Skip to main content
SpringerLink
Log in

Situated Simulation-Based Learning Environment to Improve Proportional Reasoning in Nursing Students

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

Proportional reasoning is the basis for most medication calculation processes and is fundamental for high-quality care and patient safety. We designed a simulated Medication Mathematics (siMMath) environment to support proportional reasoning in transitioning via concreteness fading between two mediators. The first mediator is simulated nursing tools of medication preparation. The second is a ratio-table setup which is used as a goal representation, which enables one to spatially hold in place different quantities in their relative proportion. We conducted a two-part study with nursing students. Part 1 was a quasi-experimental pretest–intervention–posttest design assessing the effectiveness of learning, by evaluating four categories of medical calculation questionnaire items (solid medications, unit conversion, concentrations, infusion rates). We used the Noelting proportional reasoning test to evaluate the generalizability and abstraction of proportional reasoning. Part 1 included an experimental group (n = 96) learning with siMMath, and a comparison group (n = 73) learning with an equation-based lecture approach. Part 2 employed a case study design to characterize the learning process. The experimental group’s learning gains were significantly higher than the comparison group’s for the two most challenging categories of the medication calculation problems questionnaire, namely concentrations and infusion rates. Furthermore, the experimental group’s learning gains were significantly higher than the comparison group’s for formal operational reasoning on the Noelting test. Students who used a ratio-table setup scored significantly higher on the Noelting posttest questionnaire. Nursing students who learned with the siMMath environment overcame difficulties in proportional reasoning to the highest levels and extended this understanding to other contexts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Abrahamson, D. (2013). Toward a taxonomy of design genres: Fostering mathematical insight via perception-based and action-based experiences. In J. P. Hourcade, E. A. Miller, & A. Egeland (Eds.), Proceedings of the 12th International Conference on Interaction Design and Children (IDC 2013) (pp. 218–227). New York, NY: Association for Computing Machinery.

    Chapter  Google Scholar 

  • Anderson, J. R., Reder, L. M., & Simon, H. A. (1996). Situated learning and education. Educational Researcher, 25(4), 5–11.

    Article  Google Scholar 

  • Aspden, P., Wolcott, J., Bootman, J. L., & Cronenwett, L. R. (2007). Preventing medication errors: Quality chasm series. Washington, DC: National Academies Press.

    Google Scholar 

  • Bagnasco, A., Galaverna, L., Aleo, G., Grugnetti, A. M., Rosa, F., & Sasso, L. (2016). Mathematical calculation skills required for drug administration in undergraduate nursing students to ensure patient safety. A descriptive study: Drug calculation skills in nursing students. Nurse Education in Practice, 16(1), 33–39.

    Article  Google Scholar 

  • Bart, W. M., & Williams-Morris, R. (1990). A refined item digraph analysis of a proportional reasoning test. Applied Measurement in Education, 3(2), 143–165.

    Article  Google Scholar 

  • Basak, T., Aslan, O., Unver, V., & Yildiz, D. (2016). Effectiveness of the training material in drug-dose calculation skills. Japan Journal of Nursing Science, 13, 324–330.

    Article  Google Scholar 

  • Bates, D. W. (2007). Preventing medication errors: A summary. American Journal of Health, 64(14), S3–S9.

    Google Scholar 

  • Bindler, R., & Bayne, T. (1991). Medication calculation ability of registered nurses. Journal of Nursing Scholarship, 23(4), 221–224.

    Article  Google Scholar 

  • Brown, J., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42.

    Article  Google Scholar 

  • Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Carraher, T. N. (1986). From drawings to buildings: Working with mathematical scales. International Journal of Behavioral Development, 9(4), 527–544.

    Article  Google Scholar 

  • Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3(1), 21–29.

    Article  Google Scholar 

  • Coben, D., & Weeks, K. (2014). Meeting the mathematical demands of the safety-critical workplace: Medication dosage calculation problem-solving for nursing. Educational Studies in Mathematics, 86(2), 253–270.

    Article  Google Scholar 

  • Courtney-Clarke, M. & Wessels, H. (2014). Number sense of final year pre-service primary school teachers. Pythagoras, 35(1), Article 244, 1–9.

  • Deichert, D. L. (2014). The conceptual field of proportional reasoning researched through the lived experiences of nurses (Doctoral dissertation). Retrieved from Stars Electronic Theses and Dissertations. (UMI No. 660).

  • Draney, K., & Wilson, M. (2007). Application of the Saltus model to stagelike data: Some applications and current developments. In M. von Davier & C. H. Carstensen (Eds.), Multivariate and mixture distribution Rasch models (pp. 119–130). New York, NY: Springer.

