Fisher Aare2007 Fremantle2bd2

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Information about Fisher Aare2007 Fremantle2bd2

Published on February 4, 2009

Author: wpfisherjr

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First, a renewed relationship between philosophy and mathematics has important methodological implications for educational research. Though it has largely been forgotten today, philosophy is fundamentally mathematical. We need to revive, reinvigorate, and reinvent the ancient connection between philosophy and mathematics because something vitally important has been lost.
Second, we’re going to apply what we learn from the connection between mathematics and philosophy to educational measurement. Not all quantitative methods are reductionistic. And some might be surprised to learn how much good math there can be in qualitative methods.
Third, with our new appreciation for mathematically meaningful measurement in hand, we are going to bring out the whole range of relevant applications. We are witnessing the birth of a new human science of caring that will support a new era of socially and environmentally sustainable economic activity.

Recovering Science’s Meaning for Life in Educational Research William P. Fisher, Jr., Ph.D. AARE 2007 Annual Meeting Fremantle, Western Australia

Overview Today’s shifting paradigms A new paradigm in educational measurement Implications for the future

Today’s shifting paradigms

A new paradigm in educational measurement

Implications for the future

First Basic Thesis Close reading of the philosophical works informing the shift in educational research to qualitative methods reveals an unexpected, fresh perspective on mathematical thinking.

Second Basic Thesis When the philosophical critique of modern science is applied to educational research, a new potential for blending qualitative and quantitative methods comes to light.

Third Basic Thesis The new paradigm of a living universe, and its integrated qualitative/quantitative methodologies, will inform a new ecological economics of human, social, and natural capital.

We have created a new class of problems that cannot be solved from within the paradigm that created them. The Problem is the Problem

Modern Paradigm’s Scientific Model: A Clockwork Universe

But we have to ask ourselves… have we ever actually been modern?

“ In quantum mechanics as in psychiatry, in ecology as much as in anthropology, the scientific observer is now—willy-nilly—also a participant " in the creation of the thing observed. - Stephen Toulmin

Does this mean the end of objectivity?

But do these presumptions actually withstand close reading of key philosophical texts ?

“… the mathematical object is ideal. Its being is thoroughly transparent and exhausted by its phenomenality.” And so it is the “ absolute model for any object whatsoever .“ - Jacques Derrida, 1989

"When I take liberties, it's always by measuring the distance from the standards I know or that I've been rigorously trained in.“ - Jacques Derrida, 2003

"it is totally false to suggest that deconstruction is a suspension of reference. . . . I never cease to be surprised by critics who see my work as a declaration that there is nothing beyond language.“ - Jacques Derrida, 1981

"... the power of making things visible, alive , actual is inseparable from either a logical relation of proportion or a comparison...” - Paul Ricoeur, 1977

“… it is not word but number that is the real paradigm of the noetic” - Hans Georg Gadamer, 1989

“ Numerical signs … are the most ideal signs because their position in the order completely exhausts them." - Hans Georg Gadamer, 1989

So, just what does all of this mean to educational research ?

"A good implicit phenomenology is often concealed in the most objectivistic sciences ....“ - Paul Ricoeur, 1967

"We should clarify the distinction between statistics and mathematical psychology. A study can be quantitative without being mathematical. “ - Louis L. Thurstone Presidential Address Psychometric Society, 1937

“… we are now dealing with an equation whose parameters have meaning in terms of the psychological postulates that the equation represents.“ - L. L. Thurstone, 1937

“ Dimensionally invariant numerical laws correspond to meaningful qualitative relations.” - R. Duncan Luce, 1978

… mathematics … does not function merely as an aid or a tool that a psychologist can use but as the very language in which he thinks. - L. L. Thurstone, 1937

“ Geometry requires figures which we draw, but its object is the circle itself....” “… one looks right through the drawn circle and keeps the pure thought of the circle in mind.” - Hans-Georg Gadamer, 1980

The mathematical is "the fundamental presupposition of all 'academic' work" and "of the knowledge of things." - Martin Heidegger, 1967

Phenomenological Method Reduction: to a meaningful expression Construction: application of expression in practice Deconstruction: critical evaluation of anomalies and failures of invariance New reduction , rebirth of meaning - Heidegger, 1982

Reduction: to a meaningful expression

Construction: application of expression in practice

Deconstruction: critical evaluation of anomalies and failures of invariance

New reduction , rebirth of meaning

- Heidegger, 1982

"The effective progress of mathematical notation goes along with the deconstruction of metaphysics , with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.“ - Jacques Derrida, 1981

"No philosophical discourse would be possible, not even a discourse of deconstruction, if we ceased to assume what Derrida justly holds to be 'the sole thesis of philosophy,' namely 'that the meaning aimed at through these figures is an essence rigorously independent of that which carries it over.'" - Paul Ricoeur, 1977

"I try to place myself at a certain point at which—and this would be the very 'content' of what I would like to 'signify'—the thing signified is no longer easily separable from the signifier .“ - Jacques Derrida, 1968

“ ... measurement is justified and sophisticated only when reparation is made by recalling the uniqueness of the person measured . Otherwise, the abstraction does him violence.” - E. G. Ballard, 1978

Transparent Reference = = = =

Transparency = = = =

We progressively score each “Yes” a 1, |-->| 1 1 1 1 1 1 1 1 asking at each unit mark: Is the right end of the third block at this line, or to the right of it?

