Table 3 Interview coding rubric for Beer’s Law simulation
From: Cognitive framework for blended mathematical sensemaking in science
1 | Description | Students identify concentration and width of the container as variables that affect absorbance and transmittance |
Pattern | Students identify that for specific wavelength the larger the concentration the larger the absorbance, and the smaller the transmittance | |
Mechanism | Students recognize that the concentration of substance is the main causal factor behind the changing absorbance and transmittance but can’t define the exact mathematical relationship for Beer’s law | |
2 | Description | Students quantitatively describe how the change in the concentration and the container width affect absorbance and transmittance but don’t recognize quantitative patterns yet Example: when I use concentration X for substance A, the absorbance changes to Y |
Pattern | Students recognize that the relationship between concentration/container width and absorbance is positive linear, and between concentration/container width and transmittance is not linear (may say logarithmic or inverse). Students are not yet able to relate the observed patterns to the operations in a mathematical equation and can’t develop exact mathematical relationship for Beer’s law | |
Mechanism | Students can explain quantitatively (express the relationship as an equation) for how the change in concentration and container width affects absorbance. The formula derived: A = concentration • width of vial• molar absorption coefficient (MAC). Students can’t fully explain why MAC should be included in the equation and can’t justify multiplication operations beyond the fact that numerical values of the variables otherwise don’t agree. Students recognize that the cause for changing absorbance is concentration of the substance Note: MAC is an unobserved variable because it is not reflected in the PhET simulation and can only be inferred by noticing that absorbance at a given concentration and wavelength is different across various substances. MAC is provided to students in data tables | |
3 | Description | Students can express the relationship as an equation for absorbance (A = concentration • width of vial • molar absorption coefficient (MAC)) and explain that MAC relates to specific properties of a given substance, and therefore should be included in the equation. Students can’t explain why multiplication is their operation of choice beyond the fact that the numerical values of the variables otherwise don’t agree |
Pattern | Students can develop the equation for absorbance and explain how the patterns among variables in the formula relate to observations. Specifically, students recognize that concentration and container width have a positive linear relationship to absorbance, which suggests multiplication operation. They also recognize that concentration and container width relate to absorbance through the factor of MAC, which also suggests multiplication operation. Students are not yet able to provide a causal explanation of the equation structure | |
Mechanism | Students recognize that the cause for the change in absorbance is primarily the change in concentration (all other factors such as cuvette width and MAC being related to concentration) and can relate all the variables and operations in the equation to the observations of the phenomenon |