    Chapter  Google Scholar 

  • Ercole, L. K., Frantz, M., & Ashline, G. (2011). Multiple ways to solve proportions. Mathematics Teaching in the Middle School, 16(8), 482–490.

    Google Scholar 

  • Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2–18.

    Article  Google Scholar 

  • Fyfe, E. R., McNeil, N. M., & Borjas, S. (2015). Benefits of “concreteness fading” for children’s mathematics understanding. Learning and Instruction, 35, 104–120.

    Article  Google Scholar 

  • Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9–25.

    Article  Google Scholar 

  • Glaister, K. (2007). The presence of mathematical and computer anxiety in nursing students and their effects on medication dosage calculations. Nurse Education Today, 27, 341–347.

    Article  Google Scholar 

  • Grandell-Niemi, N., Hupli, M., & Leino-Kilpi, M. (2005). Finnish nurses’ and nursing students’ pharmacological skills. Journal of Clinical Nursing, 6, 685–694.

    Article  Google Scholar 

  • Gravemeijer, K., & van Galen, F. (2003). Making mathematics reasonable in school: A research companion for the principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Greenfield, S., Whelan, B., & Cohn, E. (2006). Use of dimensional analysis to reduce medication errors. Journal of Nursing Education, 45(2), 91–94.

    Google Scholar 

  • Harries, C., & Botha, J. (2013). Assessing medical students’ competence in calculating drug doses. Pythagoras, 34(2), 1–9.

    Article  Google Scholar 

  • Harris, M. A., Pittiglio, L., Newton, S. E., & Moore, G. (2014). Using simulation to improve the medication administration skills of undergraduate nursing students. Nursing Education Perspectives, 35(1), 26–29.

    Article  Google Scholar 

  • Howe, C., Nunes, T., & Bryant, P. (2010). Intensive quantities: Why they matter to developmental research. British Journal of Developmental Psychology, 28(2), 307–329.

    Article  Google Scholar 

  • Howe, C., Nunes, T., & Bryant, P. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education, 9(2), 391–417.

    Article  Google Scholar 

  • Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work: The need for techno-mathematical literacies. New York, NY: Routledge.

    Book  Google Scholar 

  • Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2013). Mathematics in the workplace: Issues and challenges. In A. Damlamian, J. F. Rodrigues, & R. Sträßer (Eds.), Educational interfaces between mathematics and industry (Vol. 16, pp. 43–50). Cham, Switzerland: Springer.

    Chapter  Google Scholar 

  • Hoyles, C., Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32, 4–27.

    Article  Google Scholar 

  • Hughes, R. G. (Ed.). (2008). Patient safety and quality: An evidence-based handbook for nurses. Rockville, MD: Agency for Healthcare Research and Quality.

    Google Scholar 

  • Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures. New York, NY: Basic Books.

    Book  Google Scholar 

  • Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320, 454–455.

    Article  Google Scholar 

  • Kapborg, I. D. (1995). An evaluation of Swedish nurse students’ calculating ability in relation to their earlier educational background. Nurse Education Today, 15(1), 69–74.

    Article  Google Scholar 

  • Kaput, J. J., & West, M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235–287). Albany, NY: State University of New York Press.

    Google Scholar 

  • Kirshner, D., & Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35(4), 224–257.

    Article  Google Scholar 

  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics and learning: A project of the National Council of Teachers of Mathematics (pp. 629–666). Charlotte, NC: Information Age.

    Google Scholar 

  • Landy, D., & Goldstone, R. L. (2007). How abstract is symbolic thought? Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(4), 720–733.

    Google Scholar 

  • Landy, D., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. The Quarterly Journal of Experimental Psychology, 63(10), 1953–1968.

    Article  Google Scholar 

  • Lave, J. (1977). Cognitive consequences of traditional apprenticeship training in West Africa. Anthropology & Education Quarterly, 8(3), 177–180.

    Article  Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Macdonald, K., Weeks, K. W., & Moseley, L. (2013). Safety in numbers 6: Tracking pre-registration nursing students’ cognitive and functional competence development in medication dosage calculation problem-solving: The role of authentic learning and diagnostic assessment environments. Nurse Education in Practice, 13(2), e66–e77.

    Article  Google Scholar 

  • McMullan, M., Jones, R., & Lea, S. (2012). Math anxiety, self-efficacy, and ability in British undergraduate nursing students. Research in Nursing & Health, 35(2), 178–186.

    Article  Google Scholar 

  • Middleton, J. A., & van den Heuvel-Panhuizen, M. (1995). The ratio table. Mathematics Teaching in the Middle School, 1(4), 282–288.

