Skip to main content

Comparison of perimeters: improving students’ performance by increasing the salience of the relevant variable

ZDM volume 48, pages 367–378 (2016)Cite this article

Abstract

Students’ difficulties in mathematics and science may stem from interference of irrelevant salient variables. We focus on the comparison of perimeters task, in which area is the irrelevant salient variable. A previous fMRI brain-imaging study related to the comparison of perimeters task suggested that increasing the level of salience of the relevant variable, perimeter, would increase participants’ performance. The brain imaging results support and enrich previous behavioral data, and thus contribute to the development of our research rationale and intervention design. In the present study we increased the level of salience of the relevant variable by drawing the perimeters of the shapes as built from separate units, matchsticks (discrete mode of presentation), rather than drawing them continuously. Such increase in salience draws participants’ attention to the perimeter. Thus strategies (such as moving of segments and/or counting them, or applying formal geometrical knowledge), that are regularly used when solving the comparison of perimeters task become more available. We explored whether the discrete mode would yield a higher success rate than the continuous mode and whether an intervention of first performing the discrete mode would improve students’ success in a subsequent continuous mode. Findings show that success in the discrete mode was higher than in the continuous mode. Moreover, success in the continuous mode increased as a result of the intervention (i.e., when performed after discrete mode). The current study suggests that altering the mode or order of presentation can serve as an educational tool that may improve students’ performance.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  • Aron, A. R., Robbins, T. W., & Poldrack, R. A. (2004). Inhibition and the right inferior frontal cortex. Trends in Cognitive Sciences, 8, 170–177.

    Article  Google Scholar 

  • Babai, R., Levyadun, T., Stavy, R., & Tirosh, D. (2006). Intuitive rules in mathematics and science: A reaction time study. International Journal of Mathematical Education in Science and Technology, 37, 913–924.

    Article  Google Scholar 

  • Babai, R., Sekal, R., & Stavy, R. (2010a). Persistence of the intuitive conception of living things in adolescence. Journal of Science Education and Technology, 19, 20–26.

    Article  Google Scholar 

  • Babai, R., Shalev, E., & Stavy, R. (2015). A warning intervention improves students’ ability to overcome intuitive interference. ZDM Mathematics Education, 47, 735–745.

    Article  Google Scholar 

  • Babai, R., Zilber, H., Stavy, R., & Tirosh, D. (2010b). The effect of intervention on accuracy of students’ responses and reaction times to geometry problems. International Journal of Mathematics and Science Education, 8, 185–201.

    Article  Google Scholar 

  • Brebner, J. T., & Welford, A. T. (1980). Introduction: An historical background sketch. In A. T. Welford (Ed.), Reaction Times (pp. 1–23). New York: Academic Press.

    Google Scholar 

  • Clement, J. (1993). Using bridging analogies and anchoring intuitions to deal with students’ preconceptions about physics. Journal of Research in Science Teaching, 30, 1241–1257.

    Article  Google Scholar 

  • D’Amore, B., & Fandiño Pinilla, M. I. (2006). Relationships between area and perimeter: Beliefs of teachers and students. Mediterranean Journal for Research in Mathematics Education, 5, 1–29.

    Google Scholar 

  • de Fockert, J. W., Rees, G., Frith, C. D., & Lavie, N. (2001). The role of working memory in visual selective attention. Science, 291, 1803–1906.

    Article  Google Scholar 

  • Dembo, Y., Levin, I., & Siegler, R. S. (1997). A comparison of the geometric reasoning of students attending Israeli ultraorthodox and mainstream schools. Developmental Psychology, 33, 92–103.

    Article  Google Scholar 

  • Denes, G., & Pizzamiglio, L. (1999). Handbook of clinical and experimental neuropsychology (pp. 28–30). Hove: Psychology Press.

    Google Scholar 

  • Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience, 15, 47–56.

    Article  Google Scholar 

  • Hoffer, A. R., & Hoffer, S. A. K. (1992). Geometry and visual thinking. In T. R. Post (Ed.), Teaching Mathematics in Grades K–8: Research-based Methods (2nd ed.). Boston: Allyn and Bacon.

    Google Scholar 

  • Lamy, D., Leber, A., & Egeth, H. E. (2004). Effects of task relevance and stimulus-driven salience in feature-search mode. Journal of Experimental Psychology: Human Perception and Performance, 30, 1019–1031.

    Google Scholar 

  • Lavie, N. (2005). Distracted and confused? Selective attention under load. Trends in Cognitive Sciences, 9, 75–82.

    Article  Google Scholar 

  • Lavie, N., Hirst, A., de Fockert, J. W., & Viding, E. (2004). Load theory of selective attention and cognitive control. Journal of Experimental Psychology: General, 133, 339–354.

    Article  Google Scholar 

  • Leikin, R., Leikin, M., Waisman, I., & Shaul, S. (2013). Effect of the presence of external representations on accuracy and reaction time in solving mathematical double-choice problems by students of different levels of instruction. International Journal of Mathematics and Science Education, 11, 1049–1066.

    Article  Google Scholar 

  • Lleras, A., & Von Mühlenen, A. (2004). Spatial context and top-down strategies in visual search. Spatial Vision, 17, 465–482.

