自然回饋是多數運動技能學習過程中主要的來源，而由於自然回饋的操弄不易，其對運動學習影響的文獻缺乏，因此在動力系統的架構下，以學習曲線的分析探討不同自然回饋強度對運動技能學習的影響。本研究的問題為：（一）不同自然回饋強度是否造成不同的學習率？（二）在相同起始行為下，先學習較困難組與先學習較容易組，其學習率的比較。（三）在轉移前、轉移後個人學習曲線適配，對數函數或是指數函數較為適配？回饋強度以相同的總質量，不同的轉動慣量來界定控觸覺回饋強度，以可程式控制器進行穩定時間的測量，實驗參加者共計16名，分派至20﹪--80﹪組、80﹪--20﹪組二組，每組各8名，紀錄前測30﹪、20﹪、80﹪、後測30﹪的穩定時間進行指數函數與對數函數的非線性迴歸分析、穩定時間的比較，本研究的結論為：（一）相同的總質量，不同的轉動慣量造成不同動作的難度。轉動慣量愈大，動作難度較低，動作表現較佳；轉動慣量愈小，動作難度較高，動作表現較差。（二）操弄不同的學習順序先學簡單或困難組對不同階段的影響，練習效果—先學習較困難組表現上優於先學習較簡單組:學習效果—二組間沒有顯著差異。（三）轉移的閾值設定過低，無法說明在不同學習階段學習曲線為何種型態。

關鍵詞：動力系統（dynamical systems）、運動技能學習（motor learning）、學習曲線（learning curve）、控觸覺回饋（haptic feedback）、自然回饋（nature feedback）

Nature feedback is the main source of feedback in motor learning process. Because natural feedback is not easily manipulated, there has been few natural feedback-related studies in the motor learning literature. The purpose of this study was to examine the influence of the intensity of natural feedback on motor skill acquisition under the dynamical systems framework.
Three research problems were raised in this study: 1. Did the intensity level of natural feedback affect practice performance? 2. Did the order of practice condition affect learning? 3. Which fitting function, exponential or power law, had better fitting result for the learning curves? Sixteen college students participated in this experiment. The participants were assigned to one of the two groups: 20%-80% and 80%-20%. The balance time of each condition was analyzed for performance. The results showed that: 1. Larger moment of inertia provides stronger haptic feedback which resulted in a easier task; 2. Practice more difficult task first resulted in better performance, but had no effect on learning; and 3. The data analyzed could not provide support for either exponential or power law learning function because the criterion of success was set too low.

Keywords: dynamical systems, motor learning, learning curve, haptic feedback

梅錦榮。（1991）。神經心理學。臺北市：桂冠心理。
劉碧華譯。(1992)。運動科學：物理定律與最佳成績表現。臺北市：財團法人徐亨體育文化基金會。
張春興。（1992）。張氏心理學辭典。台北：東華。
林齊宣譯。(1995)。解剖學原理與實用。台北：合記圖書。
林和。（1998）。混沌—不測風雲的背後。台北：天下遠見。
廖庭儀、劉有德。以學習曲線描述協調型態的轉移。未出版。
張三慧、王虎珠。(1990)。大學物理：力學。北京：清華大學。
Abraham, R. H., & Shaw, C. D. (1992). Dynamics─ the geometry of behavior. California: Addison-Wesley.
Adams, J. A. (1971). A closed-loop theory of motor learning. Journal of Motor Behavior, 3, 111-150.
Bahrich, H. P., Fitts, P. M., & Briggs, G. E. (1957). Learning curves-facts or artifacts? Psychological Bulletin, 54, 256-268.
Beek, P. J., & van Santvoord, A. A. M. (1992). Learning the cascade juggle: A dynamic systems analysis. Journal of Motor Behavior, 24, 85-94.
Burton, G., Turvey, M. T., & Solomon, H. Y. (1990). Can shape be perceived by dynamic touch? Perception & Psychophysics, 5, 477-487.
Card, S. K., English, W. K., & Burr, B. (1978). Evaluation of mouse, rate controlled isometic joystick, step keys, and text keys for text selection on a CRT. Ergonomic, 21, 601-613.
Carello, C., Fitzpatrick, P., Domaniewicz, I., Chan, T.-C., & Turvey, M. TM. (1992). Effortful touch with minimal movement. Journal of Experiment Psychology, 18, 290-302.
Chen, H. H. (2002). Constructing the Theory of Motor Learning Curve—Dynamical System Approach. Unpublished doctoral dissertation, National Taiwan Normal University.