Until the answer is “No”, which we score as “0”: |-->|-->|-->|-->|-->|-->|-->| -->|-->|-->|-->|-->|-->| -->|-->-|->| 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

Modern Data Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Score Student 1 1 0 1 0 0 1 3 Student 2 1 0 1 1 1 1 5 Student 3 0 0 1 0 0 0 1 Student 4 1 1 1 1 1 1 6 Student 5 0 0 1 0 0 1 2 Student 6 1 0 1 1 0 1 4 Score 4 1 6 3 2 5

Amodern Data: Autopoietic Self-Organized Construct Definition Item 3 Item 6 Item 1 Item 4 Item 5 Item 2 Score Student 3 1 0 0 0 0 0 1 Student 5 1 1 0 0 0 0 2 Student 1 1 1 1 0 0 0 3 Student 6 1 1 1 1 0 0 4 Student 2 1 1 1 1 1 0 5 Student 4 1 1 1 1 1 1 6 Score 6 5 4 3 2 1

Amodern Autopoeisis: Probabilistic Data Item 3 Item 6 Item 1 Item 4 Item 5 Item 2 Score Student 3 0 1 0 0 0 0 1 Student 5 1 0 1 0 0 0 2 Student 1 1 1 0 1 0 0 3 Student 6 1 1 1 0 1 0 4 Student 2 1 1 1 1 0 1 5 Student 4 1 1 1 1 1 0 5 Score 6 5 4 3 2 1

1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

|------------------------------->| Observed: 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 Expected: 1 1 .9 .8 .7 .6 .5 .5 .5 .5 .4 .3 .2 .1 .0 .0 Residual: 0 -1 .1 .2 .3 .4 -.5 .5 -.5 .5 -.4 -.3 -.2 -.1 1 0

+-----------------------------------------------------------------------------------------+ |ENTRY RAW MODEL| INFIT | OUTFIT |PTMEA|EXACT MATCH| | |NUMBER SCORE COUNT MEASURE S.E. |MNSQ ZSTD|MNSQ ZSTD|CORR.| OBS% EXP%| PERSON | |------------------------------------+----------+----------+-----+-----------+------------| | 22 57 21 611.58 23.40|2.51 3.3|3.03 3.7|A-.25| 81.0 72.6| 25211S06122| | 170 81 31 587.58 17.35|2.18 3.8|2.91 5.2|B-.40| 54.8 64.5| 25222S06226| | 94 57 21 611.58 23.40|2.35 3.1|2.65 3.2|C-.04| 81.0 72.6| 1 21S06217| | 55 56 20 634.18 27.53|2.31 2.4|2.54 2.4|D-.07| 90.0 80.6| 11111S06155| | 17 34 21 451.11 18.58|2.27 3.7|2.36 3.9|E .16| 28.6 54.8| 21211S06117| N O O I/R I/R Q Q Q Q Q Q Q D O R R N/A N/A U U U U U U U E M D D T/T T/T A A A A A A A M I I I E/I E/I L L L L L L L O N N N R/O R/O I I I I I I I G A A A V V T T T T T T T R L L L A A Y Y Y Y Y Y Y A L L P I I I I I I I H N N N N N N N I D D D D D D D C E E E E E E E S X X X X X X X

The Mathematical vs. the Quantitative Quantitative Reductionistic numerical assumptions Unjustified concrete counts or sums Test- and sample-dependent scores Mathematical Justified transparent symbolization Figure rigorously independent of meaning Measures reproducible across instruments Instruments interchangeable

Quantitative

Reductionistic numerical assumptions

Unjustified concrete counts or sums

Test- and sample-dependent scores

Mathematical

Justified transparent symbolization

Figure rigorously independent of meaning

Measures reproducible across instruments

Instruments interchangeable

Mathematical Comparisons

Numeric Comparisons

Numeric Scores Transformed into Mathematical Measures

The Question of Measurement Correlations among 11 calibrations of 8 similar items included on 4 clinical assessments of physical functioning: mean r = 0.93, mode = 0.98 Fisher, W. P., Jr. (1997). Physical disability construct convergence across instruments: Towards a universal metric. Journal of Outcome Measurement , 1 (2), 87-113.

“… the existence of quantitative correlations between the various forms of energy imposes upon men of science the duty of bringing all kinds of physical quantity to one common scale of comparison. ” - J. D. Everett, 1881 quoted in Smith & Wise 1989, pp. 684-5

“ Cognition has nothing to do with minds nor with individuals but with the propagation of representations through various media , which are coordinated by a very lightly equipped human subject working in a group, inside a culture, with many artefacts and who might have internalized some parts of the process.” - Bruno Latour

Metric System Is it just an accident of history that the emergence of the metric system coincided with the: French & American Revolutions? 2 nd Scientific Revolution? Industrial Revolution? Historians of science show that metric uniformity was co-produced with democracy, science, and capital growth.

Is it just an accident of history that the emergence of the metric system coincided with the:

French & American Revolutions?

2 nd Scientific Revolution?

Industrial Revolution?

Historians of science show that metric uniformity was co-produced with democracy, science, and capital growth.

"Just as the French Revolution had proclaimed universal rights for all people, the savants argued, so too should it proclaim universal measures.” - K. Alder, 2002

Calibrating Instruments

"We heal each other all the time, and don't even realize we're doing it. Healing comes out of a very simple human relationship--knowing your life matters to another person, and connecting to something larger and unseen. “ -Rachel Naomi Remen, M.D.

We are what we measure. It is time we measured what we want to be. - W. Fisher, 1997

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