Momentum in a constructivist vein

Laboratory 042 was an entirely new design this term. The class opens on a quote from a letter Sir Isaac Newton wrote to Ignace Gaston Pardies:

For the best and safest method of philosophising seems to be, first to enquire diligently into properties of things, and to establish those properties by experiments and then to proceed more slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.  - The Renaissance Mathematicus.

After that I demonstrated a qualitative introduction to marble collisions on a ruler track.
Sylvia discusses initial results

The pitch is rather carefully crafted. I first ask the students to predict the result prior to any marble runs. Then I release the marble. Once the students grasp "marbles in" equals "marbles out" then I focus on the penultimate marble.

How does the penultimate marble "know" whether it should stay or go? How does the penultimate marble in the line "keep count" of the number of inbound marbles?
Jermis makes calculations

I then demonstrated that "speed in" is equal to "speed out." When I ask the students to formulate explanations I often get answers such as "force" or "pressure." I then usually return that back to them, "What is force? What is pressure?" This term as in others I had the opportunity to discuss the usage of "magic" words that the speaker does not actually understand. For many of the students, tossing around "pressure" is the equivalent of saying "magic." Neither word explains how the marbles "know" what to do.

Kasinta works onthe layout while Cheryl makes notes

I almost always tie this back into the Dyson quote from laboratory one. The marbles know what to do and are doing it. Once the students have their minds wrapped around the mystery of the marbles, I ask them to form small groups and to try to attach numbers to the system. To make qualitative measurements of mass and velocity for the marbles. I provide no further guidance nor correction. I do circulate and try to be helpful to groups that seek assistance.

 A lighter moment. Alwihter,Sylvia, Fritz, and Tracy Anne.

This being new this term I was unsure what would happen. In the first class no student even referred to the old lab in the text, nor had I mentioned it. Each group chased their own concepts and did original research unguided by me. As the students challenged each other's ideas I saw science being done.

Fritz explains the results of his group's work while Silver Rose, Kasinta, Caroline, Tracy Anne, Patsipa, and Cheryl look on.

In the second portion of the laboratory the groups each presented to the other groups their findings. The findings were not always consistent and some were contradictory. I was careful not to say anything that might prejudice the opinions of the groups. I deflected questions that were phrased, "Is this the right answer?" usually by echoing the Gilbert quote from lab one. If you have measured as carefully as you can, then trust your measurements.

Jermis explains his group's results

Getting the groups to stop experimenting was actually difficult. I had to step in as even with a three hour laboratory, time was getting short. The students felt a sense of ownership in the knowledge they were generating. Some of the presentations also included passionate defenses of data gathered. Scientists hammering out knowledge from their data.
The electronic scale was found to be far faster at generating mass measurements than the quadruple beam balances

Even in this phase I steered clear of making any judgments, sticking only to asking questions as to how data was gathered. Some groups were timing linear velocities using the sloping portion of their ruler tracks. Although I did work with one group on trying to sort out average velocity versus instantaneous velocity for an accelerating marble, I let other groups proceed with this procedure without comment.
 Nancy records data for her group

The odd complication is that the marbles lose momentum in the collision - partly due to energy losses, partly friction, and partly issues involving the fact that marbles roll and thus there is rotational inertia to be dealt with. None of this is something I discuss. As a result, the average velocity of the inbound marble, which is about half of the terminal velocity of the marble, generates a speed very close to the outbound speed of the marble or marbles kicked off of the end of the line of marbles. A false positive confirmation of the conservation of momentum.
Nancy explains her results as Leslie, Mercy, Angie, Robertson, and David look on

I deliberately did not cover momentum nor seek to have the students calculate the momentum. Only on the following day did I introduce the concept of multiplying the mass and the velocity to obtain a quantity called momentum. While the students confirmed mass in equals mass out, the results for speed were only that the speed outbound is proportional to the speed inbound. Some groups found higher outbound speeds, some lower outbound speeds. The results were not conclusive.


At the end of the laboratory period I did note to the class that the method of the class had been one called "discovery learning." I noted that it can be noisy and at times a little chaotic, but that they had been scientists during the lab. I also noted that the origins of modern science were in the experiments and discussions of the Royal Society and members such as Newton, Hooke, and Boyle. Their experiments and their presentations were science, constructed shared theories and understandings.

The only difficulty I had during this wrap-up explanation was that some students had gone back to their marbles and tracks and were still trying to sort out the physics of the system. Three hours of lab and their minds were still invested in solving the system.

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