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Fisher Aare2007 Fremantle2bd2

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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, were 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.

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Recovering Sciences Meaning for Life in Educational Research William P. Fisher, Jr., Ph.D. AARE 2007 Annual Meeting Fremantle, Western Australia
Overview Todays 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 Paradigms 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 nowwilly-nillyalso 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
"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 whichand 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
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.
"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

More Related Content

Fisher Aare2007 Fremantle2bd2

  • 1. Recovering Sciences Meaning for Life in Educational Research William P. Fisher, Jr., Ph.D. AARE 2007 Annual Meeting Fremantle, Western Australia
  • 2. Overview Todays shifting paradigms A new paradigm in educational measurement Implications for the future
  • 3. 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.
  • 4. 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.
  • 5. 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.
  • 6. We have created a new class of problems that cannot be solved from within the paradigm that created them. The Problem is the Problem
  • 7. Modern Paradigms Scientific Model: A Clockwork Universe
  • 8. But we have to ask ourselves have we ever actually been modern?
  • 9. In quantum mechanics as in psychiatry, in ecology as much as in anthropology, the scientific observer is nowwilly-nillyalso a participant " in the creation of the thing observed. - Stephen Toulmin
  • 10. Does this mean the end of objectivity?
  • 11. But do these presumptions actually withstand close reading of key philosophical texts ?
  • 12. 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
  • 13. "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
  • 14. "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
  • 15. "... the power of making things visible, alive , actual is inseparable from either a logical relation of proportion or a comparison... - Paul Ricoeur, 1977
  • 16. it is not word but number that is the real paradigm of the noetic - Hans Georg Gadamer, 1989
  • 17. Numerical signs are the most ideal signs because their position in the order completely exhausts them." - Hans Georg Gadamer, 1989
  • 18. So, just what does all of this mean to educational research ?
  • 19. "A good implicit phenomenology is often concealed in the most objectivistic sciences .... - Paul Ricoeur, 1967
  • 20. "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
  • 21. 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
  • 22. Dimensionally invariant numerical laws correspond to meaningful qualitative relations. - R. Duncan Luce, 1978
  • 23. 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
  • 24. 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
  • 25. The mathematical is "the fundamental presupposition of all 'academic' work" and "of the knowledge of things." - Martin Heidegger, 1967
  • 26. 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
  • 27. "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
  • 28. "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
  • 29. "I try to place myself at a certain point at whichand 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
  • 30. ... 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
  • 33. 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?
  • 34. 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
  • 35. 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
  • 36. 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
  • 37. 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
  • 38. 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
  • 39. |------------------------------->| 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
  • 40. +-----------------------------------------------------------------------------------------+ |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
  • 41. 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
  • 44. Numeric Scores Transformed into Mathematical Measures
  • 45. 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.
  • 46. 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
  • 47. 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
  • 48. 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.
  • 49. "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
  • 51. "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.
  • 52. We are what we measure. It is time we measured what we want to be. - W. Fisher, 1997

Editor's Notes

  • #2: Recovering Sciences Meaning for Life in Educational Research The critique of science and modernity offered under the various headings of existentialism, phenomenology, hermeneutics, feminism, deconstruction, etc. has stalled in recent years, with no major new advances. Increasingly, entrenched camps each guard fixed opinions based in unexamined assumptions. Close reading of key texts, however, opens doors to the resolution of some fundamental dilemmas. For instance, what are the implications of Deweys sense of the unity of subject matter and method, echoed by Gadamer in his characterization of method as the activity of the thing itself? How might educational research make use of Heideggers description of the ontological methods three moments of phenomenological reduction, practical application, and deconstructive return to a new reduction? How might the mathematical metaphysics of all Academic thinking influence qualitative research as much asor even more thanit does quantitative research? Answers to these questions are pursued with the goal of arriving at sound recommendations for enhancing the impact of educational research and practice.