Translation of P = kT into a pictorial external representation by high school seniors

This paper describes the results achieved by high school seniors on an item which involves translation of the equation P = kT into a corresponding pictorial external representation. The majority of students (the classes of 2011, 2012 and 2013) did not give the correct answer to the multiple choice part of the translation item. They chose pictorial representations of the other gas laws (P = k/V, or V = kT) instead. Failure to choose the correct answer was surprising considering that the symbol for volume was absent which should have been the key clue. Through the analysis of students' explanations (the classes of 2011 and 2012) and interviews (the class of 2013) we considered the reasoning applied by students who chose the correct answer or distractors for the multiple choice part of the item. Among the students who answered correctly there were explanations which contained misconceptions. Several factors that lead to the unsuccessful translation between external representations have been discovered. Students interpreted the change in one quantity based on the notation for the change in another one because of deep rooted cognitive schemas about changing two quantities (volume and pressure, pressure and temperature, temperature and volume), without consideration that for such changes to be valid for gases all three quantities need to be considered for a certain amount of substance. Those cognitive schemas interfered with mathematical reasoning, i.e. students possessed limited understanding of the equations.