Neuropsychology

In collaboration with Payame Noor University and Iran Neuropsychology Association

Current Issue

By Issue

By Author

By Subject

Author Index

Keyword Index

About Journal

Aims and Scope

Editorial Board

Publication Ethics

Indexing and Abstracting

FAQ

Peer Review Process

Journal Metrics

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

Document Type : Original article

Authors

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.

Abstract

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.

Keywords

References
Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113(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. Psychophysiology, 36(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. Neuroimage, 35(3), 1365-1377.
De Jong, T., & Ferguson-Hessler, M. G. (1996). Types and qualities of knowledge. Educational psychologist, 31(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. Intelligence, 41(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 Science, 11(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 education, 1, 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 psychology, 24(5), 645-657.
Johnson, R. (1988). The amplitude of the P300 component of the event-related potential: Review and synthesis. Advances in psychophysiology, 3, 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 Research, 20(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. Neuroreport, 9(4), 765-770.
Kok, A. (1997). Event-related-potential (ERP) reflections of mental resources: a review and synthesis. Biological psychology, 45(1), 19-56.
Kok, A. (2001). On the utility of P3 amplitude as a measure of processing capacity. Psychophysiology, 38(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 neuroscience, 13(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 mathematics, 6(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. Neuroreport, 17(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 Psychophysiology, 80(2), 143-149.
Picton, T. W. (1992). The P300 wave of the human event-related potential. Journal of clinical neurophysiology, 9(4), 456-479.
Polich, J. (2007). Updating P300: an integrative theory of P3a and P3b. Clinical neurophysiology, 118(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 neuroscience, 7(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. ZDM, 42(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 Education, 12(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. ZDM, 48(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 Psychology, 47(2), 137-158.
Neuropsychology
Volume 3, Issue 11 - Serial Number 11
March 2018
Pages 55-70
Files
Share
How to cite
Statistics