Unveiling Elementary School Students' Thinking Processes In Conquering The Natural Number Bias

References

1. Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628. https://doi.org/10.1037/EDU0000384.
2. Braithwaite, D. W., & Siegler, R. S. (2018). Developmental changes in the whole number bias. Developmental Science, 21(2), e12541. https://doi.org/10.1111/desc.12541.
3. Christou, K. P., Pollack, C., Van Hoof, J., & Van Dooren, W. (2020). Natural number bias in arithmetic operations with missing numbers–a reaction time study. Journal of Numerical Cognition, 6(1), 22–49. https://doi.org/10.5964/jnc.v6i1.228.
4. Clark, R. E., Feldon, D., vanMerrienboer, J., Yates, K, and Early, S. (In Press for August2007). Cognitive Task Analysis. In Spector, J. M., Merrill, M. D., van Merriënboer, J. J.G., & Driscoll, M. P. (Eds.) Handbook of research on educational communications andtechnology (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associate
5. Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124–130.
6. Daker, R. J., & Lyons, I. M. (2018). Numerical and non-numerical predictors of first graders’ number-line estimation ability. Frontiers in Psychology, 9, https://doi.org/10.3389/fpsyg.2018.02336.
7. Deliyianni, E., Gagatsis, A., Elia, I., & Panaoura, A. (2016). Representational flexibility and problem-solving ability in fraction and decimal number addition: A structural model. International Journal of Science and Mathematics Education, 14, 397–417. https://doi.org/10.1007/S10763-015-9625-6
8. Fyfe, E. R., McNeil, N. M., & Borjas, S. (2015). Benefits of “concreteness fading” for children’s mathematics understanding. Learning and Instruction, 35, 104–120. https://doi.org/10.1016/J.LEARNINSTRUC.2014.10.004.
9. Getenet, S., & Callingham, R. (2021). Teaching interrelated concepts of fraction for understanding and teacher’s pedagogical content knowledge. Mathematics Education Research Journal, 33(2), 201–221. https://doi.org/10.1007/s13394-019-00275-0.
10. González-Forte, J. M., Fernández, C., Van Hoof, J., & Van Dooren, W. (2020). Various ways to determine rational number size: An exploration across primary and secondary education. European Journal of Psychology of Education, 35(3), 549–565. https://doi.org/10.1007/s10212-019-00440-w.
11. González-Forte, J. M., Fernández, C., Van Hoof, J., & Van Dooren, W. (2022a). Profiles in understanding operations with rational numbers. Mathematical Thinking and Learning, 24(3), 230–247. https://doi.org/10.1080/10986065.2021.1882287
12. González-Forte, J. M., Fernández, C., Van Hoof, J., & Van Dooren, W. (2022b). Profiles in understanding operations with rational numbers. Mathematical Thinking and Learning, 24(3), 230–247. https://doi.org/10.1080/10986065.2021.1882287.
13. Judd, N., & Klingberg, T. (2021). Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children. Nature Human Behaviour, 5(11), 1548–1554. https://doi.org/10.1038/s41562-021-01118-4.
14. Kahneman, D. (2011). Don’t Blink! The Hazards of Confidence.”. New York Times, 19.
15. Iuculano, T., & Butterworth, B. (2011). Understanding the real value of fractions and decimals. Quarterly Journal of Experimental Psychology, 64, 2088-2098. https://doi.org/10.1080/17470218.2011.604785.
16. Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371–387. https://doi.org/10.1016/j.jecp.2013.01.005.
17. Merriënboer, J. J. G. van. (2010). Innovatief onderwijs ontwerpen in het gezondheidsdomein. Maastricht University.
18. Meert, G., Grégoire, J., & Noël, M. (2010). Comparing the magnitude of two fractions with common components: which representations are used by 10- and 12-year-olds?. Journal of experimental child psychology, 107 3, 244-59 . https://doi.org/10.1016/j.jecp.2010.04.008.
19. Michaelidou, E., & Gagatsis, A. (2005). The geometrical model of number line as a representation of equivalence and addition of fractions.
20. Namkung, J. M., & Fuchs, L. S. (2016). Cognitive predictors of calculations and number line estimation with whole numbers and fractions among at-risk students. Journal of Educational Psychology, 108(2), 214. https://doi.org/10.1037/EDU0000055.
21. 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.
22. Obersteiner, A., Hoof, J. Van, Verschaffel, L., & Dooren, W. Van. (2016). Who can escape the natural number bias in rational number tasks? A study involving students and experts. British Journal of Psychology, 107(3), 537–555. https://doi.org/10.1111/bjop.12161.
23. Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72. https://doi.org/10.1016/J.LEARNINSTRUC.2013.05.003.
24. Ren, K., & Gunderson, E. A. (2019). Malleability of whole-number and fraction biases in decimal comparison. Developmental Psychology, 55(11), 2263. psychology. https://doi.org/10.1037/dev0000797.
25. Schneider, M., Merz, S., Stricker, J., De Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta‐analysis. Child Development, 89(5), 1467–1484. https://doi.org/10.1111/cdev.13068.
26. Schraagen, J. M., Chipman, S. F., & Shalin, V. L. (2000). Cognitive task analysis. Psychology Press.
27. Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994-2004. https://doi.org/10.1037/a0031200.
28. Stalmeijer, R. E., McNaughton, N., & Van Mook, W. N. K. A. (2014). Using focus groups in medical education research: AMEE Guide No. 91. Medical Teacher, 36(11), 923–939. https://doi.org/10.3109/0142159X.2014.917165.
29. Sun, X. H., Xin, Y. P., & Huang, R. (2019). A complementary survey on the current state of teaching and learning of Whole Number Arithmetic and connections to later mathematical content. ZDM, 51, 1–12. https://doi.org/10.1007/S11858-019-01041-Z.
30. Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344–355. https://doi.org/10.1016/J.JMATHB.2012.02.001.
31. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics. Pearson.
32. Van Hoof, J., Janssen, R., Verschaffel, L., & Van Dooren, W. (2015). Inhibiting natural knowledge in fourth graders: towards a comprehensive test instrument. ZDM, 47(5), 849–857. https://doi.org/10.1007/S11858-014-0650-7.
33. Van Hoof, J., Verschaffel, L., De Neys, W., & Van Dooren, W. (2020). Intuitive errors in learners’ fraction understanding: A dual-process perspective on the natural number bias. Memory & Cognition, 48, 1171–1180. https://doi.org/10.3758/s13421-020-01045-1.
34. Woods, D. M., Ketterlin Geller, L., & Basaraba, D. (2018). Number sense on the number line. Intervention in School and Clinic, 53(4), 229–236. https://doi.org/10.1177/1053451217712971

Keywords

Natural number bias, number sense, number line, Cognitive Task Analysis

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