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Enhancing Individualized Instruction through Hidden Markov Models
Lindberg, David Seaman, III

2014, Master of Mathematical Sciences, Ohio State University, Mathematics.
Online education in mathematics has become an important research topic. With more assessment going online, we have to ask ourselves, “How do we measure student performance through a computer?” A second question we ask is, “How do we evaluate the individualized instruction platform itself?”
We first provide a summary of personalized education in mathematics. We discuss case studies on certain individualized instruction platforms with commentary on how students are learning mathematics. Analysis of these case studies inform us on possible challenges in their design and use.
We next present a hidden Markov model as a way to analyze student learning in an individualized instruction system. The Baum-Welch algorithm provides a means to determine the parameters of a hidden Markov model. It’s these parameters that give insight into exercises and how students are performing with each exercise.
We then consider the Viterbi algorithm, which is an algorithm used to uncover the hidden states in a hidden Markov model. A student’s sequence of observations is recorded by the system, which is the input to the Viterbi algorithm. The hidden performance states of the student (unknowing, emerging, and knowing) are generated as a time-series sequence representing student understanding on a particular exercise over time.
We finally provide recommendations for implementing the hidden Markov model in individualized instruction systems and further research questions are posed.
Rodica Costin (Advisor)
Dennis Pearl (Committee Member)
Bart Snapp (Committee Member)
127 p.

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Lindberg, D. (2014). Enhancing Individualized Instruction through Hidden Markov Models. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Lindberg, David. "Enhancing Individualized Instruction through Hidden Markov Models." Electronic Thesis or Dissertation. Ohio State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Lindberg, David "Enhancing Individualized Instruction through Hidden Markov Models." Electronic Thesis or Dissertation. Ohio State University, 2014. https://etd.ohiolink.edu/

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