    Google Scholar 

  • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept: Part I—differentiation of stages. Educational Studies in Mathematics, 11(2), 217–253.

    Article  Google Scholar 

  • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept: Part II—problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331–363.

    Article  Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers.Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Noss, R., Hoyles, C., & Pozzi, S. (2002). Abstraction in expertise: A study of nurses’ conceptions of concentration. Journal for Research in Mathematics Education, 33, 204–229.

    Article  Google Scholar 

  • Perlstein, P. H., Callison, C., White, M., Barnes, B., & Edwards, N. K. (1979). Errors in drug computations during newborn intensive care. American Journal of Diseases of Children, 133(4), 376–379.

    Google Scholar 

  • Piaget, J. (1950). The psychology of intelligence. London, UK: Lowe & Brydone.

    Google Scholar 

  • Price-Williams, D., Gordon, W., & Ramirez, M. (1969). Skill and conservation: A study of pottery-making children. Developmental Psychology, 1(6, Pt. 1), 769.

    Article  Google Scholar 

  • Reed, H. J., & Lave, J. (1981). Arithmetic as a tool for investigating between culture and cognition. In R. Casson (Ed.), Language, culture and cognition: Anthropological perspectives (pp. 437–455). New York, NY: Macmillan.

    Google Scholar 

  • Rice, J. N., & Bell, M. L. (2005). Using dimensional analysis to improve drug dosage calculation ability. Journal of Nursing Education, 44(7), 315–318.

    Google Scholar 

  • Saxe, G. B. (1988). Candy selling and math learning. Educational Researcher, 17(6), 14–21.

    Article  Google Scholar 

  • Schwartz, J. L. (1988). Intensive quantity and referent transforming arithmetic operations. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (Vol. 2, pp. 41–52). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1(2), 127–155.

    Article  Google Scholar 

  • Van Lancker, A., Baldewijns, K., Verhaeghe, R., Robays, H., Buyle, F., Colman, R., & Van Hecke, A. (2016). The effectiveness of an e-learning course on medication calculation in nursing students: A clustered quasi-experimental study. Journal of Advanced Nursing, 9, 2054–2064.

    Article  Google Scholar 

  • Vergnaud, G. (1982). Cognitive and developmental psychology and research in mathematics education: Some theoretical and methodological issues. For the Learning of Mathematics, 3(2), 31–41.

    Google Scholar 

  • Wright, K. (2004). An investigation to find strategies to improve student nurses’ math skill. British Journal of Nursing, 13, 1280–1284.

    Article  Google Scholar 

  • Wright, K. (2007). Student nurses need more than math to improve their drug calculating skills. Nurse Education Today, 27, 278–285.

    Article  Google Scholar 

  • Wright, K. (2008). Can effective teaching and learning strategies help student nurses to retain drug calculation skills? Nurse Education Today, 7, 856–864.

    Article  Google Scholar 

  • Wright, K. (2009). The assessment and development of drug calculation skills in nurse education—a critical debate. Nurse Education Today, 5, 544–548.

    Article  Google Scholar 

Download references

Acknowledgements

We appreciate and thank Ms. Dalit Wilhelm, the head of the clinical unit at the Cheryl Spencer Department of Nursing, University of Haifa, for her major contributions to planning and enacting the research, as well as a source of support. We are especially grateful to the nursing students who voluntarily participated in our research and whose insights helped to improve siMMath environment.

This research was supported in part by the Cheryl Spencer Institute of Nursing Research, University of Haifa, and by the MEITAL Foundation, which assists Israeli institutions of higher education in advancing the use of e-learning technologies.

Author information

Authors and Affiliations

  1. Faculty of Education, Department of Learning, Instruction and Teacher Education, University of Haifa, 199 Aba Khoushy Avenue, Mount Carmel, Haifa, Israel

    Ilana Dubovi & Sharona T. Levy

  2. Faculty of Social Welfare and Health Sciences, the Cheryl Spencer Department Nursing, University of Haifa, 199 Aba Khoushy Avenue, Mount Carmel, Haifa, 3498838, Israel

    Ilana Dubovi & Efrat Dagan

Authors
  1. Ilana Dubovi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sharona T. Levy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Efrat Dagan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilana Dubovi.

Electronic Supplementary Material

ESM 1

(DOCX 14 kb)

ESM 2

(DOCX 398 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dubovi, I., Levy, S.T. & Dagan, E. Situated Simulation-Based Learning Environment to Improve Proportional Reasoning in Nursing Students. Int J of Sci and Math Educ 16, 1521–1539 (2018). https://doi.org/10.1007/s10763-017-9842-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-017-9842-2

Keywords

Search

Navigation