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

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Talking Statistics/Talking Ourselves: SomeConstructionist Lessons from the Workof the Psychologist George Kelly

James Edward Clayson

Published online: 5 March 2013� Springer Science+Business Media Dordrecht 2013

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)

1 George Kelly’s Personal Construct Psychology

In this paper I describe my use of a technique, repertory grid analysis, based on George

Kelly’s personal construct psychology (PCP) (Kelly 1991a, b; Maher 1979). This approach

attempts to break through students’ reluctance to discuss statistical notions in words that

are meaningful to them. I argue that PCP, if used in familiar and attractive contexts, can

encourage students to explore linkages between statistical ideas and their own personali-

ties, and those of their friends and family.

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguingcomputer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in whichcomputer environments have transformed the practice of mathematics or mathematics pedagogy. They couldalso include puzzles or brain teasers involving the use of computers or computational theory. Snapshots aresubject to peer review from the Column Editor Uri Wilensky, Northwestern University.Email: [email protected].

J. E. Clayson (&)Department of Mathematics and Computer Science, American University of Paris, Paris, Francee-mail: [email protected]

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Tech Know Learn (2013) 18:181–199DOI 10.1007/s10758-013-9197-x

I will show how using Kelly’s grid technique can open a new channel of learning. Kelly

and his group argued (Kelly 1991c; Fransella 2003; Fransella et al. 2003) that ‘‘doing

grids’’ presents students and teachers with visual artifacts that trigger new modes of

conversation and analysis. Words and calculations are seen to be complementary. I write

from a constructivist point of view (Harel and Papet 1991) that stresses the importance of

talking about our sense making in a public place. Kelly’s repertory grid method can help

get the conversation started.

1.1 Four Big Kelly Ideas

Here are four big ideas that I have distilled from George Kelly, and which have informed

my teaching with liberal arts undergraduates.

• We are all personal scientists

The most powerful of George Kelly’s notions and the basis of his work is his claim that

we are all personal scientists. As scientists we build models about the people, things, ideas

and actions of our world. We do this to predict and to give meaning to our world in order to

minimize our own anxiety about uncertainty. The irony here is that we all practice science

automatically without being taught how to do it by scientists, statisticians or philosophers.

• Our internal scientific models can be made explicit

George Kelly suggests that people make sense of the elements of our world by dif-

ferentiating them along bipolar constructs. For example: beautiful-ugly, like me-not like

me, pushy-humble, etc. He gives methods for eliciting from us a collection of word-labeled

constructs that we use in specific situations.

• Our models can be extended, explored and refined through visualization, vocalization

and computer manipulation

Kelly argued that visual representations of construct/element interactions are never ends

in themselves but rather are good ways to elicit additional constructs. Figures, pictures and

words, he said, facilitate the extension or revising of constructs and the way they are used.

In effect, he suggested that statistical analysis needs to be visualized and vocalized in order

for it to help us in our personal scientific task of proposing, testing, revising and rejecting

hypotheses about our world.

• Basic statistical ideas and methods will become part of our construct system if they are

seen to be useful in understanding ourselves and our world

When we explore the relationship between one construct and another using, for

example, a statistical notion like correlation, this idea is added to our model of con-

struing and extends it reach. The methods for analyzing constructs, therefore, are not

separate from construing but now part of it. This suggests that a Kelly approach can

encourage students to integrate talk about how they make sense of themselves and their

worlds with talk about basic statistical ideas might offer an environment that so intrigues

students that they might forget or at least put aside their math anxieties. Indeed I have

found that Kelly explorations are a good hook for pulling math-anxious students out of

their reticence.

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1.2 Models of the Self

There are, of course, myriads of models of the self and methods of sense making. Con-

sciousness Studies is a growth industry (see, for example, the last 20 some years of:

Journal of Consciousness Studies and Theory and Psychology), but the one offered by the

American psychologist George Kelly (1905–1967) seems especially appropriate to the task

I am discussing in this paper: getting students to talk about statistical ideas while also

watching themselves resolve ambiguities and make sense of their world.

