Traditionally, symbolic reasoning has been thought of as the ability to internally represent numbers, logical and mathematical rules in an abstract and amodal way. The focus has been on the "inner" i.e. notations are "translated" into corresponding mental structures and processes.
More recent studies suggest that symbols may act as targets for powerful perceptual and sensorimotor systems as Landy et al propose in their "Perceptual Manipulation Theory"[1]. This theory states that much of the capacity for symbolic reasoning is implemented as the perception, manipulation and modal and cross-modal representation of externally perceived notations.
The extant account of the symbolic reasoning include computational view, semantic processing view and cyborg view. All the theories provide limited functionality in the core reasoning part of symbolic reasoning to sensorimotor faculties. Though cyborg view provides much greater abilities than just simple symbol pushing by suggesting that sensorimotor modalities are involved in simplifying the reasoning process, they limit their use in actual reasoning. The work by Landy[1] et al propose a distinct view that the symbolic reasoning is embodied in the sensorimotor modalities in their Perceptual Manipulation Theory.
Landy and Goldstone (2009)[1] suggest that this reference to motion is no mere metaphor. Subjects with significant training in calculus found it easier to solve problems of this form when an irrelevant field of background dots moved in the same direction as the variables, than when the dots moved in the contrary direction. Our current hypothesis will try to test the Perceptual Manipulation Theory i.e. the embodied symbolic reasoning.
The strategies implemented by the experts when solving medium level equations.
As suggested by the D. Landy "mediocre mathematics students get the right answer by reasoning using 'backup' strategies, while experts just have bettertrained visual systems (and using back strategies, of course). It should be possible to force novices/regular folks into a speed paradigm where
they are selectively impaired on visually challenging problems-they have time to get the right answer, but not to fix their ordering error and get the right answer. For experts, this pattern shouldn't so much exist, or should be attenuated." The analysis of time taken and accuracy will try to test the above suggestions.
We propose to conduct two experiments inspired from the work done by Landy et al in [1] and [3].
Experiment 1: Impact of non-mathematical grouping pressures
- The subject will be given a set of 20 questions with 4-5 seconds for each.
- The subjects will be given instructions regarding the format of the experiment.
- The task will consist of equations with non-standard spatial relationships designed to test the effect of perceptual grouping on mathematical reasoning.
The equations are the mix of three parameters- sensitivity, consistency and validity as explained above.
- The responses and the time for each response will be noted for individual subject.
Experiment 2: Impact of background motion to test the strategy used for simple arithmetic equations.
- The subjects will again be given a set of 20 questions with 4-5 seconds for each.
- The subjects will be given short instructions regarding the format of the experiment with an example depicting the unwind strategy to test if instruction priming has any
effect.
- The task will consist of simple equations involving natural numbers from 1 to 36 at any stage of the equation solving and a variable x, y or z.
- The background will consists small circles moving across the screen with 7 levels of horizontal velocity.
- The responses and the time for each response will be noted for individual subject.
An applet built using JavaScript and PHP to conduct the experiment. The experiments will be conducted on a group of 20 high school and 20 undergraduate students. The experiments will be conducted in a supervised settings using a laptop.
[1] Landy, D., and Goldstone, R. L. (2009). "Pushing symbols", Proceedings of the 31st
Annual Conference of the Cognitive Science Society. Amsterdam.
[2] Landy, D., and Goldstone, R. L. (2007a). How abstract is symbolic thought? J. Exp.
Psychol. Learn. Mem. Cogn. 33, 720-733. doi: 10.1037/0278-7393.33.4.720
[3] Landy D, Allen C and Zednik C (2014) A perceptual account of symbolic reasoning. Front. Psychol. 5:275. doi: 10.3389/fpsyg.2014.00275
[4] Landy, D., and Goldstone, R. L. (2007c). "How space guides interpretation of a
novel mathematical system", in The 29th Annual Conference of the Cognitive
Science Society. Nashville, TX