In this presentation we describe computer aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects also a lot of timestamped data about every action a student makes. Furthermore, information about students’ learning styles, motivation and perception of self efficacy is collected by questionnaires.
Mika Seppälä started intensive work at the University of Helsinki to develop online materials and tools for learning mathematics since 2001. He worked also as a professor at the Florida State University where he utilized these methods in Calculus teaching. The open online course “Single Variable Calculus” was held in Helsinki 2004. This seminal 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 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. Automated diagnostic tests give students information where they stand before starting to study Calculus and feedback about how to rehearse for that. Peer assessment is also used in online Calculus courses. There students evaluate and give constructive feedback to other students’ work, which should be a complete and clear presentation of a solution to a problem with correct argumentation.
