Sentido numérico y perseverancia académica entre estudiantes de secundaria: un modelo de mediación en serie de conciencia metacognitiva matemática y ansiedad matemática
Resumen
El presente estudio examinó si el sentido numérico estaba relacionado con la perseverancia académica y si esta relación estaba mediada por la conciencia metacognitiva matemática y la ansiedad matemática. Se recopilaron datos de 231 estudiantes de séptimo y octavo grado de escuelas intermedias mediante medidas de autoinforme de sentido numérico, perseverancia académica, conciencia metacognitiva y ansiedad matemática. Los resultados revelaron una asociación positiva significativa entre el sentido numérico y la conciencia de metacognición matemática, así como una asociación negativa significativa entre el sentido numérico y la ansiedad matemática. Además, los resultados indicaron que el sentido numérico facilitó la perseverancia académica a través de la conciencia de la metacognición matemática y luego de la ansiedad matemática. Estos hallazgos contribuyen a la comprensión de cómo estos factores pueden afectar la perseverancia académica en los estudiantes de secundaria.
Descargas
Citas
Ak, Y., & Ertekin, E. (2020). A study on the relationship between number sense and math anxiety of 7th and 8th grade students. International Journal of Society Researches 16(31), 4047-4076. https://doi.org/10.26466/opus.725845
Alkaş-Ulusoy, C., (2020). Effects of number sense-based instruction on sixth-grade students’ self-efficacy and performance. Education and Science, 45(202), 417-439. http://dx.doi.org/10.15390/EB.2020.8381
Anobile, G.; Arrighi, R.; Castaldi, E.; Grassi, E.; Pedonese, L.; Moscoso, P.A.M.; Burr, D.C. (2018). Spatial but not temporal numerosity thresholds correlate with formal math skills in children. Dev. Psychol., 54, 458.
Artz, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137-175. https://doi.org/10.1207/s1532690xci0902_3
Ashcraft, M. H., Krause, J. A., & Hopko, D. R. (2007). Is math anxiety a mathematical learning disability? In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 329–348). Paul H. Brookes Publishing Co.
Asık, G. (2009). A model study to examine the relationship between metacognitive and motivational regulation and metacognitive experiences during problem solving in mathematics [Unpublished master's thesis]. Boğaziçi University.
Asık, G., & Erktin, E. (2019). Metacognitive experiences: Mediating the relationship between metacognitive knowledge and problem solving. Education and Science, 44(197), 85-103. http://dx.doi.org/10.15390/EB.2019.7199
Aşık, G., & Sevimli, E. (2015). Investigation of students’ metacognitive calibration within the context of math achievement: Case of engineering students. Bogazici University Journal of Education, 32(2), 19-36. https://dergipark.org.tr/en/pub/buje/issue/29712/319692
Baker, M. J. (2019). Number sense and the effects on students’ mathematical success. (Master’s Dissertation). Retrieved from https://nwcommons.nwciowa.edu/cgi/viewcontent.cgi?article=1160&context=education_masters
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.
Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
Calvert, L. M. G. (1999). A dependence on technology and algorithms or a lack of number sense. Teaching Children Mathematics, 1(1), 6-7.
Carey, E., Hill, F., Devine, A., & Szűcs, D. (2017). The modified abbreviated math anxiety scale: A valid and reliable instrument for use with children. Frontiers in psychology, 8, 11. https://doi.org/10.3389/fpsyg.2017.00011
Carpenter, T. (1989). Number sense and other nonsense. In J. Sowder & B. Schappelle (Eds.), Establishing foundations for research on number sense and related topics: Report of a Conference (pp. 89–91). San Diego, CA: San Diego State University.
Chen, P. C., Li, M. N., & Yang, D. C. (2013). An effective remedial instruction in number sense for third graders in Taiwan. New Waves, 16(1), 3.
Çekirdekci, S., Şengül, S., & Doğan, M. C. (2016). Examining the relationshıp between number sense and mathematıcs achıevement of the 4th grade students. Qualitative Studies (NWSAQS), 11 (4), 48-66. http://dx.doi.org/10.12739/NWSA.2016.11.4.E0028
Çekirdekci, S., Şengül, S., & Doğan, M. C. (2018). The relationship between number sense and metacognition. International Journal of Eurasia Social Sciences, 9(34), 2465-2481.
