was much better at the end of the hour than at the beginning. And it got me thinking about other ways to incorporate nonsensical fun like this in a legitimate instructional way -- and Human Dimensional Analysis was born.

 I love teaching dimensional analysis because I believe in its power and its ability to help in other areas outside of the chemistry classroom. For those of you who are non-science folks out there, dimensional analysis is basically a slick, no-mess way to convert units--that is, once you learn how to do it.  It can be very messy if you haven't mastered it.  I have had several students go away to college only to return telling me how valuable it is.

In my head I'm all like, "I KNOW...why do you think I spent so much time in class trying to tell you that?",

but in my heart I'm all like, "AWWWWW! I looooooove my job so much!"

and with my mouth I'm all like, "Good!  I'm so glad!"

Anyway, I like teaching it and it's important to me that they get it.  But it's not always easy, and it's an area where there is initially a wide range of ability.  Some students get it after only one short example. Some are totally clueless after 3 days of instruction.  Some saw it in pre-calculus and know it coming into my class.

So, here's what I did this year.

I taught the material like I normally do.  This entails explaining the steps and rationale to my students and going through a couple of examples in detail.

Then, instead of assigning a set of practice problems to work individually, I instead took the practice problems I normally assign and made a post it note for each numerical value that showed up in those problems.

For example, if a problem said, "If you are traveling 108 ft/sec across London Bridge, and the speed limit is 32 km/hr, are you speeding?" I would make the following post-its:

108 ft
1 sec
60 min
1 hr
60 sec
1 min
3.4 ft
1 m
1000 m
1 km

This represents all of the numbers needed for answering this particular question using dimensional analysis.  I did this for a grand total of about 5 questions, ranging from those with only 1 conversion factor to ones like this, which I saved for the end.

I asked students in my first hour to create a sign on 11 x 17 white paper that showed the number value in whatever color marker they wanted and the unit in black.

Along the back wall in my classroom is a countertop that spans the width of the classroom.  I told the students that a number on top of the counter represented the numerator and a number on the floor represented the denominator.

Then we talked about conversion factors.  I asked whoever had the sign with 60 seconds on it to come up to the counter.  I let them choose whether to stand on the ground or on the counter.  Then, I asked for someone who was equal to the 60 s person to also come up.  Of course, the person with 1 minute walked up.  If the 60 seconds person stood on the counter, then the 1 min person stood on the floor.  We talked about why it was okay for them to stand either way, why the numerical value of the conversion factor was actually one, and why it was so important to make sure that two people standing together as a conversion factor were equal to one another.

Then we set up a simple problem.  I asked a student volunteer to read the question.  For example, "Adelai Joy Sharp weighed exactly 7 lbs at birth.  What is her weight in grams?"

Someone out in the crowd had the given.  I decided to include the given because I often see students try to use conversion factors first or put the units for the given in weird places.  So we talked about how the given always goes on top and is not a conversion factor.

Then, we talked about how we would choose the first conversion factor to use by looking at the units of the given.  I asked students to look at the list of their conversion factors to find one that made use of pounds.  We would then get the two members of the 2.2 lbs = 1 kg conversion factor.  We talked through how if the 2.2 lbs person went on the bottom, then the "lb" unit would cancel, which I first started having students show by simply putting their hands over the unit, but eventually moved to folding the paper so that the unit no longer showed.  Then we would continue until the only unit(s) left showing were the ones asked for in the question.

This isn't the best picture, but it gives you the idea...I love the range of facial expressions.

You can't really tell from this picture, but this dimensional analysis reads (from left to right, not including me):

   7 lbs   x   1 kg      x   1000 g 
                 2.2 lbs          1 kg
                     
After about 1 example, they started catching on pretty quick, and students would start getting out of their chairs when they saw that they were needed without me having to lead them too much.  My favorite part of all of this was the students shrieking "YES!" when they were needed and running up to the counter, or students helpfully waving students around from the audience to get their classmates in the right spots.  If a student was a part of the problem, they were excused from doing that one on their paper.  If they weren't a part of it, they were expected to copy it down as it appeared to them from the audience.
 
Another thing that was cool about this was that it was easy to see how to calculate the answer.  The given was multiplied by anything on top of the counter and divided by anything on the floor.  I think it made it visually simple for them to process.

I loved doing this and I believe the students loved doing it.  It got them up and out of their seats, made use of the bodily-kinesthetic mode of learning (good for a Friday afternoon), and made the hour fly by. It wasn't boring for the students who were already getting it, either. But I also feel that it truly helped the ones who were struggling still.  And while I wouldn't go as far to say that everyone gets it 100%, I think those stragglers now have a huge head start of where they would have been after struggling through one practice problem on their own in the same amount of time.

Finally, I felt empowered because I tried something new.  It wasn't perfect, but it was pretty darn good and definitely a step in the right direction.  It also helped me with my mission to have more fun and provided me with one more piece of evidence to support my hypothesis that standing on desks really does make you less grumpy. :)