International Electronic Journal of Mathematics Education

Reasoning Abilities and Learning Math: A Möbius Strip?
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Brito LP, Almeida LS, Osório AJM. Reasoning Abilities and Learning Math: A Möbius Strip?. INT ELECT J MATH ED. 2020;15(2), em0565. https://doi.org/10.29333/iejme/6259
APA 6th edition
In-text citation: (Brito et al., 2020)
Reference: Brito, L. P., Almeida, L. S., & Osório, A. J. M. (2020). Reasoning Abilities and Learning Math: A Möbius Strip?. International Electronic Journal of Mathematics Education, 15(2), em0565. https://doi.org/10.29333/iejme/6259
Chicago
In-text citation: (Brito et al., 2020)
Reference: Brito, Luciana Pereira, Leandro Silva Almeida, and António José Meneses Osório. "Reasoning Abilities and Learning Math: A Möbius Strip?". International Electronic Journal of Mathematics Education 2020 15 no. 2 (2020): em0565. https://doi.org/10.29333/iejme/6259
Harvard
In-text citation: (Brito et al., 2020)
Reference: Brito, L. P., Almeida, L. S., and Osório, A. J. M. (2020). Reasoning Abilities and Learning Math: A Möbius Strip?. International Electronic Journal of Mathematics Education, 15(2), em0565. https://doi.org/10.29333/iejme/6259
MLA
In-text citation: (Brito et al., 2020)
Reference: Brito, Luciana Pereira et al. "Reasoning Abilities and Learning Math: A Möbius Strip?". International Electronic Journal of Mathematics Education, vol. 15, no. 2, 2020, em0565. https://doi.org/10.29333/iejme/6259
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Brito LP, Almeida LS, Osório AJM. Reasoning Abilities and Learning Math: A Möbius Strip?. INT ELECT J MATH ED. 2020;15(2):em0565. https://doi.org/10.29333/iejme/6259

Abstract

Long have we known that reasoning abilities are linked to learning, and specifically to learning mathematics. Even intelligence, considered a controversial construct, plays a significant role in the research on the explanation of academic performance. This article intends to highlight some important cognitive abilities or dimensions relevant to learning mathematics, synthesizing some research that defines such constructs and relates them to mathematical learning and achievement. General considerations about designing and implementing meaningful learning experiences are presented.

References

  • Almeida, L., & Araújo, A. (2014). Aprendizagem e sucesso escolar: variáveis pessoais dos alunos (ADIPSIEDUC Ed.). Braga: ADIPSIEDUC.
  • Almeida, L., Guisande, M. A., & Ferreira, A. I. (2009). Inteligência: Perspetivas teóricas. Coimbra: Almedina.
  • Almeida, L., & Lemos, G. (2006). Bateria de Provas de Raciocínio: Versões 5/6, 7/9 e 10/12 (Manual Técnico). In. Braga: Universidade do Minho.
  • Almeida, L., Miranda, L., Salgado, A., Silva, M., & Martins, V. (2012). Impacto da capacidade cognitiva e das atribuições causais no rendimento escolar na matemática. Quadrante, 11(1), 55-66.
  • Alves, M., Coutinho, C., Rocha, A., & Rodrigues, C. (2016). Fatores que influenciam a aprendizagem de conceitos matemáticos em cursos de engenharia: Um estudo exploratório com estudantes da Universidade do Minho. Revista Portuguesa de Educação, 29(1), 259-293. https://doi.org/10.21814/rpe.5998
  • Alzahrani, K. S. (2017). Metacognition and its role in mathematics learning: an exploration of the perceptions of a teacher and students in a secondary school. International electronic journal of mathematics education, 12(3), 521-537.
  • Asia, S., & OECD. (2018). Teaching for Global Competence in a Rapidly Changing World. https://doi.org/https://doi.org/10.1787/9789264289024-en
  • Ausubel, D., Novak, J., & Hanesian, H. (1980). Psicologia educacional (E. Nick, Trans.). Rio de Janeiro: Interamericana.
