This paper examines students' achievements in solving problems and their misunderstandings when using models. A mixed research methodology was applied. Quantitative research investigated how the performance of students with various levels of high school GPAs correlated with their rating of their lecturers' teaching proficiency. Four lecturers and 336 mechanical and electronics engineering students participated in the study. Achievement tests, consisting of problems to be solved by using models of a diode and an ideal operational amplifier, were implemented in introductory courses in electronics. Students taught by lecturers whom they rated as having high levels of teaching expertise achieved significantly higher grades on these tests than did students taught by lecturers receiving lower ratings for their teaching expertise. The tests investigated performance on three taxonomy levels, and the results were consistent on all three levels. The grades on the knowledge taxonomy level were higher than the grades on the routine level, and both were higher than the grades on the interpretation level, as expected. Qualitative research, based on analysis of students' written explanations and on face-to-face interviews, exposed three kinds of misunderstanding: 1) that the purpose of engineering models is just to simplify calculations, not to yield usable, reliable results; 2) that a nonlinear problem can be solved using linear concepts; and 3) that the accuracy of a solution is indicated by the number of decimal places in the result, rather than by its closeness to the actual value.