Cohen, J., Dunbar, D. K., & MacClelland, J. L. (1990). On the control of automatic processes: A parallel distributed processing account of stroop effect. Psychological Review, 97, 332-361.
Crossman, E. R. (1976). A theory of the acquisition of speed-skill. Ergonomic, 2, 153-166.
Diedrich, F. J., & Warren, W. H. (1995). Why change gaits? Dynamics of the walk-run transition. Journal of Experimental Psychology, 21(1), 183-202.
Del Rey, P. (1971). The effects of video-tape feedback on form, accuracy, and latency in an open and closed environment. Journal of Motor Behavior, 3, 281-287.
Estes, K. W. (1956). The problem of inference from curves based on group data. Psychological Bulletin, 53, 134-140.
Fowler, C. A., Turvey, M. T. (1978). Skill acquisition: An event approach for the optimum of several variables. In G. E. Stelmach (Ed.), Information processing in motor control and learning ( pp. 1-40). New York: Academic Press.
Gentile, A. M. (1972). A working model of skill acquisition with application to teaching. Quest, 17, 3-23.
Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.
Grillner, S. (1985). Neurobiological bases of rhythmic motor acts in vertebrates. Science, 228, 143-149.
Hannaford, B. (1991). Kinesthetic Feedback Techniques in Teleoperated Systems. In C. Leondes (Ed.), Advances in Control and Dynamic Systems(pp. 1-32). San Diego: Academic Press.
Heathcote, A., Brown, S., & Mewhort, D. J. K. (2000). The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review, 7(2), 185-207.
Hirsch, W. Z. (1952). Manufacturing progress functions. Review of Economics and Statistics, 34, 143-155.
Kelso, J. A. S. (1997). Dynamical Pattern--the self-organization of brain and behavior. Mass: MIT Press.
Kernodle, M. W., & Carlton, L. G. (1992). Information feedback and the learning of multiple-degree-of-freedom activities. Journal of Motor Behavior, 24, 187-196.
Kling, J. W. (1971). Learning: An introductory survey. In J. W. Kling & L. A. Riggs(Eds.), Woodworth and Schlosberg’s Experimetnal Psychology( pp. 551-613). New York: Holt, Rinehart & Winston.
Kramer, A. F., Strayer, D. L., & Bucklley, J. (1990). Development and transfer of automatic processing. Journal of Experimental Psychology: Human Perception & Performance, 16, 505-522.
Krinskil, V. I., & Shik, M. L. (1964). A simple motor task. Biophysics, 9, 661-666.
Kugler. P. N., & Turvey, M. T. (1987). Information, Nature Law and the Self-Assembly of Rhythmic Movement. Hillsdale, NJ: Erlbaum.
Landin, D. E., Hebert, E. P., & Fairweather, M. (1993). The effects of variable practice on the performance of a basketball skill. Research Quarterly for Exercise and Sport, 64, 232-237.
Langdon, P., Keates, S., Clarkson, P. J., Robinson, P. (2000). Using haptic feedback to enhance computer interaction for motion-impaired users. Proceedings of the 3rd Int'l Conference on Disability, Virtual Reality and Associated Technologies (ICDVRAT 2000), 25-32.
Laskowski, E. R., Newcomer-Aney, K., & Smith, J. (1997). Refining rehabilitation with proprioception Training: Expediting return to play. The Physician and Sports Medicine, 25(10),100-110.
Lee, D. N. (1978). The functions of vision. In H. L. Pick, Jr. & E. Saltzman(Eds.), Modes of perceiving and processing information, ( pp.159-170). Hillsdale, NJ: Erlbaum.
Lee, S. (2002). Proprioception: how and why? Serendip, 2002(2), Retrieved date April, 26, 2003, from http://serendip.brynmawr.edu/bb/neuro/neuro02/web2
Liu, Y. T., Mayer –Kress, G. & Newell, K. M. ( 2003). Beyond curve fitting: a dynamical systems account of exponential learning in a discrete timing task. Journal of Motor Behavior, 35(2), 197-207.
Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95, 492-527.
Magill, R. A. (1998). Motor learning: Concepts and applications(5th ed.). Dubuque, IA: Wm. C. Brown.
Mazur, J. E., & Hastie, R. (1978). Learning as a accumulation: A reexamination of the learning curve. Psychological Bulletin, 85, 1256-1274.
Neisser, U., Novick, R., & Lazar, R. (1963). Searching for ten targets simultaneously. Perceptual and Motor Skills, 17, 955-961.
Newell, K. M. (1976). Knowledge of results and motor learnging. In J. Keogh, & R.S. Hutton,. (Eds.), Exercise and Sport Science Reviews (pp. 195-228). Allihakes. Santa Barbara: Journal publication.
