Teachers’ Perceived Impacts of Finger-Counting Manipulative as Basis for a Solid Foundation in Mathematics in Nigeria
Abstract
This paper was designed to determine preschool, primary school teachers, and secondary school Mathematics teachers’ and special educators’ views of finger-counting as the basis for a solid foundation in learning Mathematics. One hundred Participants were selected using purposive sampling. One research question and three hypotheses were raised to guide the study. The adapted instrument from Mutlu et al. (2020) titled the finger-counting questionnaire with a reliability index of 0.78 was used to gather data for the study. Data collected were analyzed using percentage, mean, t-test, and ANOVA statistics. The results showed that teachers perceived impacts of finger-counting that; it facilitates learning by touching, turns abstract into concrete resulting in meaningful learning, makes counting practical and accessible, facilitates retention and internalization, increases numerical, arithmetic, and problem-solving skills, and also improves attitudes towards mathematics. Findings also revealed no differences exist among teachers on the perceived impact of finger-counting as the basis for a solid foundation in learning Mathematics based on their gender and teachers’ category but significant differences exist in their years of teaching experience. In conclusion, finger counting should not be seen as an alternative or optional but as an indispensable tool in teaching and learning Mathematics. The researchers recommended that because people abandon finger-counting strategies once they develop cognitive and affective skills, finger-counting should be seen as a transition process rather than an obstacle to the development of mental arithmetic skills.
References
[2] Albayrak, M. 2010. An experimental study on preventing first graders from finger counting in basic calculations. In Electronic Journal of Research in Educational Psychology, 8 (3): 1131– 1150.
[3] Alibali, M. W., and DiRusso, A. 1999. The function of gesture in learning to count: more than keeping track. Cogn. Dev. 14: 37–56. DOI: 10.1016/S0885-2014(99)80017-3
[4] Andres, M., Ostry, D. J., Nicol, F., and Paus, T. 2008. Time course of number magnitude interference during grasping. Cortex, 44(4): 414–419.
[5] Badets, A., and Pesenti, M. 2010. Creating number semantics through finger movement perception. Cognition, 115(1): 46–53.
[6] Badets, A., Pesenti, M., and Olivier, E. 2010. Response-effect compatibility of a finger-numeral configurations in an arithmetical context. Quarterly Journal of Experimental Psychology (2006), 63(1): 16–22.
[7] Barrouillet, P., and Lépine, R. 2005. Working memory and children’s use of retrieval to solve addition problems. J. Exp. Child Psychol. 91: 183–204. DOI: 10.1016/j.jecp.2005.03.002
[8] Bender, A. and Beller, S. 2012. Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool. Cognition, 124 (2): 156-182. DOI: https://doi.org/10.1016/j.cognition.2012.05.005
[9] Bender, A., and Beller, S. 2011. Fingers as a tool for counting—Naturally fixed or culturally flexible? Frontiers in Psychology, 2, 256.
[10] Berteletti, I., and Booth, J. R. 2015. Perceiving fingers in single-digit arithmetic problems. Frontiers in Psychology, 6, 226. DOI: http://dx.doi.org/10.3389/fpsyg.2015.00226
[11] Boaler, J., Chen, L., Williams, C., and Cordero, M. 2016. Seeing as understanding: The importance of visual mathematics for our brain and learning. Journal of Applied and Computational Mathematics, 1-17. DOI: https://doi.org/10.4172/2168-9679.1000325
[12] Butterworth, B. 1999. What Counts: How the Brain is Hardwired for Math. New York: The Free Press.
[13] Chinello, A., Cattani, V., Bonfiglioli, C., Dehaene, S., and Piazza, M. 2013. Objects, numbers, fingers, space: Clustering of ventral and dorsal functions in young children and adults. Developmental Science, 16(3): 377–393.
[14] Di Luca, S., and Pesenti, M. 2008. Masked priming effect with canonical finger numeral configurations. Experimental Brain Research, 185(1): 27–39.
[15] Di Luca, S., and Pesenti, M. 2011. Finger numeral representations: More than just another symbolic code. Frontiers in Psychology, 2, 272.
[16] Di Luca, S., Granà, A., Semenza, C., Seron, X., and Pesenti, M. 2006. Finger-digit compatibility in Arabic numeral processing. Quarterly Journal of Experimental Psychology, 59(9): 1648–1663.
[17] Duncan, G. J., et al. 2007. School readiness and later achievement. Developmental Psychology, 43(6): 1428-1446.
