Qualitative/Quantitative translation

What you might be asked to do on a QQT:

Work with multiple representations. You may be given one representation and asked to create another representation of the same situation. Representations can include math equations, worddescriptions, graphs, diagrams, and data tables.

Evaluate a student’s words and deconstruct their arguments, identifying what is correct or incorrect. Sometimes you will have to connect the correct (or incorrect) features of arguments to physics principles or equations. You may have to create a correct response based on your answers.

Evaluate a student’s representations. You may be shown a student’s graph or mathematical work that describes the situation, but there may be features of the graph or equation that are wrong. You will need to identify the correct or incorrect features of the graph.

Things to look for when evaluating a graph:

  1. Does it have a slope (positive/negative/zero) that makes sense? If you draw a graph of energy over time and the slope is, then there is a real problem!
  2. Does it have an intercept (on the y-axis or x-axis or none at all) that makes sense? Some graphs should go through the origin (if I work zero hours, I should be paid zero money). Other graphs, like “height of a person vs. age” should not go through the origin (my baby wasn’t born zero-feet-zero).
  3. Should the graph be a line or a curve? Sometimes this matters depending upon the situation.

Things to look for when evaluating equation proposed by a student:

  1. The symbols in the numerator - when they increase, does the quantity of interest increase?
  2. The symbols in the denominator - when they increase, does the quantity of interest decrease?

Things to look for when evaluating a student’s words:

  1. If the student uses proportional reasoning (sounds like this: “if the spring’s compression doubles, then the spring has twice the energy”) check the equation that shows this relationship (in this case, \(U_s = ½kx^2\)) and see if there is actually a direct relationship (in this case, no it is a quadratic relationship). You would need to correct the student on this (it is actually four times the energy).
  2. If the student says that something increases or decreases (sounds like this: “if the ball moves faster, then the time it takes to pass through the photogate increases”), check to see if that makes sense (“no it doesn’t—a faster ball would spend less time passing through a photogate) and correct it.
Source: National Math + Science Initiative