Students' answers to tasks provide a valuable source of information in teaching as they result from applying cognitive processes to a learning content addressed in the task. Due to steadily increasing course sizes, analyzing student answers is frequently the only means of obtaining evidence about student performance. However, in many cases, resources are limited, and when evaluating exams, the focus is solely on identifying correct or incorrect answers. This overlooks the value of analyzing incorrect answers, which can help improve teaching strategies or identify misconceptions to be addressed in the next cohort. In teacher training for secondary education, assessment guidelines are mandatory for every exam, including anticipated errors and misconceptions. We applied this concept to a university exam with 462 students and 41 tasks. For each task, the instructors developed answer classes -- classes of expected responses, to which student answers were mapped during the exam correction process. The experiment resulted in a shift in mindset among the tutors and instructors responsible for the course: after initially having great reservations about whether the significant additional effort would yield an appropriate benefit, the procedure was subsequently found to be extremely valuable. The concept presented, and the experience gained from the experiment were cast into a system with which it is possible to correct paper-based exams on the basis of answer classes. This updated version of the paper provides an overview and new potential in the course of using the digital version of the approach.

Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a rich type system, but has rather substantial conceptual differences to HOL, as well as comparatively poor proof automation support. We introduce a dependently-typed extension DHOL of HOL that retains the style and conceptual framework of HOL. Moreover, we build a translation from DHOL to HOL and implement it as a preprocessor to a HOL theorem prover, thereby obtaining a theorem prover for DHOL.

Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards "big mathematics", its relation to human cognition, and how machine support for big math can be organized. The central contribution of this position paper is an information model for "doing mathematics", which posits that humans very efficiently integrate four aspects: inference, computation, tabulation, and narration around a well-organized core of mathematical knowledge. The challenge for mathematical software systems is that these four aspects need to be integrated as well. We briefly survey the state of the art.

We mark up a corpus of LaTeX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from students and lecturers, and paves the path towards an integration of our corpus with external sites.