Celik, H. C., & Arslan, İ. (2022). Prediction of mathematics achievement: the role of mathematical metacognition and problem posing self-efficacy. Uludağ University Journal of Education Faculty, 35(2), 385-406.
Cheung, K. L., & Yang, D. C. (2018). Examining the differences of Hong Kong and Taiwan students’ performance on the number sense three-tier test. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), 3329–3345. https://doi.org/10.29333/ejmste/91682
Collie, R. J., Martin, A. J., Malmberg, L. E., Hall, J., & Ginns, P. (2015). Academic buoyancy, student achievement, and the linking role of control: A crosslagged analysis of high school students. British Journal of Psychology, 85, 113-130. http://dx.doi.org/10.1111/bjep.12066
Collie, R. J., Ginns, P., Martin, A. J., & Papworth, B. (2017). Academic buoyancy mediates academic anxiety’s effects on learning strategies: an investigation of English- and Chinese-speaking Australian students. Educational Psychology, 37, 947–964.
Colmar, S., Liem, G. A. D., Connor, J., & Martin, A. J. (2019). Exploring the relationships between academic buoyancy, academic self-concept, and academic performance: a study of mathematics and reading among primary school students. Educational Psychology, 39(8), 1068-1089. https://doi.org/10.1080/01443410.2019.1617409
Datu, J. A. D., & Yang, W. (2016). Psychometric validity and gender invariance of the academic buoyancy scale in the Philippines: A construct validation approach. Journal of Psychoeducational Assessment, 36(3), 278–283.
Datu, J. A. D., & Yuen, M. (2018). Predictors and consequences of academic buoyancy: A review of literature with implications for educational psychological research and practice. Contemporary School Psychology, 22(3), 207–212.
Desoete, A., & Veenman, M. (2006). Metacognition in mathematics: Critical issues on nature, theory, assessment and treatment. In A. Desoete & M. Veenman (Eds.), Metacognition in mathematics education (pp. 1-10). New York: Nova Science Publishers, Inc.
Djudin, T. (2017). Using metacognitive strategies to improve reading comprehension and solve a word problem. Journal of Education, Teaching and Learning 2(1), 124-129.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55.
El Walida, S., & Sa'dijah, C. (2022). A Portrait of Controversial Mathematics Problems and Students' Metacognitive Awareness: A Case of Indonesia. Journal of Higher Education Theory and Practice, 22(12), 51-62.
Eme, E. & Rouet, J. (2001). Metacognitive knowledge in reading comprehension: Some issues in development and individual differences, Enfance, 53, 309- 328.
Faulkner, V. N., & Cain, C. (2009). The Components of Number Sense: An Instructional Model for Teachers. Teaching Exceptional Children, 41(5), 24-30.
Flavell, J. H., 1976, “Metacognitive Aspects of Problem Solving”, in L. B. Resnick (ed.), The Nature of Intelligence, pp. 231- 235, Hillsdale N. J.: Erlbaum.
Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
Ilko, T. (2021). Metacognition's role in improving the number sense development in students. Unpublished dissertation. University of Lethbridge.
Jordan, N. C., Glutting, J., & Ramineni, C. (2009). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88. https://doi.org/10.1016/j.lindif.2009.07.004
Jöreskog, K. G., & Sörbom, D. (1986). LISREL VI: Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares methods. Mooresville, IN: Scientific Software.
Kankaraš, M., Montt, G., Paccagnella, M., Quintini, G., & Thorn, W. (2016). Skills matter: Further results from the survey of adult skills. OECD Skills Studies, OECD Publishing, Paris.
Kaplan, A., & Duran, M. (2016). Mathematical metacognition awareness inventory towards middle school students: validity and reliability study. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 32, 1-17. https://dergipark.org.tr/tr/download/article-file/264531
Kayhan-Altay, M., & Umay, A. (2013). The Development of Number Sense Scale towards Middle Grade Students. Education and Science, 38(167), 241-255.
