Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 78

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Measuring fraction comparison strategies with eye-tracking

Obersteiner, Andreas, Tumpek, Christine·2016·ZDM

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/s11858-015-0742-z

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 1 references

Research works printed but not linked: 51

  1. Alibali, M. W., & Sidney, P. G. (2015). Variability in the natural number bias: who, when, how, and why. Learning and Instruction, 37, 56–61. doi: 10.1016/j.learninstruc.2015.01.003 . · DOI
  2. Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447–455. doi: 10.1016/j.jecp.2012.06.004 . · DOI · Paper page
  3. Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: a clinical teaching experiment. Journal of Research in Mathematics Education, 15, 323–341. doi: 10.2307/748423 . · DOI
  4. Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1985). Construct a sum: a measure of children’s understanding of fraction size. Journal for Research in Mathematics Education, 16, 120–131. doi: 10.2307/748369 . · doi:10.2307/748369
  5. Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33, 1410–1419. doi: 10.1037/0096-1523.33.6.1410 . · DOI
  6. Booth, J. L., & Newton, K. J. (2012). Fractions: could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37, 247–253. doi: 10.1016/j.cedpsych.2012.07.001 . · DOI
  7. Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. (1981). Results from the second mathematics assessment of the National Assessment of Educational Progress. Washington, DC: National Council of Teachers of Mathematics.
  8. Carraher, D. W. (1996). Learning about fractions. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 241–266). New Jersey: Lawrence Erlbaum Associates.
  9. Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72, 127–138. doi: 10.1007/s10649-009-9198-9 . · doi:10.1007/s10649-009-9198-9
  10. Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth- grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–144. doi: 10.2307/749646 . · DOI · Paper page
  11. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. doi: 10.1080/02643290244000239 . · DOI · Paper page
  12. DeWolf, M., Grounds, M. A., & Bassok, M. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40, 71–82. doi: 10.1037/a0032916 . · DOI
  13. Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87, 215–251. doi: 10.1037/0033-295X.87.3.215 . · DOI
  14. Faulkenberry, T. J., & Pierce, B. H. (2011). Mental representations in fraction comparison. Holistic versus component-based strategies. Experimental Psychology, 58, 480–489. doi: 10.1027/1618-3169/a000116 . · DOI
  15. Ganor-Stern, D., Karasik-Rivkin, I., & Tzelgov, J. (2011). Holistic representation of unit fractions. Experimental Psychology, 58, 201–206. doi: 10.1027/1618-3169/a000086 . · DOI
  16. Gómez, D. M., Jiménez, A., Bobadilla, R., Reyes, C., & Dartnell, P. (2015). The effect of inhibitory control on general mathematics achievement and fraction comparison in middle school children. ZDM Mathematics Education,. doi: 10.1007/s11858-015-0685-4 . · DOI
  17. Grant, E. R., & Spivey, M. J. (2003). Eye movements and problem solving: guiding attention guides thought. Psychological Science, 14, 462–466. doi: 10.1111/1467-9280.02454 . · DOI · Paper page
  18. Green, H. J., Lemaire, P., & Dufau, S. (2007). Eye movement correlates of younger and older adults’ strategies for complex addition. Acta Psychologica, 125, 257–278. doi: 10.1016/j.actpsy.2006.08.001 . · DOI
  19. Huber, S., Klein, E., Willmes, K., Nuerk, H.-C., & Moeller, K. (2014a). Decimal fraction representations are not distinct from natural number representations—evidence from a combined eye-tracking and computational modeling approach. Frontiers in Human Neuroscience, 8, 172. doi: 10.3389/fnhum.2014.00172 . · DOI
  20. Huber, S., Moeller, K., & Nuerk, H.-C. (2014b). Adaptive processing of fractions—evidence from eye-tracking. Acta Psychologica, 148, 37–48. doi: 10.1016/j.actpsy.2013.12.010 . · doi:10.1016/j.actpsy.2013.12.010
  21. Ischebeck, A., Schocke, M., & Delazer, M. (2009). The processing and representation of fractions within the brain. Neuroimage, 47, 403–413. doi: 10.1016/j.neuroimage.2009.03.041 . · DOI
  22. Ischebeck, A., Weilharter, M., & Körner, C. (2015). Eye movements reflect and shape strategies in fraction comparison. The Quarterly Journal of Experimental Psychology. Advance online publication. doi: 10.1080/17470218.2015.1046464 . · DOI
  23. Jacob, S. N., & Nieder, A. (2009a). Notation-independent representation of fractions in the human parietal cortex. The Journal of Neuroscience, 29, 4652–4657. doi: 10.1523/JNEUROSCI.0651-09.2009 . · doi:10.1523/jneurosci.0651-09.2009
  24. Jacob, S. N., & Nieder, A. (2009b). Tuning to non-symbolic proportions in the human frontoparietal cortex. European Journal of Neuroscience, 30, 1432–1442. doi: 10.1111/j.1460-9568.2009.06932.x . · DOI
  25. Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. doi: 10.1093/biomet/73.1.13 . · DOI · Paper page
  26. Matthews, P. G., & Chesney, D. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology, 78, 28–56. doi: 10.1016/j.cogpsych.2015.01.006 . · DOI