Kelly received degrees in psychology and education and was well versed in statistical

analysis and combined with teaching and clinical work. His major contribution to psy-

chology was his Personal Construct Psychology (PCP) (Fransella 1995).

1.3 Constructs and Construing

Central to PCP are bipolar constructs. Constructs are the dimensions of the space in which

we place elements in our environment in order to give them meaning. This is a precursor of

Marvin Minsky’s phrase: ‘‘The secret of what anything means to us depends on how we’ve

connected it to the other things we know’’ (Minsky 1986). The meaning of constructs, in

Kelly’s scheme, is seen by how they are used to spatialize elements in construct space; the

meanings of elements is seen by how they are construed and related to other elements.

Each construct is bipolar: each end is meaningful in terms of its opposite. Examples might

be labeled: light–dark; loves me-hates me; sentimental-realistic; passive-aggressive … but

any set of constructs would have meaning only in terms of the elements on which they are

used: for example one’s family and the layers of contexts that surrounds and supports the

construal exercise. Kelly’s major point is that the word labels of a construct’s poles have

meaning only in terms of how that construct is used to differentiate a set of elements.

One implication is that we could see a person’s meaning-making if we could watch how

that person uses constructs in specific situations.

Another implication, of course, is that two people might have similarly named con-

structs but use them in entirely different ways or perfectly similar ways or in between those

two extremes. In effect, Kelly suggests that we speak our own language, or what linguist

call idiolect (George 1990), and this may or may not be shared with others even within our

own linguistic family.

To Kelly each individual is a personal scientist. But what kind of scientist? I would

argue that since we are not only concerned with our own idiolect but that of others, Kelly’s

individual is an anthropologist who is always surrounded by alien tribes. Kelly offers an

approach that aids us in not just understanding each other’s languages but in learning how

to speak them. Kelly’s method might offer us an arena where language talking, listening

and learning can take place.

2 How Did Kelly Suggest that We Do All This?

2.1 Repertory Grid As Heuristic Device

As already mentioned, Kelly was both teacher and therapist and he believed that neither of

these professions could be practiced effectively without learning to speak the personal

languages of his clients and students. By language he did not mean the name of the

language that was spoken in the analyst’s study or in the classroom, such as English or

Talking Statistics/Talking Ourselves 183

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French, but the personal idiolect that each of us speaks. Idiolect is defined as the collection

of words, expressions, idioms and pronunciation rules that we use in our own and idio-

syncratic way. In fact, we may speak several different idiolects for different uses: one with

close friends, another with our parents and yet another with teachers. But the words of our

idiolects may or may not be used in the same way as others use them even when they are in

our close conversational clusters.

Language learning is far more complicated than just learning words and grammatical

rules (the literature on language teaching is especially rich and useful: e.g. McGlothlin

1997) and here is where Kelly is so useful. Kelly helps us see how a person’s use of words

and grammar constructs meaning. Kelly’s repertory grid is a technique for eliciting both

the words we use to differentiate between elements in our world and for analyzing how

these words are related to the other words we use and how they are used collectively. In

addition, Kelly’s repertory grid technique helps us to explore and compare the idiolects

spoken by different individuals.

2.2 The Repertory Grid Method

2.2.1 Beginning with Family

Kelly suggested that our families might be a good place to start exploring the repertory grid

method since we all have strong views about our families—they do bring out strong

emotions and value judgments—and we are used to thinking and talking about them. And,

too, here is an area where we could ‘‘test’’ whether Kelly’s method offers us any useful

insight into a subject that we already know very well. In Kelly’s words: ‘‘When … a client

describes the other people who populate his intimate world, he is essentially stating the

coordinate axes with reference to which he must plot his own behavior. He is stating his

personal-construct system.’’ (Kelly 1991d)

