Skip to main content
SpringerLink
Log in

Mathematical and Interdisciplinary Modeling in Optimizing Young Children’s Learning

  • Chapter
  • First Online:
Exploring Mathematical Modeling with Young Learners

Part of the book series: Early Mathematics Learning and Development ((EMLD))

Abstract

This chapter explores mathematical and interdisciplinary modeling within the early and elementary school years, where children’s learning potential often remains untapped. Interdisciplinary modeling, as used in this chapter, encompasses the STEM disciplines as well as aspects of the humanities. Different forms of modeling for grades K-6 are reviewed including model-eliciting activities and STEM-based modeling. Modeling contexts with a focus on cultural and community issues are also explored. To illustrate how elementary students can work effectively with these problems, an MEA and a follow-up STEM-based modeling problem implemented in fourth-grade classrooms (9-year-olds) are presented.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Anhalt, C. O., Cortez, R., & Smith, A. (2017). Mathematical modeling: Creating opportunities for participation in mathematics. In A. Fernandes, S. Crespo, & M. Civil (Eds.), Access and equity: Promoting high quality mathematics in grades 6-8 (pp. 105–119). Reston, VA: National Council of Teachers of Mathematics (NCTM).

    Google Scholar 

  • Anhalt, C. O., Staats, S., Cortez, R., & Civil, M. (2018). Mathematical modeling and culturally relevant pedagogy. In Y. J. Dori, Z. R. Mevarech, & D. R. Baker (Eds.), Cognition, metacognition, and culture in STEM education (pp. 307–330). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-66659-4_14

    Chapter  Google Scholar 

  • Anhalt, C. O., Turner, E. E., Aguirre, J. M., Foote, M.Q., & Roth McDuffie, A. (2018). The price of guacamole: Designing rigorous and relevant mathematical modeling tasks that build on the strengths of community and cultural contexts. Presentation at the bi-annual meeting of TODOS: Mathematics for all, Scottsdale, AZ.

    Google Scholar 

  • Arleback, J. B., Doerr, H. M., & O’Neil, A. H. (2013). A modeling perspective on interpreting rates of change in context. Mathematical Thinking and Learning, 15(4), 314–336. https://doi.org/10.1080/10986065.2013.834405

    Article  Google Scholar 

  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.

    Google Scholar 

  • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.

    Article  Google Scholar 

  • Bryan, L. A., Moore, T. J., Johnson, C. C., & Roehrig, G. H. (2015). Integrated STEM education. In C. C. Johnson, E. E. Peters-Burton, & T. J. Moore (Eds.), STEM road map: A framework for integrated STEM education (pp. 23–37). New York, NY: Routledge.

    Chapter  Google Scholar 

  • Bybee, R. W. (2013). The case for STEM education: Challenges and opportunities. Arlington, VA: NSTA Press.

    Google Scholar 

  • California Department of Education. (2018). Appendix B: Mathematical modeling of the mathematics framework for California public schools: Kindergarten through grade twelve. Sacramento, CA: California Department of Education. https://www.cde.ca.gov/ci/ma/cf/documents/mathfw-appendixb.pdf

    Google Scholar 

  • Carpenter, & Romberg. (2004). Powerful practices in mathematics and science. Madison, WI: National Center for Improving Student Learning and Achievement in Mathematics and Science.

    Google Scholar 

  • Carr, P. G. (2018, May 25). Implementing the proposed mathematics framework: Recommendations for PISA 2021. National Center for Education Statistics (NCES).

    Google Scholar 

  • Cirillo, M., Bartell, T. G., & Wager, A. A. (2016). Teaching mathematics for social justice through mathematical modeling. In C. Hirsch (Ed.), Annual perspectives in mathematics education: Mathematical modeling and modeling mathematics (pp. 87–96). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Common Core State Standards for Mathematics. (2013). http://www.corestandards.org/Math/

  • Crismond, D. P., & Adams, R. S. (2012). The informed design teaching and learning matrix. Journal of Engineering Education, 101(4), 738–797.