  • Baddeley, A. (2010). Working memory. Current Biology, 20(4), R136-R140. https://doi.org/10.1016/j.cub.2009.12.014
  • Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). New York: Academic Press.
  • Bishop, A. J. (2008). Spatial Abilities and Mathematics Education – A Review. In P. Clarkson & N. Presmeg (Eds.), Critical Issues in Mathematics Education: Major Contributions of Alan Bishop (pp. 71-81). Boston, MA: Springer US.
  • Buehl, M. M., & Alexander, P. A. (2004). Seeing the possibilities: Constructing and validating measures of mathematical and analogical reasoning for young children. In Mathematical and analogical reasoning of young learners (pp. 35-58): Routledge.
  • Chung Yen, L., Jacqueline, T., Beatrix, K., & Roi Cohen, K. (2016). The Neuroscience of Mathematical Cognition and LearningIS 136. https://doi.org/https://doi.org/10.1787/5jlwmn3ntbr7-en
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics. (pp. 420-464). New York, NY, England: Macmillan Publishing Co, Inc.
  • Cormier, D. C., Bulut, O., McGrew, K. S., & Singh, D. (2017). Exploring the Relations between Cattell–Horn–Carroll (CHC) Cognitive Abilities and Mathematics Achievement. Applied Cognitive Psychology, 31(5), 530-538. https://doi.org/10.1002/acp.3350
  • Corso, L. V., & Dorneles, B. V. (2012). Qual o papel que a memória de trabalho exerce na aprendizagem da matemática? Bolema: Boletim de Educação Matemática, 26, 627-648.
  • de Koning, E., Hamers, J. H. M., Sijtsma, K., & Vermeer, A. (2002). Teaching Inductive Reasoning in Primary Education. Developmental Review, 22(2), 211-241. https://doi.org/10.1006/drev.2002.0548
  • Delamater, A. R., & Lattal, K. M. (2014). The study of associative learning: mapping from psychological to neural levels of analysis. Neurobiology of learning and memory, 108, 1-4. https://doi.org/10.1016/j.nlm.2013.12.006
  • Devlin, K. (2002). Matemática: a ciência dos padrões. Porto: Porto Editora.
  • Elliott, J. (2012). Reconstructing teacher education (Vol. 221): Routledge.
  • Embretson, S. E., & McCollam, K. M. S. (2000). Psychometric Approaches to Understanding and Measuring Intelligence. In R. J. Sternberg (Ed.), Handbook of Intelligence (pp. 423-444). Cambridge: Cambridge University Press.
  • English, L. D. (2013). Mathematical reasoning: Analogies, metaphors, and images: Routledge.
  • Entwistle, N. (1991). Approaches to learning and perceptions of the learning environment. Higher Education, 22(3), 201-204. https://doi.org/10.1007/BF00132287
  • Entwistle, N., & Ramsden, P. (1982). Understanding Student Learning (routledge revivals): Routledge.
  • Fauskanger, J., & Bjuland, R. (2018). Deep Learning as Constructed in Mathematics Teachers’ Written Discourses. 13(3), 149-160. https://doi.org/10.12973/iejme/2705
  • Findley, K., Whitacre, I., & Hensberry, K. (2017). Integrating Interactive Simulations into the Mathematics Classroom: Supplementing, Enhancing, or Driving? Paper presented at the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Indianapolis. Retrieved from https://files.eric.ed.gov/fulltext/ED581367.pdf
  • Flanagan, D., & Harrison, E. (2018). Contemporary intellectual assessment: Theories, tests, and issues. NY: The Guilford Press.
  • Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906-911. https://doi.org/10.1037/0003-066X.34.10.906
  • Floyd, R. G., Evans, J. J., & McGrew, K. S. (2003). Relations between Measures of Cattell-Horn-Carroll (CHC) Cognitive Abilities and Mathematics Achievement across the School-Age Years. Psychology in the Schools, 40(2), 155-171.
  • Fung, W., & Swanson, H. L. (2017). Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence? Memory & Cognition, 45(5), 804-823. https://doi.org/10.3758/s13421-017-0697-0
  • Ganda, D. R., & Boruchovitch, E. (2018). A autorregulação da aprendizagem: principais conceitos e modelos teóricos. Psicologia da Educação. Programa de Estudos Pós-Graduados em Educação: Psicologia da Educação. ISSN 2175-3520(46).
  • Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Developmental psychology, 47(6), 1539-1552. https://doi.org/10.1037/a0025510
  • Gilligan, K. A., Flouri, E., & Farran, E. K. (2017). The contribution of spatial ability to mathematics achievement in middle childhood. Journal of Experimental Child Psychology, 163(Supplement C), 107-125. https://doi.org/10.1016/j.jecp.2017.04.016
  • Gomes, C., Brocardo, J., Pedroso, J., Carrillo, J., Ucha, L., Encarnação, M., ... Rodrigues, S. (2017). Perfil dos alunos à saída da escolaridade obrigatória. Ministério da Educação/Direção Geral de Educação
  • Green, C., Bunge, S., Chiongbian, V. B., Barrow, M., & Ferrer, E. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology, 157, 19. https://doi.org/10.1016/j.jecp.2016.12.005
  • Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35, 34-49. https://doi.org/10.1016/j.cogdev.2015.02.001
  • Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. (2000). Solving inductive reasoning problems in mathematics: not-so-trivial pursuit. Cognitive Science, 24(2), 249-298. https://doi.org/10.1016/S0364-0213(00)00019-7
  • Inglis, M., & Simpson, A. (2009). Conditional inference and advanced mathematical study: further evidence. Educational Studies in Mathematics, 72(2), 185-198. https://doi.org/10.1007/s10649-009-9187-z
  • Joly, M. C. R. A., Muner, L. C., Silva, D. V., & Prieto, G. (2011). Visualização espacial e desempenho em matemática no ensino médio e profissional. Avaliação Psicológica, 10, 181-191.
  • Julià, C., & Antolì, J. Ò. (2017). Enhancing spatial ability and mechanical reasoning through a STEM course. International Journal of Technology and Design Education. https://doi.org/10.1007/s10798-017-9428-x
  • Kaufman, S. B., DeYoung, C. G., Gray, J. R., Brown, J., & Mackintosh, N. (2009). Associative learning predicts intelligence above and beyond working memory and processing speed. Intelligence, 37(4), 374-382. https://doi.org/10.1016/j.intell.2009.03.004
  • Kell, H. J., & Lubinski, D. (2013). Spatial Ability: A Neglected Talent in Educational and Occupational Settings. 35(4), 219.
  • Knowlton, B., L.M. Siegel, A., & D. Moody, T. (2017). Procedural Learning in Humans. In.
  • Kösa, T. (2016). Effects of Using Dynamic Mathematics Software on Preservice Mathematics Teachers' Spatial Visualization Skills: The Case of Spatial Analytic Geometry. Educational Research and Reviews, 11(7), 449-458.
  • Lannin, J., Ellis, A., Elliot, R., & Zbiek, R. M. (2011). Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Grades Pre-K–8. Reston: NCTM.
  • Legg, S., & Hutter, M. (2007). A Collection of Definitions of Intelligence. In B. Goertzel & P. Wang (Eds.), Advances in Artificial General Intelligence: Concepts, Architectures and Algorithms (pp. 17-24): IOS Press.
  • Lemos, G., Casanova, J., & Almeida, L. (2015). Habilidades cognitivas e interesses vocacionais na adolescência: Promovendo percursos de sucesso. In G. Lemos & L. Almeida (Eds.), Cognição e aprendizagem: Promoção do sucesso escolar (pp. 35-67).
  • Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent identification and development. 49(4), 344. https://doi.org/10.1016/j.paid.2010.03.022
  • M. Laamena, C., Nusantara, T., Irawan, E., & Muksar, M. (2018). How do the Undergraduate Students Use an Example in Mathematical Proof Construction: A Study based on Argumentation and Proving Activity (Vol. 13).
  • Martin, W. (2009). Making Reasoning and Sense Making the Focus for Mathematics Education. In. Reston, VA: NCTM.
