Psychological Development and Education ›› 2016, Vol. 32 ›› Issue (4): 463-470.doi: 10.16187/j.cnki.issn1001-4918.2016.04.10

Previous Articles     Next Articles

The Processing of Fractions Comparison Task in Elementary Students: Reaction Time and Trial-by-Trial Strategy Reports as Evidences

GAO Ting, LIU Rude, LIU Ying, ZHUANG Hongjuan   

  1. Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, Beijing 100875
  • Online:2016-07-15 Published:2016-07-15

PDF (PC)

Abstract: This study aimed at exploring the processing of fraction comparison tasks in fifty-three elementary school students through direct and indirect evidences. The students were asked to compare fraction magnitudes under different fraction comparison materials: fractions with common denominators/numerators, fractions without common components. The direct evidence was the processing strategies of making each comparison reported trial-by-trial by the students. The indirect evidence came from the regression analysis of the component distance and the real numerical value distance between the two fractions compared, and the size of the two fractions compared to the RT in each trial. The results showed that:(1) The three types of fraction comparisons were all processed in terms of the components in each fraction pair s instead of the real numerical value of the fractions compared, which indicates that most of the fraction comparisons were completed with componential processing instead of holistic processing;(2) The indirect evidences from the regression analysis of reaction time was not entirely consistent with the direct evidences from the trial-by-trial strategy reports, which proved the instability of the regression analysis methods broadly used in previous references.

Key words: fraction comparison, componential processing, holistic processing, trial by trial strategy reports, reaction time

CLC Number: 

  • G442

Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1), 75-106.

Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410-1419.

Clarke, D. M., & Roche, A. (2009). Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138.

Cohen Kadosh, R., & Walsh, V. (2009). Numerical representation in the parietal lobes: abstract or not abstract? Behavioral and Brain sciences, 32(3), 313-328.

Faulkenberry, T. J., & Pierce, B. H. (2011). Mental representations in fraction comparison: Holistic versus component-based strategies. Experimental psychology, 58(6), 480-489.

Huber, S., Moeller, K., & Nuerk, H. C. (2014). Adaptive processing of fractions — Evidence from eye-tracking. Acta Psychologica, 148(3), 37-48.

Liu, C., Xin, Z., Lin, C., & Thompson, C. A. (2013). Children's mental representation when comparing fractions with common numerators. Educational Psychology, 33(2), 175-191.

Meert, G., Grégoire, J., & Nol, M. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62(8), 1598-1616.

Meert, G., Grégoire, J., & Nol, M. (2010). Comparing the magnitude of two fractions with common components: Which representations are used by 10-and 12-year-olds? Journal of Experimental child psychology, 107(3), 244-259.

Moyer, R. S., & Landauer, T. K. (1967). Time required for Judgements of Numerical Inequality. Nature, 215(5109), 1519-1520.

Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28(4), 64-72.

Schleppenbach, M., Perry, M., Miller, K. F., Sims, L., & Fang, G. (2007). The answer is only the beginning: Extended discourse in Chinese and US mathematics classrooms. Journal of Educational Psychology, 99(2), 380-396.

Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227-1238.

Sprute, L., & Temple, E. (2011). Representations of fractions: Evidence for accessing the whole magnitude in adults. Mind, Brain, and Education, 5(1), 42-47.

Zhang, L., Fang, Q., Gabriel, F. C., & Szücs, D. (2014). The componential processing of fractions in adults and children: Effects of stimuli variability and contextual interference. Frontiers in Psychology, 5(3), 250-253.

Zhou, X., Chen, C., Chen, L., & Dong, Q. (2008). Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task.Cognition,106(3),1525-1536.

辛自强, 李丹. (2013). 小学生在非符号材料上的分数表征方式. 心理科学,36(2),364-371.
[1] LU Zhang-long, LV Yong, SHEN De-li. Attentional load has no Effect on Implicit Sequence Learning: Evidence from Event-Related Potential Studies [J]. Psychological Development and Education, 2011, 27(6): 561-568.
[2] LI Hong, SHU Hua, XUE Jing, YANG Jian-feng. Evidence for Skill-Automatization in Dyslexia [J]. Psychological Development and Education, 2008, 24(1): 101-105.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of Psychological Development and Education
Supported by Beijing Magtech Co.Ltd