نوع مقاله : پژوهشی

نویسندگان

1 دانشجو دکتری فلسفه تعلیم و تربیت، دانشگاه خوارزمی

2 دانشیار/دانشگاه خوارزمی

3 استاد دانشکده توان‌بخشی، دانشگاه علوم پزشکی ایران

4 دانشیار فلسفه تعلیم و تربیت، دانشگاه خوارزمی

چکیده

هدف اصلی این پژوهش تبیین یادگیری تحلیل ریاضیاتی مبتنی بر تلفیق تحلیل فلسفی و یافته­های علوم اعصاب شناختی است. بدین منظور یادگیری تحلیل ریاضیاتی، به عنوان یکی از جنبه­های تفکر ریاضیاتی، مبتنی بر یادگیری نمادهای عددی در کودکان با بهره­گیری از روش عصب-فلسفی بررسی شده است. بر این اساس سه گزاره مشاهده­ای که نتایج پژوهش­های علوم اعصاب شناختی پیرامون ریاضیات نمادین است اخذ شده است. این گزاره­ها عبارت‌اند از: یادگیری نمادین اعداد در کودکان، مغز را تغییر می­دهد؛ پردازش اعداد نمادین و اعداد غیرنمادین به صورتی ناهمسان است و ارتباطی مبهم و دوسویه بین آن‌ها وجود دارد؛ دانش نمادین عدد، نقش مهمی در پیشرفت­های آینده کودکان در ریاضیات سطح بالاتر دارد. بر مبنای این سه گزاره تلاش شده است تا پرسش­های فلسفی پژوهش و چالش­های مرتبط با آن‌ها بررسی شود. نتایج این پژوهش حاکی از آن است که همراه شدن یادگیری اعداد نمادین با چگونگی به وجود آمدن نمادهای عددی و تشویق کودکان به ایجاد ارتباط پیاپی بین نمادهای عددی و معنای ذهنی و بیان کلامی آن‌ها می­تواند اسباب لازم برای غنای توانایی­های فراشناختی مانند تشخیص خطاها را فراهم کند. اما لازم است چالش­هایی مانند چگونگی آشنایی کودکان با نظریه تکامل با توجه به مسائل فرهنگی، نوع راهبردهای لازم برای بهبود ارتباط درک معنایی و نمادین اعداد در کودکان و سطح تأکید بر فرآیندهای حل مسئله­ (که نیازمند تحلیل مبتنی بر نمادها هستند) در برنامه‌های آموزش ریاضی به منظور بهبود توانایی­های تفکر کودکان بررسی شود.