Kelly gave (1991e) a list of role titles for an initial repertory grid experiment that

included characters from family, friends, neighborhood and school. In addition, he sug-

gested that everyone who does the grid exercise should add themselves to the list of

elements but as three separate characters: the real-me, the public-me and the wished-for-

me. I also recommend, as did Kelly, that some really extreme characters be included such

as a personal enemy, an especially disliked character or someone who has rejected us. I’ve

added a suggestion to include a tyrant from history, an odious politician or even an

especially strong character from literature or mythology. Or, on the positive side, you could

add a person who you judge to be exceptionally successful, beautiful, happy or loving, for

example. But in all cases, I insist that a real person’s name be given to each of the

elements. The first step is to make a list of these elements. I’ve found with my students that

ten to twelve elements make a good number.

2.2.2 Eliciting Constructs

The second step is to elicit the constructs that we may be using to differentiate the

elements; that is, to make sense of them. Kelly suggested a technique that he called the

method of triads (Kelly 1991f). In order to elicit a new construct from the client he would

indicate three specific elements and ask the client to quickly suggest a bipolar construct

that would place two of the selected elements at one end of the construct and the third at

the other. Once the client was offered a triad, he would then be asked to judge where each

of the other elements would fall on the most recently elicited construct. Kelly used binary

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constructs so each element could fall in only two possible positions but most researchers,

as do I, use wider scales. I’ve found that a 1–5 scale works well.

Kelly did not pick his triads randomly. He presented his clients with a list of triads that

were associated with his rather precise rules on selecting elements. You can see examples

of grids that Kelly elicited from his own clients in (Kelly 1991a): the mathematical

structure of ‘‘Kelly psychological space’’ along with the triads that he used. You could also

note the limited amount of statistical analysis that he carried out. He did all of his analysis

manually and suggested clever shortcuts for the calculating row and column correlations.

He also gave a shortcut for estimating the principal components of repertory grids.

3 From Kelly Theory to Classroom Tasks

In the following sections I describe how I have built my own computational environment1

to explore and extend Kelly’s repertory grid method for use in the classroom. I describe the

visual and statistical ways that I have analyzed several specific grid studies. But, most

importantly, I speak about how such grid explorations can encourage students to think

more deeply about basic statistical notions and calculations.

3.1 Repertory Grid as Data Object

Here is an example of a repertory grid that I constructed when thinking about my own

family. I have used this example from my own experience when introducing Kelly’s ideas

to my students. I want them to see how I use the method.

Note that this grid is a two-dimensional matrix with the elements (the family members)

as columns and the constructs (the methods used to construe or interpret family members)

as rows. The element column for any family member, say, my mother, shows the locations

of her on each of the eight constructs or rows. The whole grid, then, shows the relationships

between all of these eleven family members (the columns) and all of the nine constructs

(the rows) used to differentiate them.

The grayed items in each row indicate the element triads that were used to elicit

constructs from me. For example, look at the first row of the grid. Three elements were

given to me at random and I was asked to come up with a bi-polar construct that would

place two of the grayed three elements (older sister, younger sister, academic enemy) at

one of the construct and the third towards the other end. Once a construct was named by

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

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

I have shown techniques based on variance in this article. That is, correlation and principal componentanalysis. 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 Richard1997) for a list of useful analytic approaches for both single grids and multiple ones. See (Scheer 2006) forsoftware available (both free and otherwise) to elicit repertory grid data and then to analyze and displayresults it in a variety of ways.


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http://www.microapl.co.uk/apl/

http://www.microapl.co.uk/apl/

me—in this case: likes me/dislikes me—I ‘‘placed’’ each of the elements along this con-

struct axis using the numbers 1–5. In this example the numbers run from 1 at the likes-me

pole to 5 at the dislikes-me pole. The orientation of these numbers is, of course arbitrary.

The likes-me pole could have been placed at the 5-end rather than at the 1-end. Numbers on

constructs help us see how we might use a construct to differentiate between elements and

this should be independent of their 1–5 orientation.