  • Marton, F., & Säljö, R. (1976). On qualitative differences in learning: I — Outcome and Process. British Journal of Educational Psychology, 46(1), 4-11. https://doi.org/10.1111/j.2044-8279.1976.tb02980.x
  • Mata-Pereira, J., & Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186.
  • McGrew. (2009). CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 37(1 (Editorial)), 1-10.
  • McGrew, & Evans. (2004). Internal and External Factorial Extensions to the Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities: A Review of Factor Analytic Research since Carroll's Seminal 1993 Treatise. Retrieved from http://www.iapsych.com/HCARR2.pdf
  • McGrew, & Wendling. (2010). Cattell–Horn–Carroll cognitive-achievement relations: What we have learned from the past 20 years of research. Psychology in the Schools, 47(7), 651-675. https://doi.org/10.1002/pits.20497
  • Mitchell, C. J., De Houwer, J., & Lovibond, P. F. (2009). The propositional nature of human associative learning. Behavioral and Brain Sciences, 32(2), 183-198. https://doi.org/10.1017/S0140525X09000855
  • Molnár, G., Greiff, S., & Csapó, B. (2013). Inductive reasoning, domain specific and complex problem solving: Relations and development. Thinking Skills and Creativity, 9, 35-45. https://doi.org/10.1016/j.tsc.2013.03.002
  • Mondragón, E., Alonso, E., & Kokkola, N. (2017). Associative Learning Should Go Deep. Trends in Cognitive Sciences, 21(11), 822-825. https://doi.org/10.1016/j.tics.2017.06.001
  • Mulligan, J. (2015). Looking within and beyond the geometry curriculum: connecting spatial reasoning to mathematics learning. 47(3), 511-517. https://doi.org/10.1007/s11858-015-0696-1
  • Murtonen, M., Gruber, H., & Lehtinen, E. (2017). The return of behaviourist epistemology: A review of learning outcomes studies. Educational Research Review, 22, 114-128. https://doi.org/10.1016/j.edurev.2017.08.001
  • NCTM. (2000). Principles and standards for school mathematics. In (Vol. 1). Reston, VA: National Council of Teachers of Mathematics.
  • NCTM. (2009). Focus in High School Mathematics: Reasoning and Sense Making. In. Reston, VA: The National Council of Teachers of Mathematics Inc.
  • Neisser, U., Boodoo, G., Bouchard Jr, T. J., Boykin, A. W., Brody, N., Ceci, S. J., . . . Sternberg, R. J. (1996). Intelligence: Knowns and unknowns. American psychologist, 51(2), 77.
  • Nisbett. (2016). Culture and Intelligence. In: London School of Economics and Political Science.
  • Nisbett, Aronson, J., Blair, C., Dickens, W., Flynn, J., Halpern, D., & Turkheimer, E. (2012). Intelligence New Findings and Theoretical Developments (Vol. 67).
  • Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., & Carraher, J. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25(1), 147-166. https://doi.org/10.1348/026151006X153127
  • OECD. (2014). PISA 2012 Results: Creative Problem Solving: Students’ Skills in Tackling Real-Life Problems. In (PISA ed., Vol. 5): OECD Publishing.
  • Oliveira, A. B. d., Osório, A. J., & Dourado, L. G. P. (2018, 2018). Compreender a Biologia através do Design de Jogos Digitais: Programando nova estratégia na formação de professores. Paper presented at the Encontro Internacional "A Voz dos Professores de Ciência e Tecnologia".
  • Ponte, J. P. d., Mata-Pereira, J., & Henriques, A. (2012a). O raciocínio matemático nos alunos do ensino básico e do ensino superior. Praxis Educativa, 7, 355-377.
  • Ponte, J. P. d., Mata-Pereira, J., & Henriques, A. (2012b). O raciocínio matemático nos alunos do ensino básico e do ensino superior.
  • Prieto, G., & Velasco, A. D. (2008). Entrenamiento de la visualización espacial mediante ejercicios informatizados de dibujo técnico. Psicologia escolar e educacional, 309-317.
  • Primi, R., Ferrão, M. E., & Almeida, L. S. (2010). Fluid intelligence as a predictor of learning: A longitudinal multilevel approach applied to math. Learning and Individual Differences, 20(5), 446-451. https://doi.org/10.1016/j.lindif.2010.05.001
  • Pólya, G. (1990). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. 1): Princeton University Press.
