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Interpreting histograms. As easy as it seems?

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Abstract

Histograms are widely used, but recent studies have shown that they are not as easy to interpret as it might seem. In this article, we report on three studies on the interpretation of histograms in which we investigated, namely, (1) whether the misinterpretation by university students can be considered to be the result of heuristic reasoning, (2) whether we could influence performance by stimulating or hindering the analytic processing of histograms, and (3) whether experts still show signs of this heuristic misinterpretation. We found that both university students and experts show signs of incorrect heuristic reasoning when comparing the mean of two data sets presented by histograms. Stimulating or hindering analytic processing did not affect performance. These indications of heuristic reasoning and the impossibility to affect this analytic processing suggest that the incorrect heuristic misinterpretation of histograms is very persistent. Implications for theory and methodology, scientific and educational practice are discussed.

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Notes

  1. This is of course only the case when the histogram represents absolute frequencies, not in the case of relative frequencies or cumulative frequencies. In this manuscript, we will only address frequency histograms.

  2. Cohen’s d between 0.2 and 0.3 can be considered a small effect, around 0.5 the effect can be considered medium, and a Cohen’s d of 0.8 or higher can be considered to be large (Cohen, Manion, & Morrison 2007).

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Acknowledgments

Stephanie Lem holds a PhD fellowship of the Research Foundation – Flanders (Fonds Wetenschappelijk Onderzoek – Vlaanderen). This research was partially supported by grant GOA 2006/01 “Developing adaptive expertise in mathematics education” from the Research Fund KU Leuven, Belgium.

Author information

Authors and Affiliations

  1. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, PO Box 3773, 3000, Leuven, Belgium

    Stephanie Lem, Lieven Verschaffel & Wim Van Dooren

  2. Methodology of Educational Sciences Research Group, KU Leuven, Dekenstraat 2, PO Box 3700, 3000, Leuven, Belgium

    Patrick Onghena

Authors
  1. Stephanie Lem
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  2. Patrick Onghena
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  3. Lieven Verschaffel
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  4. Wim Van Dooren
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Corresponding author

Correspondence to Stephanie Lem.

Additional information

Stephanie Lem. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2 PO Box 3773, 3000 Leuven, Belgium

Current themes of research:

Problem solving. Statistics education. Graphical representations. Dual-process theories of reasoning.

Most relevant publications in the field of Psychology of Education:

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning and Instruction, 26(4), 22–35.

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). On the misinterpretation of histograms and box plots. Educational Psychology: An International Journal of Experimental Educational Psychology, 33(2), 155–174.

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). External representations for data distributions: in search of cognitive fit. Statistics Education Research Journal, 12(1), 4–19.

Lem, S., Van Dooren, W., Gillard, E., Verschaffel, L. (2011). Sample size neglect problems: A critical analysis. Studia Psychologica, 53(2), 123–135.

Lem, S., Van Dessel, K., Vanhoof, S., Onghena, P. (2011). Attitudes toward statistics: How do they evolve during students’ curriculum and what is the relation with students’ evaluation of their course?. Mediterranean Journal for Research in Mathematics Education, 10(1–2), 43–60.

Patrick Onghena. Methodology of Educational Sciences Research Group, KU Leuven, Dekenstraat 2 PO Box 3700, 3000 Leuven, Belgium

Current themes of research:

Statistics education. N = 1 experiments. Mixed methods research. Nonparametric statistics.

Most relevant publications in the field of Psychology of Education:

Luwel, K., Foustana, A., Onghena, P., Verschaffel, L. (2013). The role of verbal and performance intelligence in children’s strategy selection and execution. Learning & Individual Differences, 24, 134–138.

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning and Instruction, 26(4), 22–35.

Schillemans, V., Luwel, K., Onghena, P., Verschaffel, L. (2011). The influence of the previous strategy on individuals’ strategy choices. Studia Psychologica, 53(4), 339–350.

Castro Sotos, A., Vanhoof, S., Van Den Noortgate, W., Onghena, P. (2007). Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2, 98–113.

Gielen, S., Peeters, E., Dochy, F., Onghena, P., Struyven, K. (2010). Improving the effectiveness of peer feedback for learning. Learning and Instruction, 20(4), 304–315.

Lieven Verschaffel. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2 PO Box 3773, 3000 Leuven, Belgium

Current themes of research:

Problem solving. Mathematics education. Learning and instruction.

Most relevant publications in the field of Psychology of Education:

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning and Instruction, 26(4), 22–35.

Dewolf, T., Van Dooren, W., Verschaffel, L. (2011). Upper elementary school children’s understanding and solution of a quantitative problem inside and outside the mathematics class. Learning and Instruction, 21(6), 770–780.

Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27(3), 421–438.

De Smedt, B., Ansari, D., Grabner, R., Hannula-Sormunen, M., Schneider, M., Verschaffel, L. (2011). Cognitive neuroscience meets mathematics education: It takes two to tango. Educational Research Review, 6(3), 232–237.

De Smedt, B., Torbeyns, J., Stassens, N., Ghesquière, P., Verschaffel, L. (2010). Frequency, efficiency and flexibility of indirect addition in two learning environments. Learning and Instruction, 20(3), 205–215.

Wim Van Dooren. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2 PO Box 3773, 3000 Leuven, Belgium

Current themes of research:

Problem solving. Mathematics education. The use of representations in mathematical problem solving. Intuitionsand biases in human reasoning. Conceptual change.

Most relevant publications in the field of Psychology of Education:

Lem, S., Onghena, P., Verschaffel, L., Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning fand Instruction, 26(4), 22–35.

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.

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(2), 323–330.

Acevedo Nistal, A., Van Dooren, W., Verschaffel, L. (2012). What counts as a flexible representational choice? An evaluation of students’ representational choices to solve linear function problems. Instructional Science, 40(6), 999–1019.

Van Hoof, J., Lijnen, T., Verschaffel, L., Van Dooren, W. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education, 15(2), 154–164

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Lem, S., Onghena, P., Verschaffel, L. et al. Interpreting histograms. As easy as it seems?. Eur J Psychol Educ 29, 557–575 (2014). https://doi.org/10.1007/s10212-014-0213-x

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  • DOI: https://doi.org/10.1007/s10212-014-0213-x

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