163
Views
0
CrossRef citations to date
0
Altmetric
LEARNING, INSTRUCTION, AND COGNITION

Promoting 5th Grade Students’ Spontaneous Focusing on Quantitative Relations

, , , , &

References

  • Braham, E. J., Libertus, M. E., & McCrink, K. (2018). Children’s spontaneous focus on number before and after guided parent-child interactions in a children’s museum. Developmental Psychology, 54(8), 1492–1498. https://doi.org/10.1037/dev0000534
  • Braithwaite, D. W., & Siegler, R. S. (2018). Developmental changes in the whole number bias. Developmental Science, 21(2), 1–13. https://doi.org/10.1111/desc.12541
  • Brezovszky, B., McMullen, J., Veermans, K., Hannula-Sormunen, M. M., Rodríguez-Aflecht, G., Pongsakdi, N., Laakkonen, E., & Lehtinen, E. (2019). Effects of a mathematics game-based learning environment on primary school students’ adaptive number knowledge. Computers & Education, 128(2017), 63–74. https://doi.org/10.1016/j.compedu.2018.09.011
  • Cohen, D. J., & Blanc-Goldhammer, D. (2011). Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin & Review, 18(2), 331–338. https://doi.org/10.3758/s13423-011-0059-z
  • Fazio, L. K., DeWolf, M., & Siegler, R. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology. Learning, Memory, and Cognition, 42(1), 1–16. https://doi.org/10.1037/xlm0000153
  • Greipl, S., Klein, E., Lindstedt, A., Kiili, K., Moeller, K., Karnath, H.-O., Bahnmueller, J., Bloechle, J., & Ninaus, M. (2021). When the brain comes into play: Neurofunctional correlates of emotions and reward in game-based learning. Computers in Human Behavior, 125, 106946. https://doi.org/10.1016/j.chb.2021.106946
  • Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15(3), 237–256. https://doi.org/10.1016/j.learninstruc.2005.04.005
  • Hannula, M. M., Mattinen, A., & Lehtinen, E. (2005). Does social interaction influence 3-year-old children’s tendency to focus on numerosity? A quasi-experimental study in day care. In L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds.), Powerful environments for promoting deep conceptual and strategic learning (pp. 63–80) Leuven University Press.
  • Hannula-Sormunen, M. M. (2015). Spontaneous focusing on numerosity and its relation to counting and arithmetic. In A. Dowker & R. Cohen Kadosh (Eds.), Oxford handbook of mathematical cognition (pp. 275–290) Oxford university press. https://doi.org/10.1093/oxfordhb/9780199642342.013.018
  • Hannula-Sormunen, M. M., Nanu, C. E., Luomaniemi, K., Heinonen, M., Sorariutta, A., Södervik, I., & Mattinen, A. (2020). Promoting spontaneous focusing on numerosity and cardinality-related skills at day care with one, two, how many and count, how many programs. Mathematical Thinking and Learning, 22(4), 312–331. https://doi.org/10.1080/10986065.2020.1818470
  • Harju, H., Lehtinen, E., & Hannula-Sormunen, M. (2022). Focusing on numerical order in preschool predicts mathematical achievement six years later. In C. Fernández, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 347–354). PME.
  • Hedges, L. V., & Rhoads, C. (2010). Statistical power analysis. International Encyclopedia of Education, NCSER 2010-3006, 436–443. https://doi.org/10.1016/B978-0-08-044894-7.01356-7
  • Hornburg, C. B., Schmitt, S. A., & Purpura, D. J. (2018). Relations between preschoolers’ mathematical language understanding and specific numeracy skills. Journal of Experimental Child Psychology, 176, 84–100. https://doi.org/10.1016/j.jecp.2018.07.005
  • Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001
  • Kiili, K., Moeller, K., & Ninaus, M. (2018). Evaluating the effectiveness of a game-based rational number training – In-game metrics as learning indicators. Computers & Education, 120, 13–28. https://doi.org/10.1016/j.compedu.2018.01.012
  • Koskinen, A., McMullen, J., Hannula-Sormunen, M., Ninaus, M., & Kiili, K. (2023). The strength and direction of the difficulty adaptation affect situational interest in game-based learning. Computers & Education, 194, 104694. https://doi.org/10.1016/j.compedu.2022.104694
  • Lehtinen, E., & Hannula, M. M. (2006). Attentional processes, abstraction and transfer in early mathematical development. In Instructional psychology: Past, present and future trends. Fifteen essays in honour of Erik De Corte (Vol. 49, 39–55). Elsevier.
  • Lehtinen, E., Hannula-Sormunen, M. M., McMullen, J., & Gruber, H. (2017). Cultivating mathematical skills: From drill-and-practice to deliberate practice. ZDM, 49(4), 625–636. https://doi.org/10.1007/s11858-017-0856-6
  • Lobato, J., Rhodehamel, B., & Hohensee, C. (2012). “Noticing” as an alternative transfer of learning process. Journal of the Learning Sciences, 21(3), 433–482. https://doi.org/10.1080/10508406.2012.682189
  • McMullen, J., Chan, J., Mazzocco, M. M. M., & Hannula-Sormunen, M. M. (2019). Spontaneous mathematical focusing tendencies in mathematical development and education. In Constructing number: Merging perspectives from psychology and mathematics education (pp. 69–86). Springer. https://doi.org/10.1007/978-3-030-00491-0_4
