Abstract:

We present a corpus-based approach to mathematical knowledge test generation.

The approach is based on the parallel informal/formal corpus of educational mathematical texts, developed by the authors. This corpus consists of mathematical statements extracted from educational mathematical textbooks, manually annotated by its formula representation in LaTeX and by formalization of the formula in OpenMath. Symbols used in OpenMath representations are defined in OntoMathEdu (https://github.com/CLLKazan/OntoMathEdu), a new original educational mathematical ontology presented by the authors at INTED 2019.

In order to generate a question, the method retrieves an OpenMath statement expressing functional dependence between variables, and substitutes generated values for independent variables. The domain of variables is determined by their types, defined by the OntoMathEdu ontology. A student is asked to input the value of the dependent variable given the values of the independent ones. The correctness of the answer is automatically checked by evaluation of OpenMath expression tree. Currently the approach selects only simple universally quantified equality statements, but we are going to extent it to more complex statements too.

On the base of the proposed method we have developed a software prototype for automated assessment of plane geometry knowledge. This prototype is intended to be a component of a new digital educational platform under development at Kazan Federal University.

Keywords:

Knowledge assessment, mathematical education, corpus, ontology, OpenMath, OntoMathEdu, formal mathematics.