Kena, G., Hussar, W., McFarland, J., de Brey, C., Musu-Gillette, L., Wang, X., ... Dunlap Velez, E. ( 2016 ). The condition of education 2016 (NCES 2016–144). Washington, DC: National Center for Education Statistics.
Kitsansas, A. (2002). Test preparation and performance: A Self-Regulatory Analysis”, The Journal of Experimental Education, 70 (2), 101- 113.
Kline, R. B. (2023). Principles and practice of structural equation modeling. New York, NY: Guilford publications.
Kul, U., Aksu, Z., & Satıcı, S.A. (2024). Adaptation of the modified abbreviated math anxiety scale: its relationship with mathematics self-efficacy and academic buoyancy. Current Psychology. https://doi.org/10.1007/s12144-024-05908-7
Legg, A. M., and Locker, L. (2009). Math performance and its relationship to math anxiety and metacognition. N. Am. J. Psychol. 11, 471–486.
Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5), 451-459. https://doi.org/10.1177/0022219408321126
Louange, J., & Bana, J. (2010). The relationship between the number sense and problem solving abilities of year 7 students. Paper presented at the 33rd Annual Conference of the Mathematics Education Research Group of Australasia, Fremantle, Australia.
Maghfirah, M., and Mahmudi, A. (2018). Number sense: The result of mathematical experience. Journal of Physics: Conference Series, 1097(1), 012141.
Maldonado Moscoso, P. A., Anobile, G., Primi, C., & Arrighi, R. (2020). Math anxiety mediates the link between number sense and math achievements in high math anxiety young adults. Frontiers in psychology, 11, 1095. https://doi.org/10.3389/fpsyg.2020.01095
Maloney, E. A. (2016). Math anxiety: Causes, consequences, and remediation. In K. R. Wentzel & D. B. Miele (Eds.), Handbook of motivation at school (pp. 408-423). New York, NY: Taylor and Francis
Maloney, E.A.; Ansari, D.; Fugelsang, J.A. (2011). The effect of mathematics anxiety on the processing of numerical magnitude. Q. J. Exp. Psychol.,64, 10–16.
Markovits, Z. & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4-29
Marsh, H.W., & Yeung, A.S.(1997). Causal effects of academic self-concept on academic achievement: Structural equation models of longitudinal data. Journal of Educational Psychology,89, 41–54.
Martin, A. J. (2013). Academic buoyancy and academic resilience: exploring ‘everyday’ and ‘classic’ resilience in the face of academic adversity. School Psychology International, 34, 488–500.
Martin, A. J., & Marsh, H. W. (2008). Academic buoyancy: Towards an understanding of students' everyday academic resilience. Journal of School Psychology, 46(1), 53-83. https://doi.org/10.1016/j.jsp.2007.01.002
Martin A. J., Marsh H. W. (2009). Academic resilience and academic buoyancy: Multidimensional and hierarchical conceptual framing of causes, correlates, and cognate constructs. Oxford Review of Education, 35, 353–370. https://doi.org/10.1080/03054980902934639
Martin, A. J., Colmar, S. H., Davey, L. A., & Marsh, H. W. (2010). Longitudinal modelling of academic buoyancy and motivation: Do the 5Cs hold up over time?. British Journal of Educational Psychology, 80(3), 473-496. https://doi.org/10.1348/000709910X486376
Martin, A. J., Yu, K., Ginns, P., & Papworth, B. (2017). Young people’s academic buoyancy and adaptability: A cross-cultural comparison of China with North America and the United Kingdom. Educational Psychology, 37, 930–946. http://dx.doi.org/10.1080/01443410.2016.1202904
Martin, A.J., & Marsh, H.W. (2006). Academic buoyancy and its psychological and educational correlates: A construct validity approach. Psychology in the Schools, 43(3), 267-282. https://doi.org/10.1002/pits.20149
Mazzocco, M.M.M.; Feigenson, L.; Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Dev., 82, 1224–1237.
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2-8.
