مقایسه دامنه مؤلفه P300 دانشجویان دارای دانش مفهومی و رویه ای سطح بالا با دانشجویان دارای دانش مفهومی و رویه ای سطح پایین در حل مسائل انتقال بین بازنمایی نموداری و جبری تابع

نوع مقاله: مقاله پژوهشی


1 دانشجوی دکتری آموزش ریاضی دانشگاه فردوسی مشهد،مشهد،ایران.

2 استاد گروه ریاضی کاریردی،دانشکده علوم ریاضی، دانشگاه فردوسی مشهد،مشهد،ایران.

3 استاد گروه زیست شناسی،دانشکده علوم، دانشگاه فردوسی مشهد،مشهد،ایران.

4 استادیار گروه برق،دانشکده مهندسی، دانشگاه فردوسی مشهد،مشهد،ایران.

5 استادیار،گروه آمار،دانشکده علوم ریاضی،دانشگاه فردوسی مشهد،مشهد،ایران.


مقدمه: در این مقاله به کمک پتانسیل‌های وابسته به رویداد (ERPs)، به بررسی تفاوت‌های الکتروفیزیولوژی دو گروه از دانشجویان، هنگام حل مسائل انتقال بین بازنمایی نموداری و جبری تابع، پرداخته می‌شود. روش: این پژوهش از نوع کمی و به روش نیمه آزمایشی می‌باشد. جامعه آماری شامل 177 نفر از دانشجویان سال اول رشته‌های مهندسی دانشگاه فردوسی مشهد هستند که به کمک یک آزمون ریاضی محقق ساخته به دو گروه دانش مفهومی و رویه‌ای سطح بالا (دانش سطح بالا) و گروه دانش مفهومی و رویه‌ای سطح پایین (دانش سطح پایین) تقسیم بندی شدند. از هر گروه 14 نفر به طور تصادفی انتخاب شده و در آزمایش اصلی شرکت کردند. یافته‌ها: نتایج نشان داد که تعداد پاسخ‌های درست در گروه دانش سطح بالا بیشتر از گروه دانش سطح پایین است. تفاوت معناداری بین سرعت پاسخ دوگروه مشاهده نشد. از لحاظ الکتروفیزیولوژی دامنه مؤلفه P300 گروه دانش سطح پایین، بیشتر از گروه دانش سطح بالا در الکترودهای نواحی O2,O1,P4,PZ,P3,CP6,CP5 بود. نتیجه‌گیری: تفاوت دامنه مؤلفه P300 در گروه دانش سطح پایین و دانش سطح بالا موید این است که افراد دارای دانش سطح بالا نسبت به افراد دارای دانش سطح پایین، از کارکرد مغزی بهینه‌تری برخوردار بوده و از استراتژی متفاوتی برای پردازش اطلاعات در حل مسائل استفاده می‌کنند. نتیجه‌ای که شاید نتوان به راحتی از داده‌های سنتی قلم و کاغذی به آن دست یافت.


عنوان مقاله [English]

The comparison of P300 amplitude in students with high and low conceptual and procedural knowledge on graphical and algebraic representation of function

نویسندگان [English]

  • Najmeh farsad 1
  • Hassan Alamolhodaei 2
  • Ali Moghimi 3
  • Sahar Moghimi 4
  • Mehdi Jabbari Nooghabi 5
1 Ph.D. student of mathematical education, Ferdowsi University of Mashhad, Mashhad, Iran.
2 Professor of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
3 Professor of Biology, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran.
4 Assistant Professor of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
5 Assistant Professor, Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
چکیده [English]

Aim: The aim of this paper was to examine the electrophysiological differences between two groups of students during solving problems on translation between graphical and algebraic representations of functions. Methods: The research method of this paper was quantitative and quasi-experimental. We recruited 177 undergraduate male students studing engineering at Ferdowsi University of Mashhad. Using a a researcher-made mathematics exam they were divided into two groups; high conceptual and procedural knowledge group (HKG) and low conceptual and procedural knowledge group (LKG). Fourteen individuals were randomly selected from each group and participated in the ERPs experiment. Results: The number of true responses were higher for the HKG compared to the LKG. No significant differences were found between speed of response time of two groups. The ERP results showed that the P300 amplitude for the LKG was significantly higher than that of the HKG over CP5, CP6, P3, PZ, P4, O1 and O2 electrodes. Conclusion: It seems possible that the differences between P300 amplitude between LKG and HKG are probably due to different mental strategies adopted by the two aforementioned groups during problem solving.

کلیدواژه‌ها [English]

  • P300 amplitude
  • conceptual and procedural knowledge
  • graphical and algebraic representation
Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences113(18), 4909-4917.

Bajrič, J., Rösler, F., Heil, M., & Hennighausen, E. (1999). On separating processes of event categorization, task preparation, and mental rotation proper in a handedness recognition task. Psychophysiology36(3), 399-408.

Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for research in mathematics education, 115-131.

Booth, J. L., Koedinger, K. R., & Siegler, R. S. (2007, January). The effect of prior conceptual knowledge on procedural performance and learning in algebra. In Proceedings of the Cognitive Science Society (Vol. 29, No. 29).

Carlson, M. (1999). A Study Of Second Semester Calculus Students'  Function Conceptions. Published in Proceeding of PME 23.

