There is abundant empirical evidence that argument mapping (AM) really can work for developing critical thinking skills ( why 'can'? : you need to exercise a lot and receive timely, good-quality feedback).
As Tim van Gelder writes in this review of empirical research on the impact of AM instruction:
“Indeed, at this stage it seems fair to say that high-intensity AM-based instruction is one of the most effective techniques we know for accelerating CT skill gains in higher education.”
Maralee Harrell noted in her paper No Computer Program Required: Even Pencil-and-Paper Argument Mapping Improves Critical Thinking Skills (2008), that you can map arguments using paper & pencil or software.
‘’To my knowledge there has been no research to determine whether the crucial factor is the mere ability to construct argument maps, or the aid of a computer platform and tutor, or possibly both.’’
In the online journal Education Technology Research & Development of February 2016 Maryam Eftekhari , Elaheh Sotoudehnama and S. Susan Marandi (English Language Department, Alzahra University, Tehran, Iran) just published a research paper in which they try to answer this question, using Rationale.
Their conclusion: ‘’Results suggested that students in the software group significantly outperformed those in the paper and pencil group on overall CCTST and the sub-skills of inference and inductive reasoning. They also scored significantly higher on all tests compared to the comparison group.’’
For their paper see here.
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