Validation of the “5L” Method of mathematics instruction/learning
DOI:
https://doi.org/10.31637/epsir-2024-580Keywords:
numerical subjects, cognitive and emotional unconscious, work memory, math anxiety, cognitive load, mathematics instruction, mathematics learning, pillars of learningAbstract
Introduction: The objective of this study is to show with evidence that the "5L" Method of instruction/learning improves academic performance in mathematics, and provides a satisfactory study experience. Methodology: The methodology used responds to a field study aimed at a sample of volunteer students from a population of students of the subject of Fundamentals of Mathematics in the Degrees of Business Administration and/or Marketing and Digital Communication at Euncet Business School, to whom Closed satisfaction surveys were completed weekly, based on a Likert scale (from 1 - very unsatisfactory - to 5 - very satisfactory -), and they were subjected to four evaluative tests, measuring their academic performance (grades from 0 to 100) against a similar control group. Results: Students who implemented the "5L" Method obtained significantly better grades (87,09 vs. 59,65) and they claimed to have had a satisfactory study experience (4,07). Discussion: biases in the sample should be avoided by assessing possible differences in the level of intrinsic motivation. Conclusions: the "5L" Method of instruction/learning adequately manages the cognitive load of the training sessions according to neuroeducational doctrine; significantly improves academic performance compared to traditional study methods; and generates a satisfactory learning experience.
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References
Alloway, T. P. y Passolunghi, M. C. (2011). La relación entre la memoria de trabajo, el CI y las habilidades matemáticas en niños. Learning and Individual Differences, 21(1), 133-137. https://doi.org/10.1016/j.lindif.2010.09.013 DOI: https://doi.org/10.1016/j.lindif.2010.09.013
Alloway, T. P. y Alloway, R. G. (2014). Understanding working memory. SAGE Publications. DOI: https://doi.org/10.4324/9780203094600
Ashcraft, M. H. (2002). Ansiedad matemática: consecuencias personales, educativas y cognitivas. Orientaciones actuales en la ciencia psicológica, 11(5), 181-185. https://doi.org/10.1111/1467-8721.00196 DOI: https://doi.org/10.1111/1467-8721.00196
Ashcraft, M. H. y Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243-248. https://doi.org/10.3758/BF03194059 DOI: https://doi.org/10.3758/BF03194059
Baddeley, A. D. (2000). The episodic buffer: a new component of working memory? Trends in Cognitive Sciences, 4(11), 417-422. https://doi.org/10.1016/S1364-6613(00)01538-2 DOI: https://doi.org/10.1016/S1364-6613(00)01538-2
Baddeley, A. D. y Hitch, G. J. (1974). Working memory. En G. A. Bower (ed.), The psychology of learning and motivation: Advances in research and theory, 8, 47-89. Academic Press. https://www.sciencedirect.com/science/article/pii/S0079742108604521 DOI: https://doi.org/10.1016/S0079-7421(08)60452-1
Ball, D. L., Thames, M. H. y Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554 DOI: https://doi.org/10.1177/0022487108324554
Bandura, A. (1997). Self-efficacy: The exercise of control. Macmillan.
Bargh, J. (2018). ¿Por qué hacemos lo que hacemos? El poder del inconsciente. Ediciones B.
Beck, A. T. y Freeman, A. (1995). Terapia cognitiva de los trastornos de personalidad. Paidós.
Beilock, S. L., Gunderson, E. A., Ramirez, G. y Levine, S. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences, 107(5), 1860-1863. https://doi.org/10.1073/pnas.0910967107 DOI: https://doi.org/10.1073/pnas.0910967107
Bishop, A. J. (1988). Aspectos sociales y culturales de la educación matemática. Enseñanza de las Ciencias, 6(2), 121-125. https://bit.ly/3K8kJ6v DOI: https://doi.org/10.5565/rev/ensciencias.5078
Bjork, R. A. y Bjork, E. L. (2007). Making memories work for you: The role of retrieval practice in the improvement of learning. Psychological Science, 18(1), 71-77. https://doi.org/10.1111/j.1467-9280.2007.01855.x DOI: https://doi.org/10.1111/j.1467-9280.2007.01855.x
Bransford, J. D., Brown, A. L. y Cocking, R. R. (2000). How people learn: Brain, mind, experience, and school. National Academy Press.
