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Master's lecture in Statistics - Þórarinn Jónmundsson

Thu, 28/05/2020 - 14:00 to 15:00
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 Master's student: Þórarinn Jónmundsson

Title: Models and methods to evaluate learning: a case study of students enrolled in mathematical analysis


Faculty: Faculty of Physical Sciences

Advisor:  Gunnar Stefánsson, Professor at the Faculty of Physical Sciences

Other member of the masters committee: Anna Helga Jónsdóttir, Associate Professor at the Faculty of Physical Sciences

Examiner: Jenný Brynjarsdóttir, Associate Professor at Case Western Reserve University


The goal of this thesis was to develop models and methods to evaluate learning. To do so, data from, an online repository of lectures, examples and multiple-choice questions for various subjects in mathematics, was examined. The data was generated by students enrolled in Applied Mathematical Analysis at the University of Iceland in 2018 and 2019. First, statistical models were developed to determine which factors influenced students' performance on the multiple-choice questions. Then, various hypotheses tests were proposed to detect learning and their corresponding statistics which rejected the null hypothesis with the most power were derived and evaluated with simulations. The results were that either questions on tutor-web are too easy, that students are being given easy questions for too long or potentially both. Regardless, some of the inner workings of tutor-web need to be redesigned with the results of this thesis in mind.