Calculus Course Assessment Data


  • Matti J. Pauna University of Helsinki



Assessment data, automatic assessment, peer assessment, Calculus


In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of timestamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors. We also describe late professor Mika Seppälä’s seminal work at the University of Helsinki to develop online materials and tools for learning mathematics since 2001. He also utilized these methods in Calculus teaching at Florida State University. The open online course “Single Variable Calculus” was held in Helsinki in 2004. This intensive work evolved into a complete online English Calculus curriculum starting from the Fall 2013 and soon recognized as an alternative route for taking traditional university Calculus courses in Helsinki. Automatic assessment systems of mathematical competencies, such as STACK and WeBWorK, can take a student’s answer as a mathematical object, e.g. a function or an equation, and check whether it satisfies the requirements set for a correct answer as well as give immediate and meaningful feedback. That is a powerful tool especially for formative assessment: log data shows that many students prefer to start with quizzes and when necessary, consult lecturing materials


Caprotti, O., Ojalainen, J., Pauna, M., & Seppälä, M. (2013). WEPS Peer and Automatic Assessment in Online Math Courses. Electronic Proc. 21st Int. Conf. Technology in Collegiate Mathematics. Retrieved from

Pointon, A., & Sangwin, C. J. (2003). An analysis of undergraduate core material in the light of hand-held computer algebra systems. International Journal of Mathematical Education in Science and Technology, 34 (5), 671–686.

Rämö, J., Oinonen, L., & Vikberg, T. (2015). Extreme Apprenticeship – Emphasising Conceptual Understanding in Undergraduate Mathematics. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 2242–2248). Prague: Charles University in Prague, Faculty of Education and ERME.

Sangwin, C. (2013). Computer Aided Assessment of Mathematics. Oxford University Press.

Xambó Deschamps, S., Bass, H., Bolaños Evia, G., Seiler, R., & Seppälä, M. (2006) e-Learning Mathematics. Proc. Int. Conf. of Mathematicians. Madrid, Spain: ICM.




How to Cite

Pauna, M. J. (2017). Calculus Course Assessment Data. Journal of Learning Analytics, 4(2), 12–21.



Special section: Shape of Educational Data