  • Resnick. (1987). Education and learning to think. Washington D.C.: National Academy Press.
  • Resnick, M. (1997). Mathematics as a science of patterns. Oxford: Clarendon Press.
  • Richland, L. E., & Hansen, J. (2013). Reducing cognitive load in learning by analogy. International Journal of Psychological Studies, 5(4), 69.
  • Schneider, W. J., & McGrew, K. S. (2012). The Cattell-Horn-Carroll model of intelligence. In D. Flanagan & P. Harrison (Eds.), Contemporary intellectual assessment: Theories, tests, and issues, 3rd ed. (pp. 99-144). New York: Guilford Press.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grows (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New York: MacMillan.
  • Schwartz, F., Epinat-Duclos, J., Léone, J., & Prado, J. (2017). The neural development of conditional reasoning in children: Different mechanisms for assessing the logical validity and likelihood of conclusions. NeuroImage, 163, 264-275. https://doi.org/10.1016/j.neuroimage.2017.09.029
  • Scott, C. L. (2015). The Futures of learning 2: what kind of learning for the 21st century? In Education, research and foresight: working papers (UNESCO) (14th november 2015 ed.).
  • Shute, V. J. (1992). Learning processes and learning outcomes. In T. Husen & T. N. Postlethwaite (Eds.), International encyclopedia of education (2 ed., pp. 3315-3325). New York: Pergamon.
  • Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: an ICME-13 survey team report. ZDM, 48(5), 691-719. https://doi.org/10.1007/s11858-016-0796-6
  • Stelzer, F., Andrés, M. L., Canet Juric, L., Urquijo, S., & Marta Richards, M. (2019). Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding (Vol. 14).
  • Sternberg, R. J. (1983). Components of human intelligence. Cognition, 15(1), 1-48. https://doi.org/10.1016/0010-0277(83)90032-X
  • Stevenson, C. E., Bergwerff, C. E., Heiser, W. J., & Resing, W. C. M. (2014). Working Memory and Dynamic Measures of Analogical Reasoning as Predictors of Children's Math and Reading Achievement. Infant & Child Development, 23(1), 51-66. https://doi.org/10.1002/icd.1833
  • Szűcs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014). Cognitive components of a mathematical processing network in 9-year-old children. Developmental science, 17(4), 506-524. https://doi.org/10.1111/desc.12144
  • Säljö, R. (1979). Learning about learning. Higher Education, 8(4), 443-451. https://doi.org/10.1007/BF01680533
  • UNESCO. (2016). Education 2030: Incheon Declaration and Framework for Action for the implementation of Sustainable Development Goal 4: Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all. Retrieved from https://unesdoc.unesco.org/ark:/48223/pf0000245656
  • Vale, I. (2013). Patterns in figurative contexts: a way to the generalization in mathematics. Revemat: Revista Eletrônica de Educação Matemática, 8(2), 64-81.
  • Wang, T., Ren, X., & Schweizer, K. (2017). Learning and retrieval processes predict fluid intelligence over and above working memory. Intelligence, 61, 29-36. https://doi.org/10.1016/j.intell.2016.12.005
  • Yen, L., Jacqueline, T., Beatrix, K., & Cohen, K. (2016). The Neuroscience of Mathematical Cognition and Learning. https://doi.org/https://doi.org/10.1787/5jlwmn3ntbr7-en
  • Yildiz, S. G., & Özdemir, A. S. (2017). Development of the Spatial Ability Test for Middle School Students. Acta Didactica Napocensia, 10(4), 41-54.
  • Zakeri, J., & Khatibi, M. B. (2014). A Much-needed Boost to EFL Learners’ Vocabulary; The Role of Associative Learning. Procedia - Social and Behavioral Sciences, 98, 1983-1990. https://doi.org/10.1016/j.sbspro.2014.03.632
  • Zimmerman, B. (1990). Self-Regulated Learning and Academic Achievement: An Overview (Vol. 25).

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.