W3480Y WEEK 12: NUMERICAL REPRESENTATION AND CALCULATION

REQUIRED  [I recommend that you read these in the order listed]

1. Noel, M-P. (2001) Numerical cognition. In B. Rapp (Ed.), The Handbook of Cognitive Neuropsychology: What Deficits Reveal About the Human Mind, Philadelphia: Psychology Press.

[BE SURE TO READ THE FOOTNOTES! This chapter is (arguably) a little on the "dense" side. However, it does cover all the important points relevant to the study of numerical representation and calculation. I recommend reading this first, but then skimming the descriptions of the McCloskey and Dehaene models again after reading the Cohen et al. (2000) article.] 2. Cohen, L., Dehaene, S., Chochon, F., Lehericy, S., & Naccache, L. (2000). Language and calculation within the parietal lobe: a combined cognitive, anatomical and fMRI study. Neuropsychologia, 38, 1426-1440.

3. Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355-361.

4. Pesenti, M., Zago, L. et al. (2001). Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas. Nature Neuroscience, 4(1), 103-107.

OPTIONAL

Deloche, G., & Willmes, K. (2000). Cognitive neuropsychological models of adult calculation and number processing: the role of the surface format of numbers. European Child and Adolescent Psychiatry, 9, II/27-II/40.

QUESTION FOR CRITICAL THINKING:

First, briefly describe the different functional components of Dehaene's triple-code model and how this model differs (specifically) from the one proposed by McCloskey and colleagues (1985). How is this model anatomically implemented and what is the role of each hemisphere? Next, using the data from adult patients (including those presented in Cohen et al. and the chapter), animals and infants, discuss the functional and anatomical relationships/associations between language and different transcoding and calculation processes.

In the last part of your essay, think about any problems that you might have with "doing math in your head." For example, do you have particular difficulty with any of the standard types of calculations (addition, subtraction, multiplication, division)? Consider your mathematical "disabilities" in the context of the models described in the papers and what types of strategies you might use to overcome this problem (refer to the "prodigy" paper). If you think that you have no problems with math, then consider my problem: I find that with any of these calculations I sometimes make errors where I'm "off by a order of magnitude." For example, I multiply 200 x 2000 and get 4,000,000 or 40,000. Why might I be making this type of error and how could I work on fixing it?

ADDITIONAL READINGS:

1.  Sokol, S., McCloskey, M., Cohen, N. J., & Alminiosa, D. (1991). Cognitive representations and processes in arithmetic: inferences from the performance of brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory and Cognition, 17(3), 355-376.

2.  McCloskey, M., Harley, W., & Sokol, S. M. (1991). Models of arithmetic fact retrieval: an evaluation in light of findings from normal and brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory and Cognition, 17(3), 377-397.

3.  Burbaud, P., Camus, O., etal. (2000). Influence of cognitive strategies on the pattern of cortical activation during mental subtraction. A functional imaging study in human subjects. Neuroscience Letters, 287, 76-80.

4.  Menon, V., Rivera, S., White, C. D., Glover, G. H., & Reiss, A. L. (2000). Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neuroimage, 12, 357-365.

5.  Stanescu-Cosson, R. Pinel, P., et al. (2000). Understanding dissociations in dyscalculia: A brain imaging study of the impact of number size on the cerebral networks for exact and approximate calculation. Brain, 123, 2240-2255.
Dehaene, S., & Cohen, L. (1991). Two mental calculation systems: A case study of severe acalculia with preserved approximation. Neuropsychologia, 29(11), 1045-1074.