STACK with state

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The question model of STACK provides an easy way for building automatically assessable questions with mathematical content, but it requires that the questions and their assessment logic depend only on the current input, given by the student at a single instant. However, the present STACK question model already has just the right form to be extended with state variables that would remove this limitation. In this article, we report our recent work on the state-variable extension for STACK, and we also discuss combining the use of state variables with our previous work on conditional output processing. As an outcome, we propose an expansion to the STACK question model, allowing the
questions to act as state machines instead of pure functions of a single input event from the student. We present a model question using the state variable extension of STACK that demonstrates some of the new possibilities that open up for the question author. This question is based on a finite state machine in its assessment logic, and it demonstrates aspects of strategic planning to solve problems of recursive nature. The model question also demonstrates how the state machine can interpret the solution path taken by the student, so as to dynamically modify the question behaviour and progress by, e.g., asking additional questions relevant to the path. We further explore the future possibilities from the point of view of learning strategic competencies in mathematics (Kilpatrick et al., 2001; Rasila et al., 2015).
Original languageEnglish
Pages (from-to)60-69
Number of pages10
JournalMSOR Connections
Issue number2
Publication statusPublished - 26 Jan 2017
MoE publication typeA1 Journal article-refereed


  • state machine
  • interactive question


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