I also have a (tank-based) water heater in the basement. This morning I washed some dishes (using the hot water) and then I wanted to make some coffee.
I have an electric caraffe that boils water. It’s awesome. You just put in some water, flip a switch, and soon your water is boiling. I assume it heats up some element inside it, which heats up the water.
Should I fill the caraffe with hot water or cold water from my tap?
If I fill it with hot water, it takes some hot water out of my hot-water tank, which means that cold water goes into my hot-water tank (bad). On the other hand, the electric caraffe doesn’t have to work as much to boil the water (good)!
If I fill it with cold water, the hot-water tank is left alone to be hot (good). But my little caraffe has to work an extra 50 degrees! Also, the hotter my hot-water tank is, the faster it leaks heat into the cold basement air! Aiee!
I hope students coming out of my classes could
- Understand the dilemma
- Notice these dilemmas around them for themselves
- Figure out what they’d need to know to answer the questions they have
- Make an intentional decision about whether the work required to answer the question is worth having the correct answer to the question (instead of just shrugging it off because they don’t want to think about it).
gasstationwithoutpumps
November 27, 2011 at 12:14 pm
Some other considerations:
1) is the hot water tank heated with gas or electricity?
2) what if you installed a European-style instant hot-water heater, rather than an American-style storage tank?
3) what is the difference in mineral and oxygen content for water in the hot-water heater and cold water from the tap? (do you have an ion-exchange column for softening your hot water?)
Riley Lark
November 27, 2011 at 12:18 pm
I especially like “how long are the pipes from the heater to the faucet, how fast do they radiate heat, and when does it matter?”
Basically, I think that if kids can ask questions like ours, they’ll be alright.
andrew
November 27, 2011 at 2:35 pm
There’s a lot of complexity in the fourth point above – that is, how do you tell wether it’s worth working towards or not. I see this sort of response constantly, and I’m not sure that “shrugging it off” is the right description. More often I think they’re looking at the the work and (still unknown) process that it would take to get a textbook answer, and then walk away because they “know” they can’t do it.
There was a math contest question last week (AMA?) that asked about how many pairs of prime numbers add to 10,001, and I watched a dozen middle schoolers walk away from it. In their heads it was an exhaustive list, probably one that had a full table of correctness on the answer sheet. So they moved on.
When you’re assessing the amount of work required, the complementary assessment is “how much do I really have to know to answer my question?”
The notion that real problems have different levels of accurate assessment and that “around 10 times as much” is perfectly actionable intelligence, makes a whole host of problems seem worth tackling.
I trace a ton of these problems back to how poorly we teach estimation as part of the math/science sequence.
Riley Lark
November 27, 2011 at 3:09 pm
In my brain this is connected to the problem of the shortest path through a parking lot. I want students to be able to ask questions that will help them take a “usefully-shorter” path, but to know they should stop before they get out the tape measure and actually find *shortest* path.
My guess was that some students just wouldn’t want to think very much about which is the shortest path, and they’d “shrug it off.” Thanks for the reminder that this is an issue that we should be sensitive about!
The problem with textbooks and math competitions is that the prize is always points and abstract satisfaction at completing a puzzle. In most situations outside of school, the prize is something like a lower energy bill or a shorter commute or a stronger building. Until we see that kind of reward in school somehow, I don’t know if we’ll be able to teach #4 easily!
What’s the Reward? |
November 29, 2011 at 10:39 am
[...] interesting discussion is happening over at Point of Inflection. How do students decide whether solving a problem is worth the time? Andrew has some great [...]
Frank Lee
December 23, 2011 at 6:31 pm
Hey I ask myself the same question when I boil water on the stove! I assumed the apartment building’s water heater has a much higher efficiency than the gas stove, plus waiting for for hot tap water takes less time than waiting for cold water to boil.
Also, I’m not the one who has to pay for the water heated by the apartment building, so that’s really what matters…
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