My computer programs manage the initial definition and entry of element names and

then carry out the eliciting of constructs using the triad method. Triads can be generated

randomly from the list of all possible triplets with no repeats or some other methods can be

used. For example, categories of elements can be set up from which one of the triads must

always be selected. In addition, the user can select to enter a construct with no element

prompting; the user then gives values for each of the elements on this construct. The

examples in this paper, however, use randomly selected, non-repeating triads.

3.2 Example Grid: Jim’s Family

Constructs, elicited by the greyed element triads, were given in the order shown.

3.3 Repertory Grid as Talk Object

What kind of talk do these data encourage? Here are some typical student questions:

How are my family members related?’’ ‘‘Who is most like me; who is least like me?’’

‘‘Who is most like my father?’’ ‘‘Who is least like anyone: is there a real loner in this

family group?’’ ‘‘How are my constructs related?’’ ‘‘Which construct does the best

job of explaining?

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3.4 The Importance of Graphs

I have found that my students have enormous difficulty reading and making sense of two-

dimensional graphs, and three-dimensional ones often are totally opaque to them (Clayson

1994). Repertory grid analysis is a way of personalizing such graphs and inviting the

student to find their place inside the visual display. Towards this end I have designed my

own minimalist graphical routines. I try to illustrate the shape of data without numbers

whenever possible (Tukey 1977). Note that no numbers are displayed on the graphs since

the dimensions and axes are word-determined, word-described. The ideas of standardi-

zation and correlation - along with the necessary assumptions for their use - can be shown

well graphically and this is especially the case with a student’s very personal repertory grid

data.

Of course the idea of correlation and variance needs to be talked about along with their

assumptions about the shape of data being explored. Visual displays of these data distri-

butions are given by my procedures but not shown here.

Too, there are other ways of measuring association between variables, and these

approaches must be discussed and explored—comparing their strengths and weaknesses

with those of the methods used in this paper.

3.5 Looking at the Relationships Between Constructs

Correlation is a standard statistical tool for measuring the strength of the relationship

between two variables. Correlation can also be described in Kelly terms, too, as one of

statistics’ major constructs: no relationship-perfect relationship. I believe that Kelly’s

notion that constructs, like correlation, can be explored and refined though visualization

and vocalization holds the key for my students’ beginning to grasp this important idea.

But pictures of a new concept, like correlation, must be built out of already under-

standable parts for it to be decoded. Repertory grids about our families offer a good

environment for this since the pictures will be constructed from characteristics of people

we know.

When my students looked at individual constructs we began by looking at their shapes

and then comparing these shapes with summary statistics. How can we try the same

approach when thinking about the relationship of one construct to another?

Perhaps plotting one construct against another might help. But, as before, we should do

this in the simplest manner with the minimal use of labels and I’ve developed my own

procedures for thinking through correlation.

Here is an example of such a plot: c4: home-travel is on the horizontal axis and c5:

concrete-intelo on the vertical. The horizontal axis starts at value 1 at the left edge of the

gray square and ends at value 5 at the square’s right edge. The vertical axis starts at value

1 at the top edge of the gray square and ends at value 5 at the bottom edge. The center

point is 3, 3 and each of the points, representing an element, is labeled with the element’s

name.

3.6 Picturing the Idea of a Strong Relationship Between Two Constructs (Raw Data

Graph)


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Is there a relationship between these values? If so how could it be summarized on the

graph? And, if there is a relationship, how strong is it? And how shall we measure

‘‘strong’’? Perhaps, most importantly, how do students approach this task? What are their

expectations of this task?

One way of describing correlation is to picture a plot of how a straight line could

summarize the relationship between two variables that have been standardized. The slope

of the line is the correlation coefficient. I have found that thinking through this idea,

playing with it visually and vocally with known data gives students an emotional access to

the construct of correlation.

