The present study explored the dimensionality of cognitive structure from two approaches. The first approach used a famous relation between Visual Spatial Working Memory (VSWM) and calculation to demonstrate the multidimensional item response analyses when true dimensions are unknown. The second approach explored the detectability of dimensions by using person fit indices. Findings from the first study demonstrated that there were shared dimensions between VSWM and calculation. Additionally, error analysis with the MIRT approach revealed only one dimension, the Number dimension, of VSWM is related to subtraction and division. These results showed the usefulness of the MIRT analysis in analyzing cognitive structure. The result of the second study revealed that person fit indices, however, were insensitive to the simulated dimensions when estimated ability parameters were used. More sensitive detection indices need to be developed. The present study combines several dimensionality analyses with perspectives from diverse areas in the hope of providing insights into the dimensionality of cognitive structures. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]