Mihalca, L., Mengelkamp, C., & Schnotz, W. (2017). Accuracy of metacognitive judgments as a moderator of learner control effectiveness in problem-solving tasks. Metacognition and Learning, 12(3), 357-379. https://doi.org/10.1007/s11409-017-9173-2
Miller, S., Connolly, P., & Maguire, L. K. (2013). Wellbeing, academic buoyancy and educational achievement in primary school students. International Journal of Educational Research, 62, 239-248. https://doi.org/10.1016/j.ijer.2013.05.004
Mohamed, M., & Johnny, J. (2010). Investigating number sense among students. Procedia-Social and Behavioral Sciences, 8, 317–324. https://doi.org/10.1016/j.sbspro.2010.12.044
Namkung, J. M., Goodrich, J. M., & Lee, K. (2023). The factor structure of mathematics anxiety and its relation to gender and mathematics performance. Psychology in the Schools, 60, 4740–4757. https://doi.org/10.1002/pits.23016
Namkung, J. M., Peng, P., & Lin, X. (2019). The relation between mathematics anxiety and mathematics performance among school‐aged students: A meta‐analysis. Review of educational research, 89, 459–496. https://doi.org/10.3102/0034654319843494
National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (2000). The Principles and Standards for School Mathematics. Reston, VA: NCTM.
Pike, C. D., & Forrester, M. A. (1997). The influence of number sense on children’s ability to estimate measures. Educational Psychology, 17(4), 483-500. https://doi.org/10.1080/0144341970170408
Putwain, D. W., Connors, L., Symes, W., & Douglas-Osborn, E. (2012). Is academic buoyancy anything more than adaptive coping?. Anxiety, Stress and Coping: An International Journal, 25, 349–358. https://doi.org/10.1080/10615806.2011.582459
Putwain, D. W., & Daly, A. L. (2013). Do clusters of test anxiety and academic buoyancy differentially predict academic performance? Learning and Individual Differences, 27, 157–162
Putwain, D. W., Daly, A. L., Chamberlain, S., & Sadreddini, S. (2015). Academically buoyant students are less anxious about and perform better in high‐stakes examinations. British Journal of Educational Psychology, 85(3), 247-263.
Putwain, D. W., Daly, A. L., Chamberlain, S., & Sadreddini, S. (2016). ‘Sink or swim’: buoyancy and coping in the cognitive test anxiety–academic performance relationship. Educational Psychology, 36(10), 1807-1825.
Putwain, D. W., Gallard, D., & Beaumont, J. (2020). Academic buoyancy protects achievement against minor academic adversities. Learning and Individual Differences, 83-84(June), 101936. https://doi.org/10.1016/j.lindif.2020.101936
Reys, B. J. (1986). Teaching computational estimation: Concepts and strategies. In H. L. Shoen & W. J. Zweng (Eds.), Estimation and mental computation – 1986 yearbook (pp. 31-44). VA: National Council of Teachers of Mathematics.
Richardson, F. C., & Suinn, R.M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551-554. https://doi.org/10.1037/h0033456
Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29, 225-237.
Sarı, M. H., & Szczygieł, M. (2023). The role of math anxiety in the relationship between approximate number system and math performance in young children. Psychology in the Schools, 60, 912–930. https://doi.org/10.1002/pits.22794
Shumway, J. F. (2016). A counting-focused instructional treatment for developing number system knowledge in second grade: A mixed methods study on children's number sense. Utah State University.
Spinillo, A.G., Correa, J., Cruz, M.S.S. (2021). Number sense in a developmental perspective: Comparing the mastery of its different components in children. In: Spinillo, A.G., Lautert, S.L., Borba, R.E.d.S.R. (eds) Mathematical Reasoning of Children and Adults. Springer, Cham. https://doi.org/10.1007/978-3-030-69657-3_3
Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371-389). New York: Macmillan.
Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25(2), 173-180.