3.7 Picturing the Idea of a Strong Relationship Between Two Constructs (Standardized

Data with a Correlation Line Whose = .84)

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Look at the balls above with their labels. For instance, what does ‘‘wife’’ mean? In this

graph and those following, ‘‘wife’’ indicates how the user has construed her along two or

more constructs. Kelly said that the meaning of an element is how it is construed. By the

same token he said that the meaning of a construct is how it is used to construe a set of

elements. There is no ‘‘true’’ meaning beyond this.

But this assumes that we have added the right set of elements and constructs for what

we are exploring. Too, we assume that the values placed in the grid are stable over time

and that constructs/elements relationship can be measured by cardinal numbers. In sta-

tistics these, and other complicated issues, are labeled specification errors.

Hence, we need to play with our grids constructively to see the effect of change. If two

balls are very close to each other, perhaps we can add another construct that makes them

less similar. We might change some of the grid values, or add or subtract elements. What

happens to the visual and statistical results? This organized play is called sensitivity

analysis and brings up the idea of truth versus usefulness almost automatically. My pro-

cedures encourages this work and keeps track of the experiments done and the results

found. But this is not shown in the paper.

3.8 Correlation as a Type of Bi-Polar Construct

The construct of correlation, in Kelly terms, is strong correlation/weak correlation. So we

need to see examples along this continuum.

3.9 Picturing the Idea of a Weak Relationship Between Two Constructs (Standardized

Raw Data with Correlation Line Slope = .05)

Here is a table summary of all the correlation values between constructs with the

strongest and weakest values marked to encourage exploration of them.


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Large and small absolute values greyed. Cutoff values can be set in the procedures.

3.10 Looking at the Relationships Between Elements (Family Members)

Most of my students immediately want to see who is most-like and least-like themselves in

their grids. Next they want to compare the relative placement of their three selves to see if

they are close together, or distant.

Can we approach this the same way as we did for the constructs? That is, could we plot

one column against another. Say, father and grandmother?

We can easily plot any two of the columns in the grid and here is an example plot: father

on the horizontal axis and grandmother on the vertical.

3.11 Father Versus Grandmother (Standardized Data with Correlation Slope = .80)

In order for the correlations between elements to be robust: that is, not to be effected by

reflecting the numbers used on a construct, I include each construct twice representing the

two ways of orienting the construct poles, 1–5 or 5–1 (Bell 2006).

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3.12 Looking at the All the Relationships Between Elements

Here is a summary of element correlations using the augmented matrix idea. I’ve marked

several large values in grey to stimulate visual explorations of these relationships.

Large and small absolute values greyed. Cutoff values can be set in the procedures

3.13 Looking at Relationships Between Elements and Constructs

Principal component analysis (PCA) offers a straightforward way to explore the rela-

tionships between the rows and columns of a two dimensional matrix using both visual and

statistical descriptions. In the context of repertory grids, therefore, PCA can illustrate both

constructs and elements on the same graph (Slater 1976a, b).

Most importantly, PCA is a technique to integrate basic statistical ideas with the psycho-

logical notions of personal construct psychology. Essentially PCA is a method for exploring

what happens when the reference system on which a set of points is addressed is altered.

Obviously, if we keep a set of points fixed in space but rotate the reference system

within the cloud of points, the address of each point on the altered reference system will

change from what it was before the reference system was moved. If the addresses along

each axis changes then the variance along each dimension might also be expected to

change—even though the sum of the variances along each of the dimensions remains

constant. But is this intuitively obvious to a beginning statistics student? I don’t think so–so

some computer simulations are useful if they are carried out slowly and by the students

themselves (Clayson 1998).

The goal of PCA, of course, is not just to reallocate variance by rotating the reference

system within a fixed cloud of points, but to reallocate the original variance in the most

useful way. That is, to put the maximum amount of the original total variance on one of the

new axes, the maximum amount of the remaining variance on the next and so forth. It

would also be convenient of none of these new axes were related to each other.

Here is an example of PCA that I carried out on the rows of the family repertory grid.

