Re: [Phys-l] coffee + cream (was: good questions)

["Cliff Parker" <cparker@charter.net>]

> This *increases* the value of the question in my eyes.  Real life is
> full of ill-posed questions.  Students do not get enough classroom
> experience dealing with ill-posed questions.  Not nearly enough.

I have used this problem for years and never thought about the temperature 
difference between the milk and room.  I wonder why not.

I agree with you John the value of the question is much higher when students 
have to figure out what is meant.  There is a time and a place for those 
kinds of questions.

This is one reason I like to kick around significant digits at the beginning 
of the year.  We don't mess with all of the rules for carrying out 
operations but I do ask them to consider how many digits in their answers 
have significance and I ask them to do so by pulling that significance out 
of the context rather by following blindly a rule like they did the previous 
year in Chemistry.  On my first test I asked how far I had run in 1971 
during each race, as a member of my schools 4 x 440 yard really team.  I 
warned them to make sure they expressed their answer with the appropriate 
number of significant digits.  As expected a good number of them resorted 
back to their rules from the year before and said there should be 2 sig fig 
because 110 has one trailing zero.  Old habits are hard to break.  We always 
spend a good deal of time discussing tests the next day.  In that process I 
explained that there should be more sig figs because using only two would 
indicate that the person who laid out the track may have made it 430 or 450 
yards and that was just not reasonable.  After about 5 minutes of give and 
take where they argued for their rules, one student who had remained silent 
said "What about the hand off zones.  If you consider those your uncertainty 
increase so that only two digits are significant since a runner may hand off 
slightly before the 110 mark or slightly after."  I LOVE IT WHEN THEY CATCH 
ME LIKE THAT.  I said ohhhhh... hadn't thought of that.  I guess I will have 
to give full credit to all of you who used that reasoning to answer with two 
sig figs.  To my complete astonishment all of my rule followers immediately 
chimed it "That's what I was thinking too."