Carver, C. S. y Scheier, M. (2001). On the self-regulation of behavior. Cambridge University Press.
Chang, H. y Beilock, S. L. (2016). The neural correlates of math anxiety: An overview of current research and its implications. Current Opinion in Behavioral Sciences, 10, 33-38. https://doi.org/10.1016/j.cobeha.2016.05.014 DOI: https://doi.org/10.1016/j.cobeha.2016.04.011
Chi, M. T. H. (2009). Active-Constructive-Interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1(1), 73-105. https://doi.org/10.1111/j.1756-8765.2008.01005.x DOI: https://doi.org/10.1111/j.1756-8765.2008.01005.x
Dehaene, S. (2016). El cerebro matemático. Siglo veintiuno.
Dehaene, S. (2019). ¿Cómo aprendemos? Siglo veintiuno.
Ericsson, K. A., Krampe, R. T. y Tesch-Römer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363-406. https://doi.org/10.1037/0033-295X.100.3.363 DOI: https://doi.org/10.1037//0033-295X.100.3.363
Ericsson, K. A. y Pool, R. (2016). Peak: Secrets from the new science of expertise. Houghton Mifflin Harcourt.
Gathercole, S. E. y Alloway, T. P. (2008). Working memory and learning: A practical guide for teachers. SAGE Publications.
Gathercole, S. E., Pickering, S. J., Ambridge, B. y Wearing, H. (2004). La estructura de la memoria de trabajo de los 4 a los 15 años de edad. Psicología del Desarrollo, 40(2), 177-190. https://doi.org/10.1037/0012-1649.40.2.177 DOI: https://doi.org/10.1037/0012-1649.40.2.177
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A five year longitudinal study. Developmental Psychology, 47(6), 1539-1552. https://goo.su/4k2VK DOI: https://doi.org/10.1037/a0025510
Greenberg, L. S., Rice, L. N. y Elliott, R. (1996). Facilitando el cambio emocional. Paidós.
Gresham, G. (2009). An examination of mathematics teacher efficacy and mathematics anxiety in elementary pre-service teachers. The Journal of Classroom Interaction, 44(2), 22-38. https://bit.ly/3rpGZX6
Guillén, J. C. (2017). Neuroeducación en el aula: De la teoría a la práctica. CreateSpace.
Guillén, J. C. (2022). Memoria de trabajo en el aula. Cuadernos de Pedagogía, 528, 142-148. https://www.grao.com/es/producto/memoria-de-trabajo-en-el-aula
Hattie, J. y Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487 DOI: https://doi.org/10.3102/003465430298487
Kandel, E. (2007). En busca de la memoria. Katz Editores. DOI: https://doi.org/10.2307/j.ctvm7bdr7
Kang, S. H. (2016). The benefits of interleaved practice for learning. En J. Horvath, J. Lodge y J. Hattie (Eds.), From the laboratory to the classroom: translating science of learning for teachers (pp. 79-93). Routledge.
