Table 5 Sample responses for sub-level “Pattern” for all levels of the framework
From: Cognitive framework for blended mathematical sensemaking in science
Level | Acceleration | Beer’s law | Energy conversion |
|---|---|---|---|
1 Qualitative | “As you apply more force and the mass stays the same, that changes acceleration and makes it faster” | “Transmittance and absorbance have sort of an opposite relationship, as absorbance goes up transmittance goes down with increasing concentration” | “A lot more energy is being put into it than coming out” |
2 Quantitative | “The more mass that you get or the greater acceleration that you are going at, the greater the force will be. So, the force is directly related to the mass and the acceleration” | “I think the transmittance is non-linear with the concentration, and the absorbance is linear with the concentration when the wavelength is held at like a standard wavelength and the volume doesn’t change (container width).” “If it is 1 cm (the vial width), the maximum absorbance goes up by 0.5 every 100 mM” | “It’s not a 100% mechanical when it goes out because there is going to be the heat generated. Every six electrical energy units that goes in, there is going to be one unit that comes out as a thermal (from the sim)” |
3 Conceptual | “As the mass increases, it will require more force. If you do like F = a/m (as opposed to F = ma), that means that as the mass increases, it will take less force to move the object, which doesn’t make sense, I think. As the mass increase, the object should be harder to move” | “As the concentration is higher, the absorbance rate gets higher as well, so that’s proportional, on top. And then, opposite of the radius, as the radius gets…oh…. (explores the sim)…I was wrong in that. As the radius gets bigger, the absorbance will go up as well, so it probably will be concentration times radius at a certain wavelength will equal to the rate of absorbance” | Student: energy output equals some sort of conversion rate, depending on what you are using, like a normal light bulb vs you are using like heating the water. The conversion rate represents the efficiency of the transfer of energy times, like, the input of the energy Interviewer: and you said that it is efficiency times the energy output. Why did you decide that it should be multiplication? Student: the efficiency was not a whole number, but a small number, like a percentage, so ranging from like a 1% to like a 100%. Multiplied just takes the maximum amount of energy that could be in an ideal system, and then shrinks that to like what it actually is |