Since there were nine original constructs, each element had an address in nine-dimensional

space. PCA will rotate the original 9-dimensional axes to best reallocate variance. The

rotated axes that accomplish this best are called the principal components. In the family

grid the sum of the variances along each of the constructs was 19.39. You will see below

how this total was reallocated along each of the new principal components. You will also


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see the accumulated percent of variance that is displayed along the first several pcs. The

first pc now displays 43 % of the original total variance; the first and second pcs displays

69 %; and the first, second and third pcs displays 85 %.

Total variance to be explained = 19.39

3.14 PC Element Addresses

Here are the element addresses in the new principal components (pc) reference system.

3.15 Family in pc Space

The elements are plotted with pc1 as the horizontal axis, pc2 as the vertical and pc3 as the

axis pointing up from the page. Balls closer to the eye, that is with a large pc3 value, are

larger than those with a smaller value. Balls with a negative pc3 value are grey, those with

a positive are white. Note that the amount of variance expressed along each of these axes is

indicated after the number of the pc axis. Note, too, that I have attached the point balls with

a minimal spanning tree. I do this to sketch the shape of the points.

3.16 Jim’s Family: Looking Down on the pc1 (Horizontal) and pc2 Plane (Vertical).

pc3 is in and Out of the Page

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3.17 What are the Meanings of the pc Axes?

Intuitively we know that a pc address must be a blend of the original address information.

In fact, we know that each element’s pc addresses is a linear combination of its original

value’s in construct space. We know, too, that the pc program will give us these coeffi-

cients or weights.

A more intuitive way to see this, to think about this, it seems to me, is to display the

correlations between each of the original construct values and each of the pcs. Here is a

table of these correlations.

For example, the number in the upper left of the table below, -.28, is the correlation

between the values of construct 1: likes me/dislikes me (1 2 2 1 1 1 3 1 3 1 5) and the pc1

values shown in the first column of the table above. This correlation value indicates how

much construct 1 ‘‘contributes’’ to pc1.

Note that these correlation values are between the heavy, or 5-end, of the construct and

the positive pole of the pc.

The largest correlation values suggest ways to assess meanings to the new pc axes so

let’s look at those. I’ve marked correlations (absolute values) greater than .8 in grey. I

picked these large values to show the strongest influences on the pc axes.


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Large and small absolute values greyed. Cutoff values can be set in the procedures.

For example:

The positive end of pc1 is a blend of open mind (.93) and intelo (.88); its negative end is

a blend of closed mind and concrete.

The positive end of pc2 is a blend of female (.89) and likes me (.80); its negative is male

(-.89) and dislikes me (-.80).

The positive end of pc3 is tense (.97) and its negative end is at ease (-.97).

If we looked further, that is, deeper into pc space: pc4 would be mostly plain on the

positive end and handsome on the negative.

3.18 Plotting the Constructs/pc Correlations

These correlations values can be plotted. For example we could imagine pc1 and pc2 space

to be a square with values in the vertical and horizontal dimensions to be between -1 to

?1 and the correlations values of each construct could be plotted in this space. No numbers

are needed on this kind of chart. The white lines indicate the axis orientation and the center

(0 0) of the chart.

3.19 Plot of All Grayed Constructs

Pc1 on the horizontal axis and pc2 on the vertical.

3.20 Overlay: Correlation Space with pc Space

I could overlay this correlation space on top of the pc space. The boxes represent constructs

in construct/pc correlation space and the balls are elements in pc space. The distances

between boxes and balls, however, mean nothing since boxes and balls are in two different

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spaces. But the placement of boxes suggests the meaning of the axes of the pc environment

and this allows us to think more about the relative placement of the balls in pc space.

In the two charts below I only plot correlation values that are larger than .8. I picked

.8 in order to only show the strongest influences on the pc axes.

3.21 Jim’s Family: Looking Down on the pc1 (Horizontal) and pc2 Plane (Vertical)

3.22 Jim’s Family: Looking Down on the pc3 (Horizontal) and pc2 Plane (Vertical)


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3.23 What Does this All Mean?