Karpicke, J. D. (2012). Aprendizaje basado en la recuperación: la recuperación activa promueve el aprendizaje significativo. Current Directions in Psychological Science, 21(3), 157-163. https://doi.org/10.1177/0963721412443552 DOI: https://doi.org/10.1177/0963721412443552
Karpicke, J. D. y Blunt, J. R. (2011). Retrieval practice produces more learning than elaborative studying with concept mapping. Science, 331(6018), 772-775. https://doi.org/10.1126/science.1199327 DOI: https://doi.org/10.1126/science.1199327
Karpicke, J. D., Butler, A. C. y Roediger, H. L. (2009). Metacognitive strategies in student learning: Do students practice retrieval when they study on their own? Memory, 17(4), 471-479. https://doi.org/10.1080/09658210802647009 DOI: https://doi.org/10.1080/09658210802647009
Karpicke, J. D. y Roediger, H. L. (2007). Expanding retrieval practice promotes short-term retention, but equally spaced retrieval enhances long-term retention. Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(4), 704-719. https://doi.org/10.1037/0278-7393.33.4.704 DOI: https://doi.org/10.1037/0278-7393.33.4.704
Karpicke, J. D. y Roediger, H. L. (2008). The critical importance of retrieval for learning. Science, 319(5865), 966-968. https://doi.org/10.1126/science.1152408 DOI: https://doi.org/10.1126/science.1152408
Lovett, M. (2013). A collaborative convergence on studying reasoning processes: A case study in statistics. En S. M. Carver y D. Klahr (Eds.), Cognition and Instruction: Twenty-Five Years of Progress (pp. 347-384). Psychology Press. https://bit.ly/3DHDlqQ
Maloney, E. A. y Beilock, S. L. (2012). Ansiedad matemática: quién la padece, por qué se desarrolla y cómo protegerse de ella. Tendencias en Ciencias Cognitivas, 16(8), 404-406. https://doi.org/10.1016/j.tics.2012.06.008 DOI: https://doi.org/10.1016/j.tics.2012.06.008
Marina, J. A. (2016). Objetivo: Generar talento. Conecta.
Mayer, R. E. (2002). Rote versus meaningful learning. Theory into Practice, 41(4), 226-232. https://doi.org/10.1207/s15430421tip4104_4 DOI: https://doi.org/10.1207/s15430421tip4104_4
Mayer, R. E. (2008). Aplicación de la ciencia del aprendizaje: principios basados en evidencia para el diseño de instrucción multimedia. Psicólogo Estadounidense, 63(8), 760-769. https://doi.org/10.1037/0003-066X.63.8.760 DOI: https://doi.org/10.1037/0003-066X.63.8.760
Millner, M., Jaroszewski, A. C., Chamarthi, H. y Pizzagalli, D. (2012). Behavioral and electrophysiological correlates of training-induced cognitive control improvements. Neuroimage, 63(2), 742-753. https://doi.org/10.1016/j.neuroimage.2012.07.029 DOI: https://doi.org/10.1016/j.neuroimage.2012.07.032
Moore, A. M. y Ashcraft, M. H. (2012). Mathematics Anxiety. In Encyclopedia of Language and Literacy Development (pp. 1-8). Canadian Language and Literacy Research Network. http://www.literacyencyclopedia.ca/pdfs/topic.php?topId=265
Oberle, E. y Schonert-Reichl, K. A. (2016). Stress contagion in the classroom? The link between classroom teacher burnout and morning cortisol in elementary school students. Social Science & Medicine, 159, 30-37. https://doi.org/10.1016/j.socscimed.2016.04.031 DOI: https://doi.org/10.1016/j.socscimed.2016.04.031
Paas, F. G. y Van Merriënboer, J. J. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. Journal of Educational Psychology, 86(1), 122-133. https://doi.org/10.1037/0022-0663.86.1.122 DOI: https://doi.org/10.1037//0022-0663.86.1.122
Posner, M. I. y Petersen, S. E. (1990). The attention system of the human brain. Annual Review of Neuroscience, 13(1), 25-42. https://doi.org/10.1146/annurev.ne.13.030190.000325 DOI: https://doi.org/10.1146/annurev.neuro.13.1.25
Prince, M. (2004). Does active learning work? A review of the research. Journal of Engineering Education, 93(3), 223-231. https://doi.org/10.1002/j.2168-9830.2004.tb00809.x DOI: https://doi.org/10.1002/j.2168-9830.2004.tb00809.x
Richardson, F. C. y 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 DOI: https://doi.org/10.1037/h0033456
Roediger, H. L. y Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249-255. https://doi.org/10.1111/j.1467-9280.2006.01693.x DOI: https://doi.org/10.1111/j.1467-9280.2006.01693.x
Rowland, C. A. (2014). The effect of testing versus restudy on retention: A meta-analytic review of the testing effect. Psychological Bulletin, 140(6), 1432-1463. https://doi.org/10.1037/a0037559 DOI: https://doi.org/10.1037/a0037559
Ruff, S. E. y Boes, S. R. (2014). The Sum of All Fears: The Effects of Math Anxiety on Math Achievement in Fifth Grade Students and the Implications for School Counselors. Georgia School Counselors Association Journal, 21(1), n1. https://bit.ly/3XYD8eP
Ruiz, H. (2020). ¿Cómo aprendemos? Una aproximación científica al aprendizaje. Graó.