    Article  Google Scholar 

  • Maglio, P. P., Matlock, T., Raphaely, D., Chernicky, B., & Kirsh, D. (1999). Interactive skill in Scrabble. Proceedings of the Twenty-first Annual Conference of the Cognitive Science Society (pp. 326–330). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Marchett, P., Medici, D., Vighi, P., & Zaccomer, E. (2005). Comparing perimeters and area children’s pre-conceptions and spontaneous procedures. Proceedings CERME, 4, 766–776.

    Google Scholar 

  • Martin, M. O., Mullis, I. V., Foy, P., & Stanco, G. M. (2012). TIMSS 2011 International Results in Science. Amsterdam: International Association for the Evaluation of Educational Achievement.

    Google Scholar 

  • Martin, T., & Schwartz, D. L. (2005). Physically distributed learning: Adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29, 587–625.

    Article  Google Scholar 

  • Martin, L., & Schwartz, D. L. (2014). A pragmatic perspective on visual representation and creative thinking. Visual Studies, 29, 80–93.

    Article  Google Scholar 

  • Minsky, M. (1985). The Society of Mind. New York: Simon & Schuster.

    Google Scholar 

  • Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 International Results in Mathematics. Amsterdam: International Association for the Evaluation of Educational Achievement.

    Google Scholar 

  • OECD (2014). PISA 2012 Results: What students know and can do: Student performance in mathematics, reading and science (Volume I, Revised edition, February 2014). OECD Publishing, Paris. doi: 10.1787/9789264208780-en.

  • Palatnik, A. (2009). The effect of presentation mode on students’ responses in comparison of perimeters task. Unpublished seminar work, Tel Aviv University, Tel Aviv, Israel. (In Hebrew).

  • Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron, 41, 983–993.

    Article  Google Scholar 

  • Shultz, T., Dover, A., & Amsel, E. (1979). The logical and empirical bases of conservation judgments. Cognition, 7, 99–123.

    Article  Google Scholar 

  • Sobel, K. V., & Cave, K. R. (2002). Roles of salience and strategy in conjunction search. Journal of Experimental Psychology: Human Perception and Performance, 28, 1055–1070.

    Google Scholar 

  • Stavy, R. (1991). Using analogy to overcome misconceptions about conservation of matter. Journal of Research in Science Teaching, 28, 305–313.

    Article  Google Scholar 

  • Stavy, R., & Babai, R. (2008). Complexity of shapes and quantitative reasoning in geometry. Mind, Brain, and Education, 2, 170–176.

    Article  Google Scholar 

  • Stavy, R., & Babai, R. (2010). Overcoming intuitive interference in mathematics: Insights from behavioral, brain imaging and intervention studies. ZDM - The International Journal on Mathematics Education, 42, 621–633.

    Article  Google Scholar 

  • Stavy, R., & Berkovitz, B. (1980). Cognitive conflict as a basis for teaching quantitative aspects of the concept of temperature. Science Education, 64, 679–692.

    Article  Google Scholar 

  • Stavy, R., Goel, V., Critchley, H., & Dolan, R. (2006). Intuitive interference in quantitative reasoning. Brain Research, 1073–1074, 383–388.

    Article  Google Scholar 

  • Stavy, R., & Tirosh, D. (2000). How Students (Mis-)understand Mathematics and Science. New York: Teachers College Press.

    Google Scholar 

  • Tamsut, E. (2014). The effect of a preliminary task which strengthens the conservation of perimeter on accuracy and reaction time of comparing perimeters. Unpublished Master’s thesis, Tel Aviv University, Tel Aviv, Israel. (In Hebrew).

  • Tirosh, D., & Tsamir, P. (1996). The role of representations in students’ intuitive thinking about infinity. International Journal of Mathematical Education in Science and Technology, 27, 33–40.

    Article  Google Scholar 

  • Tsamir, P. (2003). From “easy” to “difficult” or vice versa: The case of infinite sets. Focus on Learning Problems in Mathematics, 25, 1–17.

    Google Scholar 

  • Walter, N. (1970). A common misconception about area. Arithmetic Teacher, 17, 286–289.

    Google Scholar 

  • Woodward, E., & Byrd, F. (1983). Area: Included topic, neglected concept. School Mathematics and Science, 83, 343–347.

    Article  Google Scholar 

  • Zink, C. F., Pagnoni, G., Martin-Skurski, M. E., Chappelow, J. C., & Berns, G. S. (2004). Human striatal responses to monetary reward depend on saliency. Neuron, 42, 509–517.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Science and Technology Education, The Constantiner School of Education, Tel Aviv University, 6997801, Tel Aviv, Israel

    Reuven Babai, Laura Nattiv & Ruth Stavy

  2. Department of Mathematics, Science and Technology Education, The Sagol School of Neuroscience, Tel Aviv University, 6997801, Tel Aviv, Israel

    Reuven Babai & Ruth Stavy

Authors
  1. Reuven Babai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laura Nattiv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruth Stavy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reuven Babai.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Babai, R., Nattiv, L. & Stavy, R. Comparison of perimeters: improving students’ performance by increasing the salience of the relevant variable. ZDM Mathematics Education 48, 367–378 (2016). https://doi.org/10.1007/s11858-016-0766-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-016-0766-z

Keywords

  • Comparison of perimeters
  • Congruity
  • Continuous
  • Discrete
  • Intuitive interference
  • Mode of presentation
  • Salience