[18] Geary, D. C. 2005. The origin of mind: Evolution of brain, cognition, and general intelligence. Washington, DC: American Psychological Association.
[19] Geary, D. C., and Burlingham-Dubree, M. 1989. External validation of the strategic choice model for addition. Journal of Experimental Child Psychology, 47(2): 175–192.
[20] Gracia-Bafalluy, M., and Noël, M. P. 2008. Does finger training increase young children’s numerical performance? Cortex, 44(4): 368-375. DOI: 10.1016/j.cortex.2007.08.020
[21] Ifrah, G. 1985. From one to zero: A universal history of numbers. New York: Viking Penguin.
[22] Ifrah, G. 2000. The universal history of numbers: From prehistory to the invention of the computer (D. Vellos, E. F. Harding, S. Wood, and I. Monk, Trans.). New York, NY: John Wiley and Sons.
[23] Kaufmann, L., Vogel, S., Wood, G., Kremser, C., Schocke, M., Zimmerhackl, L.B., and Koten, J. W. 2008. A developmental fMRI study of non-symbolic numerical and spatial processing. Cortex, 44: 376–85.
[24] Klein, E., Moeller, K., Willmes, K., Nuerk, H.-C., and Domahs, F. 2011. The influence of implicit hand-based representations on mental arithmetic. Front. Psychol. 2, 197. DOI: 10.3389/fpsyg.2011.00197
[25] Lee, J., Kotsopoulos, D., Tumber, A., and Makosz, S. 2014. Gesturing about number sense. Journal of Early Childhood Research, 1–17. DOI: http://dx.doi.org/10.1177/1476718X13510914
[26] Mignon, M., and Thevenot, C. 2008. Strategies in subtraction problem-solving in children. J. Exp. Child Psychol. 99: 233–251. DOI: 10.1016/j.jecp.2007.12.001
[27] Mink, D. V. 2010. Strategies for teaching mathematics. Shell Education: Huntington Beach.
[28] Mutlu, Y., Akgün, L. and Akkuşci, Y. E. 2020. What do teachers think about Finger- Counting? International Journal of Curriculum and Instruction, 12(1): 268-288.
[29] Newman, S. D. 2016. Does finger sense predict addition performance? Cognitive Processing, 17(2): 139-146. DOI: 10.1007/s10339-016-0756-7
[30] Newman, S. D., and Soylu, F. 2013. The impact of finger counting habits on arithmetic in adults and children. Psychol. Res. 78: 549–556. DOI: 10.1007/s00426-013-0505-9
[31] Noël, M. P. 2005. Finger agnosia: a predictor of numerical abilities in children? Child Neuropsychology, 11(5): 413-430. DOI: 10.1080/09297040590951550
[32] Nyagah, G. and Gathumbi, A. 2017. Influence of teacher characteristics on the implementation of the non-formal basic education curriculum at the non-formal education centers in Nairobi, Mombassa, and Ikisumu Cities Kenya, International Journal of Education and Research. 9(28). ISSN: 1857-7881 e-ISSN1857- 7431.
[33] Penner-Wilger, M., Fast, L., LaFevre, J.-A., Smith-Chant, B. L., Skwarchuck, S.-L., Kamawar, D., and Bisanz, J. 2007. The foundations of numeracy: Subitizing, finger agnosia, and fine motor ability. In Proceedings of the Cognitive Science Society, 29: 1385-1390.
[34] Piazza, C.C., Patel, M.R., Santana, C.M., Goh, H, Delia M and Lancaster, B.M. 2002. An evaluation of simultaneous sequential presentation of preferred and non-preferred food to treat food selectivity. Journal of Applied Behavior Analysis, 35: 259–270.
[35] Pika, S., Nicoladis, E., and Marentette, P. 2009. How to order a beer: Cultural differences in the use of conventional gestures for numbers. Journal of Cross-Cultural Psychology, 40(1): 70–80.
[36] Sinclair, N., and Pimm, D. 2015. Mathematics using multiple senses: Developing finger gnosis with three- and four-year-olds in an era of multi-touch technologies. Asia-Pacific Journal of Research in Early Childhood Education, 9(3): 99–110.
[37] Sternberg, R. J., and Grigorenko, E. L. 2004. Successful intelligence in the classroom. Theory into Practice, 43: 274-280. DOI:10.1207/s15430421tip43045
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