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Talking Statistics/Talking Ourselves: Some Constructionist Lessons from the Work of the Psychologist George Kelly

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The client who attempts to communicate his/her personal constructs to a therapist can rarely depend upon simple verbal statements to communicate the precise nature of his/her constructs. He/she has to bring out for display a long list of other contextual elements before the [teacher] can understand.

The therapist, on his/her side of the table, must not be too ready to impose his/her own preexisting personal constructs upon the symbolism and behavior of the client. He/she will first have to compile a lexicon for dealing with the client.

George Kelly (1991a)

… Life consists.

Of propositions about life ….

Wallace Stevens (1990)

Logic! Good gracious! What rubbish! How can I tell what I think until I see what I say?

E. M. Forester (1927)

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Notes

  1. The reasons and methods to analyse a numeric matrix are legion. For example: how should we look at the relationships between rows, columns and both rows and columns together? Do any of the methods we might use require the data to be explored first in terms of shape using visual methods? Might transformations be necessary? How should we handle true outliers?

    I believe that beginning courses in statistics should introduce the big idea that there are many different techniques that can explore the same data set depending on your goal and, if the goal is exploratory, using several different methods might be very useful. Sometimes, for example, a mathematical method might introduce its own “artifacts” or patterns into the statistical results. So explore matrixes like the ones in this article with a variety of techniques to see if the results or patterns are stable across methods. And, if they are not, why not?

    I have shown techniques based on variance in this article. That is, correlation and principal component analysis. But my computational environment, written in APLX (MicroAPL, version 5.1, http://www.microapl.co.uk/apl/) can provide a number of visual and data reduction methods. See (Bell and Richard 1997) for a list of useful analytic approaches for both single grids and multiple ones. See (Scheer 2006) for software available (both free and otherwise) to elicit repertory grid data and then to analyze and display results it in a variety of ways.

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  1. Department of Mathematics and Computer Science, American University of Paris, Paris, France

    James Edward Clayson

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  1. James Edward Clayson
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Correspondence to James Edward Clayson.

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This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review from the Column Editor Uri Wilensky, Northwestern University. Email: uri@northwestern.edu.

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Clayson, J.E. Talking Statistics/Talking Ourselves: Some Constructionist Lessons from the Work of the Psychologist George Kelly. Tech Know Learn 18, 181–199 (2013). https://doi.org/10.1007/s10758-013-9197-x

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