Danker, J. F., & Anderson, J. R. (2007). The roles of prefrontal and posterior parietal cortex in algebra problem solving: A case of using cognitive modeling to inform neuroimaging data. Neuroimage35(3), 1365-1377.

De Jong, T., & Ferguson-Hessler, M. G. (1996). Types and qualities of knowledge. Educational psychologist31(2), 105-113.

Dodonova, Y. A., & Dodonov, Y. S. (2013). Faster on easy items, more accurate on difficult ones: Cognitive ability and performance on a task of varying difficulty. Intelligence41(1), 1-10.

Draheim, C., Hicks, K. L., & Engle, R. W. (2016). Combining reaction time and accuracy: The relationship between working memory capacity and task switching as a case example. Perspectives on Psychological Science11(1), 133-155.

Dubinsky, E., Wilson, R. T. (2013). High school students’ understanding of the function concept. Journal  of  Mathematical  Behavior  32. 83–   101

Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function transformations. Research in collegiate mathematics education1, 45-68.

Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17, 105–121.

Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational psychology24(5), 645-657.

Johnson, R. (1988). The amplitude of the P300 component of the event-related potential: Review and synthesis. Advances in psychophysiology3, 69-137.

Jost, K., Beinhoff, U., Hennighausen, E., & Rösler, F. (2004). Facts, rules, and strategies in single-digit multiplication: evidence from event-related brain potentials. Cognitive Brain Research20(2), 183-193.

Hibert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analyis. Conceptual and procedural knowledge; The case of mathematics, 1-23.

Kiefer, M., Marzinzik, F., Weisbrod, M., Scherg, M., & Spitzer, M. (1998). The time course of brain activations during response inhibition: evidence from event‐related potentials in a go/no go task. Neuroreport9(4), 765-770.

Kok, A. (1997). Event-related-potential (ERP) reflections of mental resources: a review and synthesis. Biological psychology45(1), 19-56.

Kok, A. (2001). On the utility of P3 amplitude as a measure of processing capacity. Psychophysiology38(3), 557-577.

Leikin, R., Leikin, M., & Waisman, I. (2017). What Is Special About the Brain Activity of Mathematically Gifted Adolescents?. In Creativity and Giftedness (pp. 165-181). Springer, Cham.

Leikin, M., Waisman, I., Shaul, S., & Leikin, R. (2014). Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry. Journal of integrative neuroscience13(01), 35-59.

Leinhardt, G., Zaslavsky, O., Kay Stein, M. (1990). Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Review of Educational Research, Vol. 60, No. 1, pp. 1-64

Markovits, Z., Eylon, B. S., & Bruckheimer, M. (1986). Functions today and yesterday. For the learning of mathematics6(2), 18-28.

NCTM, N. (2000). Principles and standards for school mathematics.

Núñez-Peña, M. I., Cortiñas, M., & Escera, C. (2006). Problem size effect and processing strategies in mental arithmetic. Neuroreport17(4), 357-360.

Núñez-Peña, M. I., Gracia-Bafalluy, M., & Tubau, E. (2011). Individual differences in arithmetic skill reflected in event-related brain potentials. International Journal of Psychophysiology80(2), 143-149.

Picton, T. W. (1992). The P300 wave of the human event-related potential. Journal of clinical neurophysiology9(4), 456-479.

Polich, J. (2007). Updating P300: an integrative theory of P3a and P3b. Clinical neurophysiology118(10), 2128-2148.

Rider, R. L. (2004). The Effects of Multi-Representational Methods on Students' Knowledge of Function Concepts in Developmental College Mathematics.

Rittle-Johnson, B., & Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. Oxford handbook of numerical cognition, 1102-1118.

Sohn, M. H., Goode, A., Koedinger, K. R., Stenger, V. A., Fissell, K., Carter, C. S., & Anderson, J. R. (2004). Behavioral equivalence, but not neural equivalence—neural evidence of alternative strategies in mathematical thinking. Nature neuroscience7(11), 1193-1194.

Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for research in mathematics education, 404-411.

Stern, E., & Schneider, M. (2010). A digital road map analogy of the relationship between neuroscience and educational research.

Thomas, M. O., Wilson, A. J., Corballis, M. C., Lim, V. K., & Yoon, C. (2010). Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function. ZDM42(6), 607-619.

Waisman, I., Leikin, M., Shaul, S., & Leikin, R. (2014). Brain Activity Associated with Translation between Graphical and Symbolic Representations of Functions in Generally Gifted and Excelling in Mathematics Adolescents. International Journal of Science & Mathematics Education12(3).

Wang, L., Xu, G., Yang, S., Song, Y., Wei, Y., & Yan, W. (2007). Research on Event Related Potential Elicited by Number Recognizing and Arithmetic Calculating. In Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging, 2007. NFSI-ICFBI 2007. Joint Meeting of the 6th International Symposium on (pp. 247-250). IEEE.

Waisman, I., Leikin, M., & Leikin, R. (2016). Brain activity associated with logical inferences in geometry: focusing on students with different levels of ability. ZDM48(3), 321-335.

Wilson, G. F., Swain, C. R., & Ullsperger, P. (1998). ERP components elicited in response to warning stimuli: The influence of task difficulty. Biological Psychology47(2), 137-158.