Table 4 Sample responses for sub-level “Description” for all levels of the framework
From: Cognitive framework for blended mathematical sensemaking in science
Level | Acceleration | Beer’s law | Energy conversion |
|---|---|---|---|
1 Qualitative | “In the sim you can change the mass and the force, and see how that affects acceleration” | “I feel like the variables that are really affecting absorbance are the concentration, the type of solution and the length” | Student: may be the starting amount of energy. Then more and more energy gets put in, and then more energy ends up at the end heating the water Interviewer: any other energy? Student: May be the final energy? The energy that is released after the function has been done |
2 Quantitative | “If you apply a force of 500 N and you have a mass of 50, then the net force is 500 (no friction), you see that the acceleration is 10” | “For absorbance, this one is a decimal number much smaller (than transmittance), the closer you are (to the light source), the smaller the number. As you come up here (increase the distance to the light source) it comes from 0.16 to 1.3 (absorbance)” | “Some of the energy is going away as thermal energy in the very beginning, but what energy IS going into the system into the generator is the same amount that’s coming out. So, if three things of mechanical energy go in, three things of mechanical energy come out” |
3 Conceptual | “The friction force was 84, in order to counter it, you would need, like 84 newtons of applied force, and then the weight of this mass is 50 kg. I solved on paper what the acceleration should be (using F = ma), and it should be 1.68 m/s2, and that’s what the sim is showing” | Student: I guess there is something between the wavelength and the solution type, some constant, like a certain variable that is specific to the solution that determines what wavelength gets through. Going back to the data, you would have to divide the absorbance and the length by the molar absorption coefficient to get the concentration Interviewer: why do you need to divide? Student: just by manipulating the numbers, if I divided it every time it would give me the correct number | Student: electrical energy equals 1/6 thermal plus 5/6 of the mechanical Interviewer: why you derived it in that form? Student: because the input outlet has to be equal to the output Interviewer: if you generalize from this specific set-up to across set-ups, how would you change your equation? Student: I think every energy will have a different way of showing stuff. The lightbulb would generate more heat, then, let’s say, the fan. The ratio of the thermal energy to the ratio of the light energy would be a little different |