In a classroom, a teacher attempts to convey his or her knowledge to the students, and thus it is important for the teacher to obtain formative feedback about how well students are understanding the new material. By gaining insight into the students' understanding and possible misconceptions, the teacher will be able to adjust the teaching and to supply more useful learning materials as necessary. Therefore, the diagnosis of formative student evaluations is critical for teachers and learners, as is the diagnosis of patterns in the overall learning by a class in order to inform a teacher about the efficacy of his or her teaching. This paper investigates what might be called the ''class learning diagnosis problem'' by embedding important concepts in a test and analyzing the results with a hierarchical coding scheme. Based on previous research, the part-of and type-of relationships among concepts are used to construct a concept hierarchy that may then be coded hierarchically. All concepts embedded in the test items then can be formulated into concept matrices, and the answer sheets of the learners in a class are then analyzed to indicate particular types of concept errors. The trajectories of concept errors are studied to identify both individual misconceptions students might have as well as patterns of misunderstanding in the overall class. In particular, a clustering algorithm is employed to distinguish student groups who might share similar misconceptions. These approaches are implemented as an integrated module in a previously developed system and applied to two real classroom data sets, the results of which show the practicability of this proposed method.