Physics of playthings: Slingball pull versus flight distance
The class had measured pull distance p₂ versus flight distance f₂ for Djubi Slingballs.
Sean measuring the pull distance
Looking at the data on the graph suggested a linear relationship as opposed to a non-linear relationship. Two days earlier a physics of playthings activity yielded no relationship between the variables. By comparison, the Slingball data was surprisingly linear given the lack of control applied for launch angle. By and large the students launched generally horizontally, but not exactly horizontally.
One student looked at me and said, "What's a linear relationship?" I asked the student, "What math class have you completed?" The student responded, "MS 101" which is Algebra and Trigonometry. This did not surprise me - I have become accustomed to students having completed MS 100 College Algebra and MS 101 Algebra and Trigonometry and being unable to reason algebraically. If the goal is quantitative literacy, algebraic reasoning capacity, an understanding of functions, then the current mathematics curriculum is nothing short of an abysmal failure. A delusion that there is a way to get that curriculum to produce algebraic competency. Working the even problems from one to thirty showing that one can factor or distribute or solve does not generate the ability to think mathematically, to reason algebraically.
Jocela, Fredson, and Kiora working in the rain
Although rain was falling during the measurements, the students persevered in collecting data.
Although the angle was not strongly controlled for, each group generated roughly linear data that for each group had distinct slopes. This suggests that while the launch angle was not strongly controlled, groups were generally internally consistent in launching at a common angle for their launches.
Some groups were measuring to the final location of the Slingball, others were measuring the initial landing. I suggested that the initial landing was probably a more consistent measure than the distance after a bounce.
Sanjay, Alexander, Myena, Joe Scott readying to launch, Rosie-Rita, Tommuy, Fredson, Jocela, Kiora
Launches were from west to east out on the lawn. Attempts to work on the porch ran into ricochet issues especially on longer flights. A pull distance of zero was deemed to have a zero flight distance. The pull distances were then measured from that slack elastic point - how far back the ball was pulled from that no tension position, not the distance to the front of the elastic (the attachment point). But I should think that measurement could be made, it should just impact the y-intercept.
The class wrapped up with a discussion of a linear mathematical model for the data and a look at the different slopes obtained.
Whether the approach of an equation a week tied to a physical system in physical science can engender algebraic thinking remains dubious at best.
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