Tak, C. C., Zulnaidi, H., & Eu, L. K. (2022a). Measurement model testing: adaption of metacognitive awareness toward mathematic reasoning among undergraduate education students. Contemporary Mathematics And Science Education, 3(2)
Tak, C. C., Zulnaidi, H., & Eu, L. K. (2022b). Measurement model testing: Adaption of self-efficacy and metacognitive awareness among university students. Eurasia Journal of Mathematics, Science and Technology Education, 18(9)
Tak, C. C., Zulnaidi, H., Eu, L. K., & Feng, S. P. (2023). Mediating role of metacognitive awareness between self-efficacy and mathematics reasoning among education undergraduate students during pandemic. Journal of Higher Education Theory and Practice, 23(6), 36–46
Toprak-Çelen, E. (2020). A structural equation model on efl tertiary level students' academic buoyancy, academic resilience, reconceptualized L2 motivational self system, and their academic achievement [Unpublished master's thesis] Bilkent University.
Tsao, Y. L. (2004). Exploring the connections among number sense, mental computation performance, and the written computation performance of elementary preservice school teachers. Journal of College Teaching & Learning, 1(12), 71-90. https://doi.org/10.19030/tlc.v1i12.2022
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38(1), 1-10.
Umay, A., Akkuş, O., & Duatepe Paksu, A. (2006). An Investigation of 1-5 grades mathematics curriculum by considering NCTM principles and standards. Hacettepe University Journal of Education, 31, 198–211. http://www.efdergi.hacettepe.edu.tr/shw_artcl-844.html
Wang, M.C., Haertal, G.D., & Walberg, H.J. (1994). Educational resilience in inner cities. In M.C. Wang & E.W. Gordon (Eds.), Educational resilience in inner-city America: Challenges and prospects (pp. 45–72). Hillsdale, NJ: Erlbaum.
Yang, D. C. (1995). Number sense performance and strategies possessed by sixth and eighth grade students in Taiwan [Unpublished doctoral dissertation]. University of Missouri, Columbia.
Yang, D. C. (2019). Performance of fourth graders when judging the reasonableness of a computational result. International Journal of Science and Mathematics Education, 17, 197-215. https://doi.org/10.1007/s10763-017-9862-y
Yang, D. C., & Huang, F. Y. (2004). Relationships among computational performance, pictorial representation, symbolic representation and number sense of sixth grade students in Taiwan. Educational Studies, 30(4), 373-389. https://doi.org/10.1080/0305569042000310318
Yang, D.C., Li M.F. and Li, W.J. (2008). Development of a Computerised Number Sense Scale for 3rd Graders: Reliabilty and Validity Analysis. International Electronic Journal of Mathematics Education. 3, 110-124.
Yang, D. C., & Wu, W. R. (2010). The study of number sense: Realistic activities integrated into third-grade math classes in Taiwan. The Journal of Educational Research, 103(6), 379-392. https://doi.org/10.1080/00220670903383010
Derechos de autor 2024 Servicio de Publicaciones, Universidad de Murcia (España)
Esta obra está bajo una licencia internacional Creative Commons Atribución-CompartirIgual 4.0.
Las obras que se publican en esta revista están sujetas a los siguientes términos:
1. El Servicio de Publicaciones de la Universidad de Murcia (la editorial) conserva los derechos patrimoniales (copyright) de las obras publicadas, y favorece y permite la reutilización de las mismas bajo la licencia de uso indicada en el punto 2.
© Servicio de Publicaciones, Universidad de Murcia, 2024
2. Las obras se publican en la edición electrónica de la revista bajo una licencia Creative Commons Reconocimiento-CompartirIgual 4.0 Internacional (texto legal). Se pueden copiar, usar, difundir, transmitir y exponer públicamente, siempre que: i) se cite la autoría y la fuente original de su publicación (revista, editorial y URL de la obra); ii) no se usen para fines comerciales; iii) se mencione la existencia y especificaciones de esta licencia de uso.
3. Condiciones de auto-archivo. Se permite y se anima a los autores a difundir electrónicamente las versiones pre-print (versión antes de ser evaluada y enviada a la revista) y/o post-print (versión evaluada y aceptada para su publicación) de sus obras antes de su publicación, ya que favorece su circulación y difusión más temprana y con ello un posible aumento en su citación y alcance entre la comunidad académica. Color RoMEO: verde.