Which knowledge is required in exams on analysis 1 courses at German universities?

Abstract

Abstract The purpose of this study is to describe the knowledge that is required in exams on Analysis 1 courses at German universities. To do so, we use the distinction between procedural and conceptual knowledge that is frequently used in the literature on mathematics education. For a more detailed analysis, we developed further categories for our coding scheme that better reflect the interaction of procedural and conceptual knowledge required to complete tasks. Using this coding scheme, we coded 49 exams from 12 out of 16 federal states in Germany, consisting of a total of 741 tasks. The analysis revealed that 69% of the tasks could be solved by recalling information or using procedural knowledge with only minor conceptual knowledge required, whilst 31% required substantial conceptual knowledge. Based on this analysis, we assume that most exams can be passed by focusing the knowledge of facts and procedures. These results indicate a discrepancy between the teaching focus on conceptual knowledge and the knowledge assessed, which is discussed.