  • McMullen, J., Hannula-Sormunen, M. M., Kainulainen, M., Kiili, K., & Lehtinen, E. (2019). Moving mathematics out of the classroom: Using mobile technology to enhance spontaneous focusing on quantitative relations. British Journal of Educational Technology, 50(2), 562–573. https://doi.org/10.1111/bjet.12601
  • McMullen, J., Hannula-Sormunen, M. M., Laakkonen, E., & Lehtinen, E. (2016). Spontaneous focusing on quantitative relations as a predictor of the development of rational number conceptual knowledge. Journal of Educational Psychology, 108(6), 857–868. https://doi.org/10.1037/edu0000094
  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2014). Spontaneous focusing on quantitative relations in the development of children’s fraction knowledge. Cognition and Instruction, 32(2), 198–218. https://doi.org/10.1080/07370008.2014.887085
  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2017). Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge. Contemporary Educational Psychology, 51, 356–365. https://doi.org/10.1016/j.cedpsych.2017.09.007
  • McMullen, J., Koskinen, A., Kärki, T., Lindstedt, A., Määttä, S., Halme, H., Lehtinen, E., Hannula-Sormunen, M. M., & Kiili, K. (2023). A game-based approach to promoting adaptive rational number knowledge. Mathematical Thinking and Learning, 1–17. https://doi.org/10.1080/10986065.2023.2177818
  • Määttä, S., Hannula-Sormunen, M. M., Halme, H., & McMullen, J. (2022). Guiding students’ attention towards multiplicative relations around them: A classroom intervention. Journal of Numerical Cognition, 8(1), 36–52. https://doi.org/10.5964/jnc.6363
  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf
  • Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52. https://doi.org/10.1207/s15326985ep4001_3
  • Ninaus, M., Kiili, K., McMullen, J., & Moeller, K. (2017). Assessing fraction knowledge by a digital game. Computers in Human Behavior, 70, 197–206. https://doi.org/10.1016/j.chb.2017.01.004
  • Nunes, T., & Bryant, P. E. (2015). The development of mathematical reasoning. Handbook of Child Psychology and Developmental Science., 1–48 John Wiley & Sons, Inc. https://doi.org/10.1002/9781118963418.childpsy217
  • Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge University Press.
  • Purpura, D. J., Napoli, A. R., Wehrspann, E. A., & Gold, Z. S. (2017). Causal connections between mathematical language and mathematical knowledge: A dialogic reading intervention. Journal of Research on Educational Effectiveness, 10(1), 116–137. https://doi.org/10.1080/19345747.2016.1204639
  • Rathé, S., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Spontaneous focusing on Arabic number symbols and its association with early mathematical competencies. Early Childhood Research Quarterly, 48, 111–121. https://doi.org/10.1016/j.ecresq.2019.01.011
  • Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235–252. https://doi.org/10.1080/10573569.2015.1030995
  • Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology. Human Perception and Performance, 36(5), 1227–1238. https://doi.org/10.1037/a0018170
  • Siegler, R. S., Thompson, C. A., & Opfer, J. E. (2009). The logarithmic-to-linear shift: One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3(3), 143–150. https://doi.org/10.1111/j.1751-228X.2009.01064.x
  • Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001
  • Siemon, D., Breed, M., Virgona, J. (2005). From additive to multiplicative thinking: The big challenge of the middle years [Paper presentation]. Proceedings of the 42nd Conference of the Mathematical Association of Victoria. Bundoora: The Mathematical Association of Victoria (pp. 278–286). Mav.
  • Van Hoof, J., Degrande, T., McMullen, J., Hannula-Sormunen, M. M., Lehtinen, E., Verschaffel, L., & Van Dooren, W. (2016). The relation between learners’ spontaneous focusing on quantitative relations and their rational number knowledge. Studia Psychologica, 58(2), 156–170. https://doi.org/10.21909/sp.2016.02.714
  • Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39–56. https://doi.org/10.1007/s10649-015-9613-3
  • Verschaffel, L., Rathé, S., Wijns, N., Degrande, T., van Dooren, W., De Smedt, B., & Torbeyns, J. (2020). Young children’s early mathematical competencies: The role of mathematical focusing tendencies. In M. Carlsen, I. Erfjord, & P. S. Hundeland (eds.), Mathematics Education in the Early Years. Springer, Cham. https://doi.org/10.1007/978-3-030-34776-5_2
  • Wijns, N., De Smedt, B., Verschaffel, L., & Torbeyns, J. (2020). Are preschoolers who spontaneously create patterns better in mathematics? The British Journal of Educational Psychology, 90(3), 753–769. https://doi.org/10.1111/bjep.12329
  • Yang Hansen, K., Gustafson, J. E., & Rosén, M. (2014). School performance differences and policy variations in Finland, Norway and Sweden. In K. Y. Hansen, J.-E. Gustafsson, M. Rosén, S. Sulkunen, K. Nissinen, P. Kupari, R. F. Ólafsson, J. K. Björnsson, L. S. Grønmo, L. Rønberg, & J. Mejding (Eds.), Northern lights on TIMSS and PIRLS (pp. 25–47). Nordic Council of Ministers.