http://serc.carleton.edu/spaceboston/2010activities/46691.html#discussion http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12721 Alisa Hilfinger 1277563620 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12721 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12759
Here are some rambling thoughts from a mathematician who really knows nothing.

1. (NOT RELATED TO YOUR ACTIVITY): One thing that drove me nuts as a kid in physics class was the origin of formulas. I was under the impression that quantities described in physics class (work, force, energy, etc) really "exist" and we're finding formulas for them. It took me a long while to realise that, like mathematics, we're creating concepts and creating formulas to match those concepts we created. For example, I have no idea what "force" is, but I am willing to say that F = ma is a *definition* of force, not so much an equation for it. Also, I have an intuitive feel of what "work" is: Suppose I push a box. If it is twice as massive, it is twice as hard to push. If I push it twice as far, I feel I have done double the "work." So work is some concept that I feel should exist that is directly proportional to mass and directly proportional to distance. I can make up most any formula I want, but easy is always good so let's *define* work to be: W = F*d. SO this is what phsycists do over and over again. They observe things in the universe, develop an intuitive feel for what seems to be happening, and then try to create formulas for concepts that seem to mimic what we feel. We could just as well define work to be 7*F*d or 15*F^2*d^3 (but that doesn't match our intuition as well). We always like the simplest approach.

The notion of potential energy drives me nuts. You refered to a "reference level" so if I hold a brick up in the air and ask how much potential energy does it have, I would answer mgh where h is the height above the floor. But if I told you I was actually on the second floor and want to use a different value for h, then the value of my potential energy has changed? So what does this mean for the law of conservation of energy? (My personal definition of potential energy is: that which makes the law of conservation of energy work!)

Anyway, I guess I am just saying that it might be a good pre-activity for kids (or a mental experiment at least) to derive a formula for "work" by starting with the idea of pushing a box and asking "on which variables would you like it to depend? - that is, changing what changes the amount of work you do?" and then, "what's the simplest formula you can write that relates those quantities in the way you feel is right?" I bet you'll get W = fd from this.

[BTW: The formula for KE is really from calculus. There seems to be this notion of "momentum" in our intuition and the simplest formula one might imagine for it is mv. Then "energy" is a concept that somehow affects momentum of an object. A change of energy gives a new momentum for an object, and we're in calculus land. It seems the simplest thing to define is KE is that which fits the equation:

d(KE)/dv = momentum.

Integrating gives, KE = (1/2)m v^2. It seems to me, in my naive understanding of things, that formulas in physics are really based on capturing intuive notions in the simplest mathematical way possible. We're creating them.]

2. I love the idea of doing this activity before you even use the standard vocab for any of this. That, to me, is so important. I teach many of my math classes this way, letting the kids make up names for things which happens only when there is a need for something to be named. (Why name something if there is no need yet for it being named?) We then have a discussion on "what we called it versus what the rest of the world calls it" (e.g. the word "powers" versus the word "logarithms.")

This is a great activity. Despite all my ramblings above I really have nothing deep to say about what you've put together here. I am very eager to hear how it actually goes with a group of kids. You'll see then, I am sure, what adjustments and refinements and reorderings are needed.

Grand stuff!

- J

]]> James Tanton 1277649780 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12759 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12781
I like the idea of taking a standard activity and putting on a twist to make it more educational and interesting. The resulting activity, I suspect, will be useful to a lot of teachers.

The $5 analogy troubles me since it implies there are temporal aspects to work and energy -- energy can also be right here, right now, too, just like the work you suggest. And it can be hard to store and transport energy, so not many energy banks function well.

A really good activity, seems like it's ready to go!

all the best -

Lindy

]]> Lindy Elkins-Tanton 1277731380 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12781 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12872
I think providing a common experience that everyone in the class can refer to is important. It’s inclusive, it grounds discussion in actual observations, and it also makes it easy to return to the materials/phenomena as questions or disagreements arise. The particular experience you’ve chosen is simple and well suited to your goals.

It would be helpful to me (and perhaps to teachers who consider using your activity) if the specific concepts you want kids to understand were highlighted succinctly under “Learning Goals.”

Regarding your homework assignment: Are the things that students will write in the “What I know” column their ramp and marbles observations? If so, “What I noticed” or "Observations" might capture that, and distinguish it from “What I Learned.” (You might be after something else here, though.)

I’ll be very interested to hear how Hawkins’ structure (messing about/multiply programmed, guided investigations/lecturing-discussing-theorizing) materializes in your classroom and whether you feel it serves you and the students well.

Ellen
]]> Ellen Doris 1277953560 http://serc.carleton.edu/spaceboston/2010activities/46691.html#post12872