  27. Meert, G., Grégoire, J., & Noël, M.-P. (2009). Rational numbers: componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62, 1598–1616. doi: 10.1080/17470210802511162 . · DOI
  28. Meert, G., Grégoire, J., & Noël, M.-P. (2010a). Comparing 5/7 and 2/9: adults can do it by accessing the magnitude of the whole fractions. Acta Psychologica, 135, 284–292. doi: 10.1016/j.actpsy.2010.07.014 . · DOI
  29. Meert, G., Grégoire, J., & Noël, M.-P. (2010b). 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, 244–259. doi: 10.1016/j.jecp.2010.04.008 . · DOI
  30. Merkley, R., & Ansari, D. (2010). Using eye tracking to study numerical cognition: the case of the ratio effect. Experimental Brain Research, 206, 455–460. doi: 10.1007/s00221-010-2419-8 . · DOI
  31. Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educational Psychologist, 40, 27–52. doi: 10.1207/s15326985ep4001_3 . · DOI · Paper page
  32. Obersteiner, A., Dresler, T., Reiss, K., Vogel, C. M., Pekrun, R., & Fallgatter, A. J. (2010). Bringing brain imaging to the school to assess arithmetic problem solving. Chances and limitations in combining educational and neuroscientific research. ZDM—The International Journal on Mathematics Education, 42, 541–554. doi: 10.1007/s11858-010-0256-7 . · doi:10.1007/s11858-010-0256-7
  33. Obersteiner, A., Moll, G., Beitlich, J. T., Cui, C., Schmidt, M., Khmelivska, T., & Reiss, K. (2014). Expert mathematicians’ strategies for comparing the numerical values of fractions—evidence from eye movements. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 338–345). Vancouver: PME.
  34. 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. doi: 10.1016/j.learninstruc.2013.05.003 . · DOI · Paper page
  35. Padberg, F. (2009). Didaktik der Bruchrechnung (4th ed.). Heidelberg: Spektrum Akademischer Verlag. · DOI
  36. Robinson, K. M. (2001). The validity of verbal reports in children’s subtraction. Journal of Educational Psychology, 93, 211–222. doi: 10.1037/0022-0663.93.1.211 . · doi:10.1037/0022-0663.93.1.211
  37. Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36, 1227–1238. doi: 10.1037/a0018170 . · DOI · Paper page
  38. Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., Jacobs, A. M., & Stern, E. (2008). A validation of eye movements as a measure of elementary school children’s developing number sense. Cognitive Development, 23, 409–422. doi: 10.1016/j.cogdev.2008.07.002 . · DOI
  39. Sekuler, R., & Mierkiewicz, D. (1977). Children’s judgments of numerical inequality. Child Development, 48, 630–633. · doi:10.2307/1128664
  40. Siegler, R. S. (2013). Fractions: the new frontier for theories of numerical development. Trends in Cognitive Sciences, 17, 13–19. doi: 10.1016/j.tics.2012.11.004 . · DOI · Paper page
  41. Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691–697. doi: 10.1177/0956797612440101 . · DOI · Paper page
  42. Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49, 1994–20014. doi: 10.1037/a0031200 . · DOI · Paper page
  43. Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14, 503–518. doi: 10.1016/j.learninstruc.2004.06.015 . · DOI · Paper page
  44. Sullivan, J. L., Juhasz, B. J., Slattery, T. J, & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin and Review, 18, 557–563. doi: 10.3758/s13423-011-0081-1 . · DOI
  45. Szücs, D., & Goswami, U. (2007). Educational neuroscience: defining a discipline for the study of mental representations. Mind, Brain, and Education, 1, 114–127. doi: 10.1111/j.1751-228X.2007.00012.x . · DOI
  46. Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2014). Bridging the gap: fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction,. doi: 10.1016/j.learninstruc.2014.03.002 . · DOI
  47. Tzelgov, J., Ganor-Stern, D., Kallai, A., & Pinhas, M. (2014). Primitives and non-primitives of numerical representations. Oxford Handbooks Online. Retrieved 24 July 2015. http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199642342.001.0001/oxfordhb-9780199642342-e-019 . · doi:10.1093/oxfordhb/9780199642342.001.0001/oxfordhb-9780199642342-e-019
  48. Vamvakoussi, X. (2015). The development of rational number knowledge: old topics, new insights. Learning and Instruction, 37, 50–55. doi: 10.1016/j.learninstruc.2015.01.002 . · DOI
  49. Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2013). Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction- time study. Educational Studies in Mathematics, 82, 323–330. doi: 10.1007/s10649-012-9432-8 . · doi:10.1007/s10649-012-9432-8
  50. Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction, 14, 453–467. doi: 10.1016/j.learninstruc.2004.06.013 . · DOI · Paper page
  51. Van Hoof, J., Vandewalle, J., Verschaffel, L., & Van Dooren, W. (2015). In search for the natural number bias in secondary school students’ interpretation of the effect of arithmetical operations. Learning and Instruction, 37, 30–38. doi: 10.1016/j.learninstruc.2014.03.004 . · doi:10.1016/j.learninstruc.2014.03.004

Cited by

Metadata

Authors
Obersteiner, A., & Tumpek, C.
Venue
ZDM
Published
2015-10-28
Volume
48
Issue
3
Pages
255-266
ISSN
  • 1863-9690
  • 1863-9704
Cited by
78
References
1
Language
en
Licence
www.springer.com/tdm (tdm)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.