Newell, A., & Rosenbloom, P. S. (1981). Mechanism of skill acquisition and the law of practice. In J. R. Anderson (Ed.), Cognitive skill and their acquisition (pp. 1-55). Hillsdale, NJ: Erlbaum.
Newell, K. M., & Waltter, C. B. (1981). Kinematic and kinetic parameters as information feedback in motor skill acquisition. Journal of Human Movement Studies, 7, 235-254.
Newell, K. M., Morris, L. R., & Scully, D. R. (1985). Augmented information and the acquisition of skill in physical activity. In Terjung, R. L. (ed.), Exercise and sport science reviews, 13. Lexington, MA: Collamore Press.
Newell, K. M. (1985). Coordination, control and skill. In D. Goodman, I. Franks, & R. B. Wilberg (Eds.), Differing Perspectives in Motor Learning, Memory, and Control ( pp. 295-318). Amsterdam: North Holland.
Newell, K. M., Kugler, P. N., van Emmerrik, R. E. A., & Mcdonald, P. V. (1989). Search strategies and the acquisition of coordination. In S. A. Wallace(Ed.), Perspective on the Coordination of Movement ( pp. 85-112). Elsevier Science Publishers : North Holland.
Newell, K. M. (1991). Motor Skill Acquisition. Annual Review Psychology, 12, 213-237.
Newell, K. M., Liu, Y. T., & Mayer- Kress, G. ( 2001). Time scale in motor learning and development. Psychological Review, 108(1), 57-82.
Peck, A. J., Jeffers, R. G., Carello, C., & Turvey, M. T. (1996). Hapticlly perceiving the length of one rod by means of another. Ecological Psychology, 8(3), 237-258.
Rothstein, A. L., & Arnold, R. K. (1976). Bridging the gap: Application of research on video-tape feedback and bowling. Motor Skills: Theory into Practice, 1, 35-62.
Salmoni, A. W., Schmidt, R. A., & Walter, C. B. (1984). Knowledge of results and motor learning: A review and critical reappraisal. Psychological Bulletin, 95, 355-386.
Schmidt, R. A. (1975). A schema theory of discrete motor skill learning. Psychological Review, 82, 225-260.
Schmidt, R. A.(1988). Motor control and learning: A behavior emphasis. (2nd). Champain, IL: Human Kinetics.
Schmidt, R. A. & Lee, T. D. (1999). Motor control and learning: A behavior emphasis. (3rd). Champain, IL: Human Kinetics.
Scholz, G., Kelso, J. A. S., & Schoner, G. S. (1987). Non-equilibrium phase transitions in coordinated biological motion: Critical slowing down and switching time. Physics Letters, A, 390-394.
Schoner, G., & Kelso, J. A. S. (1988). Dynamic pattern generation in behavior and neural systems. Science, 239, 1513-1520.
Seibel, R. (1963). Discrimination reaction time for a 1023 alternative task. Journal of Experimental Psychology, 66, 215-226.
Sherrington, C. (1906). The intergrative action of the nervous system. New Haven, CT: Yale University Press.
Sidman, M. (1952). A note on functional relations obtained from group data. Psychological Bulletin, 49, 263-269.
Snoddy, W. H. (1926). Learning and stability: A psychophysical analysis of a case of motor learning with clinical applications. Journal of Applied Psychology, 10, 1-36.
Solomon, H. Y., & Turvey, M. T. (1988).Haptically perceiving the distances reachable with hand-held objects. Journal of Experiment Psychology, 14, 404-427.
Solomon, H. Y., Turvey, M. T., & Burton, G. (1989). Perceiving extents of rods by wielding: haptic diagonaliztion and decomposition of the inertia tensor. Journal of Experiment Psychology, 15, 58-68.
The Baseball Bat Haptic Feedback System. (n. d.). Retrieved April 26, 2003, from http://www.sonic.net/~dfx/fait/bbhf.html
Thelen, E. & Smith, L. B. (1993). A dynamic systems approach to the development of cognition and action. Cambrideg, MA: MIT Press.
Turvey, M. T. & Carello, C. (1995). Dynamic touch. In E. William & S. J. Rogers (Eds.), Perception of space and motion ( pp. 401-490). CA: Academic press.
Vander, A. J., Sherman, J. H., & Luciano, D. S. (1998). Human Physiology (7th ed). NY: McGraw-Hill.
Yan, J. H., Thomas, J. R., & Thomas, K. T. (1998). Children’s age moderates the effect of practice variability: A quantitative review. Research Quarterly for Exercise and Sport, 69, 210-215.