کلیدواژه‌ها

Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Inglis, M. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2(1), 20.
Amiel, J. J., & Tan, Y. S. M. (2019). Using collaborative action research to resolve practical and philosophical challenges in educational neuroscience. Trends in neuroscience and education, 16, 100116.
Ansari, D. (2005). Paving the way towards meaningful interactions between neuroscience and education. Developmental science, 8(6), 466.
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278-291.
Ansari, D. (2012). Culture and education: new frontiers in brain plasticity. Trends in Cognitive Sciences, 16(2), 93-95.
Ansari, D. (2016). Number symbols in the brain. In Development of Mathematical Cognition (pp. 27-50): Elsevier.
Ansari, D., & Coch, D. (2006). Bridges over troubled waters: Education and cognitive neuroscience. Trends in Cognitive Sciences, 10(4), 146-151.
Ansari, D., Coch, D., & De Smedt, B. (2011). Connecting Education and Cognitive Neuroscience: Where will the journey take us? Educational philosophy and theory, 43(1), 37-42.
Ansari, D., De Smedt, B., & Grabner, R. H. (2012a). Introduction to the special section on. Mind Brain and Education, 6(3), 117-118.
Ansari, D., De Smedt, B., & Grabner, R. H. (2012b). Neuroeducation–a critical overview of an emerging field. Neuroethics, 5(2), 105-117.
Ansari, D., Grabner, R. H., Koschutnig, K., Reishofer, G., & Ebner, F. (2011). Individual differences in mathematical competence modulate brain responses to arithmetic errors: An fMRI study. Learning and Individual Differences, 21(6), 636-643.
Bartelet, D., Ansari, D., Vaessen, A., & Blomert, L. (2014). Cognitive subtypes of mathematics learning difficulties in primary education. Research in developmental disabilities, 35(3), 657-670.
Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency? Journal of experimental child psychology, 117, 12-28.
Beaney, M. (2013). The Oxford handbook of the history of analytic philosophy: Oxford University Press.
Beaney, M. (2020). Two dogmas of analytic historiography. British journal for the history of philosophy, 28(3), 594-614.
Bellon, E., Fias, W., Ansari, D., & De Smedt, B. (2020). The neural basis of metacognitive monitoring during arithmetic in the developing brain. Human brain mapping, 41(16), 4562-4573.
Bickle, J. (2019). Lessons for experimental philosophy from the rise and “fall” of neurophilosophy. Philosophical Psychology, 32(1), 1-22.
Blakemore, S.-J., & Frith, U. (2005). The learning brain: Lessons for education: Blackwell publishing.
Brault Foisy, L. M., Matejko, A. A., Ansari, D., & Masson, S. (2020). Teachers as orchestrators of neuronal plasticity: effects of teaching practices on the brain. Mind, Brain, and Education, 14(4), 415-428.
Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118(1), 32-44.
Bugden, S., Price, G. R., McLean, D. A., & Ansari, D. (2012). The role of the left intraparietal sulcus in the relationship between symbolic number processing and children's arithmetic competence. Developmental Cognitive Neuroscience, 2(4), 448-457.
Churchland, P. S. (1989). Neurophilosophy: Toward a unified science of the mind-brain: MIT press.
Churchland, P. S. (2017). Neurophilosophy. In D. L. Smith (Ed.), How Biology Shapes Philosophy: New Foundations for Naturalism (pp. 72-94): Cambridge University Press.
Clark, J. (2009). NEUROPHILOSOPHY, EDUCATION AND LEARNING. The Philosophy of Education Society of Australasia.
Clark, J. (2015). Philosophy, neuroscience and education. Educational philosophy and theory, 47(1), 36-46.
Daly, C. (2010). An introduction to philosophical methods: Broadview Press.
Damasio, A. R. (2006). Descartes' error: Random House.
De Smedt, B., Ansari, D., Grabner, R. H., Hannula-Sormunen, M., Schneider, M., & Verschaffel, L. (2011). Cognitive neuroscience meets mathematics education: It takes two to tango. Educational Research Review, 6(3), 232-237.
De Smedt, B., Ansari, D., Grabner, R. H., Hannula, M. M., Schneider, M., & Verschaffel, L. (2010). Cognitive neuroscience meets mathematics education. Educational Research Review, 5(1), 97-105.
De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48-55.
Dehaene, S. (2011). The number sense: How the mind creates mathematics: OUP USA.
Dehaene, S. (2014). Consciousness and the brain: Deciphering how the brain codes our thoughts: Penguin.
Dick, F., Lloyd-Fox, S., Blasi, A., Elwell, C., Mills, D., & Elwell, C. (2014). Neuroimaging methods. In D. Mareschal, B. Butterworth, & A. Tolmie (Eds.), Educational neuroscience (pp. 13-45).
Ernest, P. (2018). The ethics of mathematics: is mathematics harmful? In The philosophy of mathematics education today (pp. 187-216): Springer.
Gazzaniga, M. S. (2009). The cognitive neurosciences: MIT press.
Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68-76.
Goffin, C., Vogel, S. E., Slipenkyj, M., & Ansari, D. (2020). A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study. Human brain mapping, 41(6), 1591-1610.
Grabner, R. H., & Ansari, D. (2010). Promises and potential pitfalls of a ‘cognitive neuroscience of mathematics learning’. ZDM, 42(6), 655-660.
Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47(2), 604-608.
Gutstein, E. R. (2018). The struggle is pedagogical: Learning to teach critical mathematics. The philosophy of mathematics education today, 131-143.
Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin & Review, 1-18.
Heis, J. (2017). Russell’s Road to Logicism. In Innovations in the History of Analytical Philosophy (pp. 301-332): Springer.
Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 45(1), 62-101.
Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of experimental child psychology, 103(1), 17-29.
Holloway, I. D., Battista, C., Vogel, S. E., & Ansari, D. (2013). Semantic and perceptual processing of number symbols: evidence from a cross-linguistic fMRI adaptation study. Journal of Cognitive Neuroscience, 25(3), 388-400.
Holloway, I. D., Price, G. R., & Ansari, D. (2010). Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: An fMRI study. Neuroimage, 49(1), 1006-1017.
Hutchison, J. E., Ansari, D., Zheng, S., De Jesus, S., & Lyons, I. M. (2020). The relation between subitizable symbolic and non‐symbolic number processing over the kindergarten school year. Developmental science, 23(2), e12884.
Kim, M., & Sankey, D. (2018). Philosophy, neuroscience and pre-service teachers’ beliefs in neuromyths: a call for remedial action. Educational philosophy and theory, 50(13), 1214-1227.
Lagemann, E. C. (2002). An elusive science: The troubling history of education research: University of Chicago Press.
Leibovich, T., & Ansari, D. (2016). The symbol-grounding problem in numerical cognition: a review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale, 70(1), 12.
Leibovich, T., & Ansari, D. (2017). Accumulation of non‐numerical evidence during nonsymbolic number processing in the brain: An fMRI study. Human brain mapping, 38(10), 4908-4921.
Lyons, I. M., & Ansari, D. (2015). Numerical Order Processing in Children: From Reversing the Distance-Effect to Predicting Arithmetic. Mind, Brain, and Education, 9 (4), 207–221. In.
Lyons, I. M., Ansari, D., & Beilock, S. L. (2015). Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain. Human brain mapping, 36(2), 475-488.
Lyons, I. M., Nuerk, H.-C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144(5), 1021.
Martens, E. (2003). Methodik des Ethik-und Philosophieunterrichts: Philosophieren als elementare Kulturtechnik: Siebert.
Matejko, A. A., & Ansari, D. (2016). Trajectories of symbolic and nonsymbolic magnitude processing in the first year of formal schooling. PloS one, 11(3), e0149863.
Matejko, A. A., & Ansari, D. (2017). How do individual differences in children's domain specific and domain general abilities relate to brain activity within the intraparietal sulcus during arithmetic? An fMRI study. Human brain mapping, 38(8), 3941-3956.
Matejko, A. A., Price, G. R., Mazzocco, M. M., & Ansari, D. (2013). Individual differences in left parietal white matter predict math scores on the Preliminary Scholastic Aptitude Test. Neuroimage, 66, 604-610.
Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14-20.
Morton, J. B., Bosma, R., & Ansari, D. (2009). Age-related changes in brain activation associated with dimensional shifts of attention: an fMRI study. Neuroimage, 46(1), 249-256.
Northoff, G. (2004). What is neurophilosophy? A methodological account. Journal for general philosophy of science, 35(1), 91-127.
Northoff, G. (2018). The Spontaneous Brain: From the Mind–Body to the World–Brain Problem: MIT Press.
Novaes, C. D., & Geerdink, L. (2017). The dissonant origins of analytic philosophy: Common sense in philosophical methodology. In Innovations in the history of analytical philosophy (pp. 69-102): Springer.
Paravicini, W., Schnieder, J., & Scharlau, I. (2018). Hades—The Invisible Side of Mathematical Thinking. In The philosophy of mathematics education today (pp. 353-364): Springer.
Price, G. R., & Ansari, D. (2011). Symbol processing in the left angular gyrus: evidence from passive perception of digits. Neuroimage, 57(3), 1205-1211.
Raizada, R. D., Tsao, F.-M., Liu, H.-M., Holloway, I. D., Ansari, D., & Kuhl, P. K. (2010). Linking brain-wide multivoxel activation patterns to behaviour: Examples from language and math. Neuroimage, 51(1), 462-471.
Richardson, M., Isaacs, T., Barnes, I., Swensson, C., Wilkinson, D., & Golding, J. (2020). Trends in International Mathematics and Science Study (TIMSS) 2019: National report for England: Research report: December 2020.
Sokolowski, H. M. (2019). How Do Humans Process Magnitudes? An Examination of the Neural and Cognitive Underpinnings of Symbols, Quantities, and Size in Adults and Children.
Sokolowski, H. M., Fias, W., Mousa, A., & Ansari, D. (2017). Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging meta-analysis. Neuroimage, 146, 376-394.
Thomas, M. S., Ansari, D., & Knowland, V. C. (2019). Annual research review: Educational neuroscience: Progress and prospects. Journal of Child Psychology and Psychiatry, 60(4), 477-492.
van Atteveldt, N., & Ansari, D. (2014). How symbols transform brain function: A review in memory of Leo Blomert. Trends in Neuroscience and Education, 3(2), 44-49.
van der Meulen, A., Krabbendam, L., & de Ruyter, D. (2015). Educational neuroscience: Its position, aims and expectations. British Journal of Educational Studies, 63(2), 229-243.
Vanbinst, K., Ansari, D., Ghesquière, P., & De Smedt, B. (2016). Symbolic numerical magnitude processing is as important to arithmetic as phonological awareness is to reading. PloS one, 11(3), e0151045.
Xenidou-Dervou, I., Molenaar, D., Ansari, D., van der Schoot, M., & van Lieshout, E. C. (2017). Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement. Learning and Instruction, 50, 1-13.
Yeo, D. J., Pollack, C., Merkley, R., Ansari, D., & Price, G. R. (2020). The “Inferior Temporal Numeral Area” distinguishes numerals from other character categories during passive viewing: A representational similarity analysis. Neuroimage, 116716.
Zebian, S., & Ansari, D. (2012). Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing. Psychonomic Bulletin & Review, 19(1), 93-100.