These last two charts show a way of looking at the relationships that I see in my own

family. PC analysis has displayed all of my family members in a kind of basic meaning

space. PC suggests that I think of my family along three basic or core dimensions: (1) an

intellectual/concrete dimension, (2) a gender dimension, and (3) tense/at ease dimension.

PC analysis also suggests that this ordering of basic dimensions might indicate how I

weight these three characteristics in my mind. That is, which is the most ‘‘important’’.

Most importantly, these diagrams illustrate how some simple statistical notions can help

us explore complex psychological notions so that each can be better perceived and dis-

cussed (Kelly 1991g; Clayson 1994).

3.24 Lessons Learned

I’ve tried to illustrate the application of George Kelly’s four big ideas in terms of looking at

how I make sense of my family:

1. We are all personal scientists

2. Our internal scientific models can be made explicit.

I have modeled my family in terms of nine bi-polar constructs. My family repertory grid

illustrates how I have done this.

3. Our models can be explored and refined through visualization and vocalization.

I have illustrated how correlation analysis can explore the relationships between con-

structs and between elements. I have included visuals and the conversations that they have

elicited. I went on to use principal component analysis to look at the relationship between

constructs and elements. This analysis showed how my nine dimensional family model

could be effectively displayed in three dimensional space.

4. Basic statistical ideas and methods will become part of our construct system if they are

seen to be useful in understanding ourselves and our world.

I have suggested some evidence of this with snippets of conversation with my students

(For a more detailed discussion of how words, diagrams and models can encourage con-

structionist thinking see: Clayson 2008).

4 A Personal Breakthrough

I would like to end on a very personal note to further illustrate the breakthroughs in

communication that Kelly psychology can offer even outside the classroom. I have a young

Nigerian niece named O, who, several years ago, spent a summer in Paris working on a

novel. She would visit me in my study and we would talk about how the novel was going

and she would look around at the computers in my room without comment. One day I

asked her if she wanted to talk about what I was doing.

Jim, you know how I feel about mathematics and these computers that calculate

stuff. It is all so contrary to what I believe in and what I do. People’s emotions can’t

be measured and you can’t quantify feelings and values and, if you attempt to do so,

you might risk destroying the things being measured.

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Words and numbers are not the same, are they? …. I guess I don’t want to risk my

own position by talking about statistics and mathematical modeling or whatever it is

that you do.

I decided to experiment. I asked O if she would play a short ‘‘computer game’’ with me

and tell me at the end of it whether it made her think about anything differently. If it did

then maybe we had something basic in common; if not, then I would acknowledge that she

was right. She agreed and I gave her the background on Kelly and his famous family grid

exercise. O’s mother had been an ambassador for her country and had lived all over the

world. Naturally, O added many of good friends she had made living abroad with her

Mother.

When it came time to come up with constructs, she was hesitant but then finally got into

it. Like me/not like me came first, then sensitive/non-sensitive, then extrovert/introvert then

several others that I have forgotten. Finally, I encouraged her to talk about physical traits,

how did they look, for example? She added constructs about eye color and skin color and

methods of dress and then she stopped. ‘‘This is really silly’’, she said; ‘‘let’s get on with

it!’’

The first thing we saw was that skin color (light complexion/dark complexion) was very

highly correlated to both like me/not like me and sensitive/non-sensitive. But, O, I asked, do

you decide the nature of a person based on the color of their skin?

This was a real emotional breakthrough. We had never spoken about race, racism,

discrimination and racial aspects of beauty before and suddenly we were doing so natu-

rally. This didn’t happen because these things can be ‘‘measured’’. But they can be talked

about and statistical ideas might elicit talk. Talk might elicit more statistical ideas: back

and forth. We began to see, together, the usefulness of words and numbers to get us to talk

about difficult and important issues.

One last point to this story. At the end of our session, O asked me rather casually.