    Article  Google Scholar 

  • Dorie, B. L., Cardella, M. E., & Svarovsky, G. N. (2014). Capturing the design thinking of young children interacting with a parent. Paper presented at the 121st SEE annual conference & exposition, Indianapolis.

    Google Scholar 

  • English, L. D. (2010). Modeling with complex data in the primary school. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 287–300). New York, NY: Springer.

    Chapter  Google Scholar 

  • English, L. D. (2013). Modeling as a vehicle for philosophical inquiry in the mathematics classroom. The Journal of Analytic Teaching and Philosophical Praxis, 34(1), 46–57.

    Google Scholar 

  • English, L. D. (2014). Promoting statistical literacy through data modelling in the early school years. In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 441–458). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • English, L. D. (2017). Advancing elementary and middle school STEM education. International Journal of Science and Mathematics Education, 15(Supplement 1), 5–24.

    Article  Google Scholar 

  • English, L. D. (2018a, online first). Learning while designing in a fourth-grade integrated STEM problem. International Journal of Technology and Design Education. https://doi.org/10.1007/s10798-018-9482-z.

  • English, L. D. (2018b). Disruption and learning innovation across STEM. Plenary presented at the 5th international conference of STEM in education. Brisbane. https://stem-in-ed2018.com.au/proceedings-2/

  • English, L. D., Arleback, J. B., & Mousoulides, N. (2016). Reflections on progress in mathematical modelling research. In A. Gutierrez, G. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 383–413). Rotterdam, The Netherlands: Sense Publishers.

    Chapter  Google Scholar 

  • English, L. D., & King, D. T. (2015). STEM learning through engineering design: Fourth- grade students’ investigations in aerospace. International Journal of STEM Education, 2(14), 1–18.

    Google Scholar 

  • English, L. D., & King, D. T. (online, July 2018). STEM integration in 6th grade: Designing and constructing paper bridges. International Journal of Science and Mathematics Education. https://link.springer.com/journal/10763.10.1007/s10763-018-9912-0

  • English, L. D., & Moore, T. J. (2018). Early engineering learning. Singapore, Singapore: Springer.

    Book  Google Scholar 

  • English, L. D., & Sriraman, B. (2010). In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (Advances in mathematics education series, pp. 263–285). Berlin, Germany/Heidelberg, Germany: Springer.

    Google Scholar 

  • Gadanidis, G., & Hughes, J. (2011). Performing big math ideas across the grades. Teaching children mathematics, 17(8), 486–496.

    Article  Google Scholar 

  • Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3–36.

    Article  Google Scholar 

  • Garfunkel, S., & Montgomery, M. (Eds.). (2016). Guidelines for assessment and instruction in mathematical modeling education (GAIMME) report. Boston, MA: Consortium for Mathematics and Its Applications (COMAP)/Society for Industrial and Applied Mathematics (SIAM).

    Google Scholar 

  • Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modeling for life: Mathematics and children’s experience. In W. Blum, W. Henne, & M. Niss (Eds.), Applications and modeling in mathematics education (ICMI study 14) (pp. 89–98). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Guidelines for assessment & instruction in mathematical modeling education (GAIMME, 2nd edn.). (2019). Consortium for Mathematics and Its Applications (COMAP) and Society for Industrial and Applied Mathematics (SIAM).

    Google Scholar 

  • Gunaratne, N. M., Fuentes, S., Gunaratne, T. M., Torrico, D. D., et al. (2019). Effects of packaging design on sensory liking and willingness to purchase: A study using novel chocolate packaging. Heliyon, https://doi.org/10.1016/j.heliyon.2019.e01696

  • Honey, M., Pearson, G., & Schweingruber (Eds.). (2014). STEM integration in K-12 education: Status, prospects, and an agenda for research. Washington, DC: National Academies Press.