Salden, R. J., Paas, F. y van Merriënboer, J. J. (2006). A comparison of approaches to learning task selection in the training of complex cognitive skills. Computers in Human Behavior, 22(3), 321-333. https://doi.org/10.1016/j.chb.2004.06.003 DOI: https://doi.org/10.1016/j.chb.2004.06.003
Shenk D. (2011). El genio que todos llevamos dentro. Ariel.
Sloan, T. M. (2010). Feedback in Higher Education: The Role of the Academic Advisor. Journal of College Student Development, 51(3), 290-306. https://doi.org/10.1353/csd.0.0131 DOI: https://doi.org/10.1353/csd.0.0131
Stevenson, H. W., Lee, S. Y., Chen, C., Lummis, M., Stigler, J., Fan, L. y Ge, E. (1990). Comparisons of children's mathematical performance and classroom instruction in China and the United States. Child Development, 61(5), 1053-1066. https://doi.org/10.2307/1130870 DOI: https://doi.org/10.1111/j.1467-8624.1990.tb02841.x
Stickgold, R. (2005). Sleep-dependent memory consolidation. Nature, 437(7063), 1272-1278. https://doi.org/10.1038/nature04286 DOI: https://doi.org/10.1038/nature04286
Stoehr, K. J. (2017). Mathematics anxiety: One size does not fit all. Journal of Teacher Education, 68(1), 69-84. https://doi.org/10.1177/0022487116676316 DOI: https://doi.org/10.1177/0022487116676316
Swanson, H. L. y Jerman, O. (2007). The influence of working memory on reading growth in subgroups of children with reading disabilities. Journal of Experimental Child Psychology, 96(4), 249-283. https://doi.org/10.1016/j.jecp.2006.12.004 DOI: https://doi.org/10.1016/j.jecp.2006.12.004
Swars, S. L., Daane, C. J. y Giesen, J. (2006). Mathematics anxiety and mathematics teacher efficacy: What is the relationship in elementary preservice teachers? School Science and Mathematics, 106(7), 306-315. https://doi.org/10.1111/j.1949-8594.2006.tb17921.x DOI: https://doi.org/10.1111/j.1949-8594.2006.tb17921.x
Schwartz, M. S., Sadler, P. M., Sonnert, G. y Tai, R. H. (2009). Depth versus breadth: How content coverage in high school science courses relates to later success in college science coursework. Science Education, 93(5), 798-826. https://doi.org/10.1002/sce.20328 DOI: https://doi.org/10.1002/sce.20328
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285. https://doi.org/10.1207/s15516709cog1202_4 DOI: https://doi.org/10.1016/0364-0213(88)90023-7
Sweller, J., Van Merrienboer, J. J. y Paas, F. G. (1998). Arquitectura cognitiva y diseño instruccional. Educational Psychology Review, 10, 251-296. https://doi.org/10.1023/A:1022193728205 DOI: https://doi.org/10.1023/A:1022193728205
Sweller, J., Ayres, P. y Kalyuga, S. (2011). Cognitive Load Theory. Springer Science & Business Media. https://link.springer.com/chapter/10.1007/978-1-4419-8126-4_10 DOI: https://doi.org/10.1007/978-1-4419-8126-4
Valls, J. (2015). Genial mente: las claves de la inteligencia, el talento y la creatividad. Obelisco.
Valls, J. (2020). Se puede educar el inconsciente cognitivo matemático. Cuadernos de Pedagogía, 509, 60-63. https://bit.ly/3K4y7Js
Vigotsky, L. S. (1978). Mind in society. Harvard University Press.
Walker, M. P. (2008). The Role of Sleep in Cognition and Emotion. Annals of the New York Academy of Sciences, 1156, 168-197. https://doi.org/10.1196/annals.1417.017 DOI: https://doi.org/10.1111/j.1749-6632.2009.04416.x
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