Yes, that Tenison paper is a great example of arithmetic modelling in ACT-R, and especially connecting it to the modern fMRI approach for validation! For an example of the other sorts of math modelling that’s more psychology-experiment-based, this paper gives some of the low-level detail about how such a model would work, and maps it onto human errors: - “Toward a Dynamic Model of Early Algebra Acquisition” https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.5754&rep=rep1&type=pdf
(that work was expanded on a few times, and led to things like “Instructional experiments with ACT-R “SimStudents”” http://act-r.psy.cmu.edu/?post_type=publications&p=13890 where they made a bunch of simulated students and ran them through different teaching regimes)
The flashcard and curriculum experiments seem really awesome in terms of potential for applications. It feels like the beginnings of the kind of software technology that would exist in a science fiction novel where one of the characters goes into a “learning pod” built by a high tech race, and pops out a couple days layer knowing how to “fly their spaceship” or whatever. Generic yet plausible plot-hole-solving super powers! <3
Yes, that Tenison paper is a great example of arithmetic modelling in ACT-R, and especially connecting it to the modern fMRI approach for validation! For an example of the other sorts of math modelling that’s more psychology-experiment-based, this paper gives some of the low-level detail about how such a model would work, and maps it onto human errors:
- “Toward a Dynamic Model of Early Algebra Acquisition” https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.5754&rep=rep1&type=pdf
(that work was expanded on a few times, and led to things like “Instructional experiments with ACT-R “SimStudents”” http://act-r.psy.cmu.edu/?post_type=publications&p=13890 where they made a bunch of simulated students and ran them through different teaching regimes)
As for other cool tasks, the stuff about playing some simple video games is pretty compelling to me, especially in as much as it talks about what sort of learning is necessary for the precise timing that develops. http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2019/03/paper46a.pdf Of course, this is not as good in terms of getting a high score as modern deep learning game-playing approaches, but it is very good in terms of matching human performance and learning trajectories. Another model I find rather cool a model of driving a car, which then got combined with a model of sleep deprivation to generate a model of sleep-deprived driving: http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/9822011-gunzelmann_moore_salvucci_gluck.pdf
One other very cool application, I think is the “SlimStampen” flashcard learning tool developed out of Hedderik van Rijn’s lab at the University of Groningen, in the Netherlands: http://rugsofteng.github.io/Team-5/ The basic idea is to optimize learning facts from flashcards by presenting a flashcard fact just before the ACT-R declarative memory model predicts that a person is going to forget a fact. This seems to improve learning considerably http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/867paper200.pdf and seems to be pretty reliable https://onlinelibrary.wiley.com/doi/epdf/10.1111/tops.12183
The flashcard and curriculum experiments seem really awesome in terms of potential for applications. It feels like the beginnings of the kind of software technology that would exist in a science fiction novel where one of the characters goes into a “learning pod” built by a high tech race, and pops out a couple days layer knowing how to “fly their spaceship” or whatever. Generic yet plausible plot-hole-solving super powers! <3