    Google Scholar 

  • Kelley, T. R., & Sung, E. (2016). Sketching by design: Teaching sketching to young learners. International Journal of Technology and Design Education, 27(3). https://doi.org/10.1007/s10798-016-9354-3

  • Kennedy, N. S. (2012). Lipman, Dewey, and philosophical inquiry in the mathematics classroom. Education and Culture, 28(2), 81–94.

    Article  Google Scholar 

  • Leavy, A., & Hourigan, M. (2018). The role of perceptual similarity, context, and situation when selecting attributes: Considerations made by 5–6-year-olds in data modeling environments. Educational Studies in Mathematics, 97, 163–183.

    Article  Google Scholar 

  • Lehrer, R., & English, L. D. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (Springer international handbooks of education) (pp. 229–260). Springer.

    Google Scholar 

  • Lehrer, R., Jones, R. S., & Kim, M. J. (2014, July). Model-based informal inference. Paper presented at the 9th international conference on teaching statistics, Flagstaff, AZ.

    Google Scholar 

  • Lehrer, R., & Romberg, T. (1996). Exploring children’s data modeling. Cognition and Instruction, 14(1), 69–108.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Inventing data structures for representational purposes: Elementary grade students’ classification models. Mathematical Thinking and Learning, 2, 49–72.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (Eds.). (2002). Investigating real data in the classroom: Expanding children’s understanding of math and science. New York, NY: Teachers College Press.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 635–679.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2005). Developing modeling and argument in the elementary grades. In T. Romberg, T. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 29–53). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Lesh, R., & Doerr, H. (Eds.). (2003a). Beyond constructivism: Models and modeling perspectives on mathematics problem solving learning and teaching. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R., & Doerr, H. M. (2003b). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Erlbaum.

    Chapter  Google Scholar 

  • Lesh, R., English, L. D., & Sevis, & S. Riggs, C. (2013). Modeling as a means for making powerful ideas accessible to children at an early age. In S. Hegedus & J. Roschelle (Eds.), The SimCalc vision and contributions: Democratizing access to important mathematics (pp. 419–436). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Lipman, M. (1988). Philosophy goes to school. Philadelphia, PA: Temple University Press.

    Google Scholar 

  • Lucas, B., Claxton, G., & Hanson, J., (2014). Thinking like an engineer: Implications for the education system. A report for the Royal Academy of Engineering Standing Committee for Education and Training. Royal Academy of Engineers.

    Google Scholar 

  • Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1–24. https://doi.org/10.1080/10986065.2016.1107820

    Article  Google Scholar 

  • McKenna, A. F. (2014). Adaptive expertise and knowledge fluency in design and innovation. In A. Johri & B. M. Olds (Eds.), Cambridge handbook of engineering education research (pp. 227–242). New York, NY: Cambridge University Press.

    Chapter  Google Scholar 

  • Moore, T. J., & Smith, K. A. (2014). Advancing the state of the art of STEM integration. Journal of STEM Education, 15(1), 5–10.

    Google Scholar 

  • Mukhopadhyay, S., & Greer, B. (2007). How many deaths? Education for statistical empathy. In B. Sriraman (Ed.), International perspectives on social justice in mathematics education (pp. 169–189). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Next Generation Science Standards: For States by States (2014). https://www.nextgenscience.org/search/node. Accessed 21 Feb 2019.

  • OECD. (2015). PISA 2015 draft mathematics framework. Paris, France: OECD Publishing.

    Google Scholar 

  • OECD. (2018). PISA for development mathematics framework. In In PISA for development assessment and analytical framework: Reading, mathematics and science. Paris, France: OECD Publishing. https://doi.org/10.1787/9789264305274-5-en

    Chapter  Google Scholar 

  • Poling, L. P., Naresh, N., & Goodson-Espy, T. (2018). Empowering mathematics through modeling. Mathematics Teaching in the Middle School, 24(3), 138–146.