Jim could you explain how you actually measured some of those relationships in my

family descriptions? And how did you make those pictures? Can you try to explain it

to me in words? I mean, how did you decide where each of those balls and boxes

went on the graph. That might be worth talking about …

5 Conclusion

The title of this paper is ‘‘talking statistics: talking ourselves’’. The idea was to describe a

technique that I use with beginning statistics students to get them hooked on how simple

statistical techniques can offer them new ways of looking at things that they find important

and personally meaningful.

I suggest that the relationships that students have with each other, their family and their

teachers is so important and vivid to them that this is a wonderful place to begin the

exploration of statistical concepts. The students quoted in this paper are typical of many of

my students who have found Kelly’s method of repertory grids an easy and pleasant way to

understand basic statistical techniques like correlation, regression and principal component

analysis as they talk about themselves. And, when it works really well, the talking about

statistical ideas and the talking about us becomes one conversation. Statistical notions can

inform how we speak about our feelings, and our language of feelings might then inform

how we think and talk about doing statistics.


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I have found that the ideas and work of George Kelly have encouraged me to think and

to talk freshly about how I go about trying to make sense of my world and to make me

work harder at listening to and conversing with others as they describe their own con-

structionist journey. George Kelly’s personal construct psychology fits very well in the

constructionist world, his work in amazingly relevant today and he should be better known.

I must end by admitting two things:

1. Like other constructionists, measuring the efficacy of one pedagogical tool against

another requires a methodology that is not yet agreed upon.

2. Anecdotal evidence of the power of this method is not scientific but the Grid concept

kept me and the majority of my students excited and talking excitedly. Getting to know

myself and my students better by trying to build a common idiolect is what I can

claim.

References

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Bell, R. (2006). A note on the correlation of elements in repertory grids: How to and why. The Journal ofConstructivist Psychology, 19(3), 273–279.

Clayson, J. (1994). Visual statistical thinking: Integrating words and images. Paper presented at ICOTS IV,the 4th international conference on the teaching of statistics, Rabat, Morocco, August 1994.

Clayson, J. (1998). Confessions of a constructionist: 10 years of teaching undergraduate statistics. Paperpresented at ICOTS V, the 5th international conference on the teaching of statistics, Singapore.

Clayson, J. (2008). Radical bricolage: Building coherence in the liberal arts using art, modelling andlanguage. International Journal of Education Through Art, Fall 2008.

Forester, E. M. (1927). Aspects of the novel (p. 152). London: Edward Arnold & Co.Fransella, F. (1995). George Kelly. London: Sage.Fransella, F. (2003). International handbook of personal construct psychology (p. 47). Chichester, England:

Wiley.Fransella, F., Bell, R., & Bannister, D. (2003). A manual for repertory grid technique (2nd ed.). Chichester:

Wiley.George, A. (1990). Whose language is it anyway, some notes on idiolects. The Philosophical Quarterly,

40(160).Harel, I., & Papert, S. (Eds.). (1991). Constructionism (p. 1). Norwood, New Jersey: Ablex Publishing

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therapy. London and New York: Routledge.Kelly, G. (1991c). The psychology of personal constructs, volume one: Theory and personality (p. 239ff).

London and New York: Routledge.Kelly, G. (1991d). The psychology of personal constructs, volume one: Theory and personality (p. 92).

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London and New York: Routledge.Kelly, G. (1991g). Chapter 6, the psychology of personal constructs, volume one: Theory and personality

(p. 189ff). London and New York: Routledge.Maher, B. (Ed.). (1979). Clinical psychology and personality: The selected papers of George Kelly.

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III(10).Minsky, M. (1986). The society of mind. New York: Simon and Schuster.

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Scheer, J. (2006). The PCP portal. http://www.pcp-net.de/info/pcpindex.html.Slater, P. (Ed.) (1976a). The measurement of intrapersonal space by grid technique, Vol. 1. Explorations of

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Documents

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