Mathematical reasoning with cognitive technology

Digital tools and advances in machine learning open new opportunities for investigating how people learn mathematics and use different representations to solve problems (mathematical literacy). In the Digital Reasoning project we investigated how pupils, preservice teachers, and machine learning algorithms solve mathematical problems requiring representation-based reasoning. Based on the empirical data, we have developed models of mathematical cognition that expand current theories of learning fundamental mathematical skills. Through the project we have developed i) theoretical models of learning mathematics, ii) technology and methodology to collect and analyze digital data about mathematical reasoning processes, and iii) an NTNU-based research group and in mathematical cognition with outstanding international collaborators.

Outcomes: 10+ Conference presentations. 6 Scientific publications. 4+ Manuscripts in process for publication. A new theoretical understanding of the learning of fundamental elements of mathematical reasoning. A digital platform for research on mathematical reasoning. 12 Masters theses. 1 PhD thesis (delivered February, 2022. Expected to be defended later this year). The researcher is now transitioning into a PhD position at the department. An NTNU-based research group in mathematical cognition with a network of international experts. Impacts: During the project period the research group has narrowed its scope of mathematical reasoning to reasoning about quantities which is a very active research area, and the role of definitions in mathematical reasoning which is an underprioritized area of research in mathematics education. Building on the results and experience gained during the project period, the research group is now well positioned for A. high-impact publications in general scientific journals, B. attracting external funding from national and international sources, and C. making a fundamental impact on education through the development of a more rigorous theory of teaching and learning mathematics.

What learning processes allow us to do mathematics, and how can answers to that question translate to improved mathematics education and teaching practices? Digital Reasoning will leverage a digital learning and research platform for representation-based mathematical reasoning to collect dynamic data about the learning processes of pupils and preservice teachers. The data allows us to develop computation models of mathematical cognition that can A. shed light on general principles for learning mathematics and B. fuel next-generation education technology for artificial assessment and tutoring of mathematical literacy skills. Engaging an international network of world-leading researchers in an interdisciplinary effort towards developing new theoretical foundations and innovative cognitive technology for mathematics education, Digital Reasoning will provide an important piece of research towards improving the opportunity for pupils and preservice teachers to engage with relevant mathematical practices and for school mathematics to meet the needs of industry, science and society.