    Article  Google Scholar 

  • Portsmore, M., Watkins, J., & McCormick, M. (2012). Planning, drawing and elementary students in an integrated engineering design and literacy activity. Paper presented at the 2nd P-12 Engineering and Design Education Research Summit. Washington, DC.

    Google Scholar 

  • Shaughnessy, M. (2013). By way of introduction: Mathematics in a STEM context. Mathematics Teaching in the Middle School, 18(6), 324.

    Article  Google Scholar 

  • Splitter, L. (1995). Teaching for better thinking: The classroom community of inquiry. Melbourne, Australia: The Australian Council for Educational Research.

    Google Scholar 

  • Suh, J., Britton, L., Burke, K., Matson, K., Ferguson, L., Jamieson, S., & Seshaiyer, P. (2018). Every penny counts: Promoting community engagement to engage students in mathematical modeling. In I. Goffney & R. Gutierrez (Eds.), Rehumanizing mathematics for black, indigenous, and Latinx students (pp. 63–76). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Suh, J. M., Matson, K., & Seshaiyer, P. (2017). Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Educational Sciences, 7(62). https://doi.org/10.3390/educsci7020062

  • Suh, J. M., & Seshaiyer, P. (2019). Co-designing and implementing PBL through mathematical modeling in STEM contexts. In M. Moallem, W. Hung, & N. Dabbagh (Eds.), Handbook of problem based learning (pp. 529–550). Hoboken, NJ: Wiley-Blackwell Publishing.

    Chapter  Google Scholar 

  • Turner, E. E., Aguirre, J. M., Foote, M. Q. Anhalt, C. O., Roth McDuffie, A., Civil, M. (2018). Mathematizing the world: Routines and tasks that foster mathematical modeling with cultural and community contexts. Presentation at the bi-annual meeting of TODOS: Mathematics for all, Scottsdale, AZ.

    Google Scholar 

  • Turner, E. E., Aguirre, J. M., Foote, M. Q., & Roth McDuffie, A. M. (2018, April) Learning to leverage mathematical resources of elementary Latinx children through community-based mathematical modeling tasks. In M. Civil (Chair), Foregrounding cultural ways of being in mathematics teacher education: Cases From Latinx and Pāsifika communities. Presentation as part of a symposium at the annual research conference of the annual meeting of the American Educational Research Association, New York, NY.

    Google Scholar 

  • Vasquez, J., Sneider, C., & Comer, M. (2013). STEM lesson essentials, grades 3–8: Integrating science, technology, engineering, and mathematics. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Wright, N., & Wrigley, C. (2017). Broadening design-led education horizons: Conceptual insights and future research directions. International Journal of Technology and Design Education, 27(4).

    Google Scholar 

  • Zawojewski, J. (2010). Problem solving versus modeling. In R. A. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237–244). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Zawojewski, J. S., Hjalmarson, M. A., Bowman, K. J., & Lesh, R. (2008). A modeling perspective on learning and teaching in engineering education. In J. S. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education: Designing experiences for all students (pp. 1–16). Rotterdam, The Netherlands: Sense Publishers.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Queensland University of Technology, Brisbane, QLD, Australia

    Lyn D. English

Authors
  1. Lyn D. English
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lyn D. English .

Editor information

Editors and Affiliations

  1. College of Education and Human Development, George Mason University, Fairfax, VA, USA

    Jennifer M. Suh

  2. Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA

    Megan H. Wickstrom

  3. Queensland University of Technology, Brisbane, QLD, Australia

    Lyn D. English

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

English, L.D. (2021). Mathematical and Interdisciplinary Modeling in Optimizing Young Children’s Learning. In: Suh, J.M., Wickstrom, M.H., English, L.D. (eds) Exploring Mathematical Modeling with Young Learners. Early Mathematics Learning and Development. Springer, Cham. https://doi.org/10.1007/978-3-030-63900-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-63900-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63899-3

  • Online ISBN: 978-3-030-63900-6

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation