Skip to main content

The Genesis of Modeling in Kindergarten

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

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Success in mathematics, both in school and out, is dependent on a strong start in early childhood. Indeed, a considerable body of research has demonstrated that children’s early numeracy competence has been found to be highly predictive of their future mathematical success in school (e.g., Mazzocco & Thompson, 2005; Romano, Babchishin, & Pagani, 2010). For example, kindergarteners’ counting skills, their knowledge of symbolic representations of number (e.g., reading and interpreting written numerals), and their judgments about the relative magnitude of quantities (e.g., knowing that 7 is larger than 5 but smaller than 10) are predictive of their achievement at the end of the first grade (Jordan, Kaplan, Locuniak, & Ramineni, 2007; Martin, Cirino, Sharp, & Barnes, 2014); other studies have shown that early numeracy skills predict achievement in the third grade (Jordan, Glutting, & Ramineni, 2010; Jordan, Kaplan, Ramineni, & Locuniak, 2009) and beyond (Duncan et al., 2007; Geary, Hoard, Nugent, & Bailey, 2013; Watts, Duncan, Siegler, & Davis-Kean, 2014).

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

Access this chapter

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., Cortez, R., & Bennett, A. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20, 202–221. https://doi.org/10.1080/10986065.2018.1474532

    Article  Google Scholar 

  • Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523–545. https://doi.org/10.1007/s10857-015-9309-8

    Article  Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

    Article  Google Scholar 

  • Bautista, A., Wilkerson-Jerde, M. H., Tobin, R. G., & Brizuela, B. M. (2014). Mathematics teachers’ ideas about mathematical models: A diverse landscape. PNA, 9, 1–28.

    Article  Google Scholar 

  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 73–96). https://doi.org/10.1007/978-3-319-12688-3_9

    Chapter  Google Scholar 

  • Blum, W., & Leiss, D. (2007). How do students and teachers deal with modeling problems? In C. R. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Modeling (ICTMA–12): Education, engineering and economics (pp. 222–231). Chichester, UK: Horwood Publishing.

    Google Scholar 

  • Borromeo Ferri, R., & Blum, W. (2009). Mathematical modelling in teacher education – experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education: CERME 6 (pp. 2046–2055). Lyon, France: INRP.

    Google Scholar 

  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Education Research Journal, 26, 499–531. https://doi.org/10.3102/00028312026004499

    Article  Google Scholar 

  • Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29, 3–20.

    Article  Google Scholar 

  • Carpenter, T. P., Franke, M. L., Johnson, N. C., Turrou, A. C., & Wager, A. A. (2016). Young children’s mathematics: Cognitively guided instruction in early childhood education. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Cetinkaya, B., Kertil, M., Erbas, A. K., Korkmaz, H., Alacaci, C., & Cakiroglu, E. (2016). Pre-service teachers’ developing conceptions about the nature and pedagogy of mathematical modeling in the context of a mathematical modeling course. Mathematical Thinking and Learning, 18, 287–314. https://doi.org/10.1080/10986065.2016.1219932

    Article  Google Scholar 

  • Diefes-Dux, H. A., Zawojewski, J. S., Hjalmarson, M. A., & Cardella, M. E. (2012). A framework for analyzing feedback in a formative assessment system for mathematical modeling problems. Journal of Engineering Education, 101(2), 375–406.

    Article  Google Scholar 

  • Doerr, H. M. (2006). Teachers’ ways of listening and responding to students’ emerging mathematical models. ZDM, 38, 255–268. https://doi.org/10.1007/BF02652809

    Article  Google Scholar 

  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, W.-G. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 69–78). New York, NY: Springer Science & Business Media.

    Chapter  Google Scholar 

  • Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.

    Article  Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japeli, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. https://doi.org/10.1037/0012-1649.44.1.217

    Article  Google Scholar 

  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2–3), 225–248. https://doi.org/10.1023/B:EDUC.0000006167.14146.7b

    Article  Google Scholar 

  • English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303–323.

    Article  Google Scholar 

  • English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22, 24–47.

    Article  Google Scholar 

  • Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2013). Adolescents’ functional numeracy is predicted by their school entry number system knowledge. PLoS One, 8, e54651. https://doi.org/10.1371/journal.pone.0054651

    Article  Google Scholar 

  • Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social policy report. Society for Research in Child Development, 22, 1–24.

    Google Scholar 

  • Glaser, B., & Strauss, A. (2014). Applying grounded theory. The Grounded Theory Review, 13(1), 46–50.

    Google Scholar 

  • Handal, B., & Bobis, J. (2004). Teaching mathematics thematically: Teachers’ perspectives. Mathematics Education Research Journal, 16, 3–18.

    Article  Google Scholar 

  • Henn, H. W. (2010). Modelling pedagogy: An overview. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modelling competencies (pp. 321–324). New York, NY: Springer.

    Google Scholar 

  • Hindman, A. H. (2013). Mathematics instruction in Head Start: Nature, extent, and contributions to children’s learning. Journal of Applied Developmental Psychology, 34, 230–240. https://doi.org/10.1016/j.appdev.2013.04.003

    Article  Google Scholar 

  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.

    Article  Google Scholar 

  • Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20, 82–88. https://doi.org/10.1016/j.lindif.2009.07.004

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22, 36–46. https://doi.org/10.1111/j.1540-5826.2007.00229.x

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850–867. https://doi.org/10.1037/a0014939

    Article  Google Scholar 

  • Kaiser, G., & Maass, K. (2007). Modelling in lower secondary mathematics classrooms – problems and opportunities. In W. Blum, P. Galbraith, W.-G. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 99–108). New York, NY: Springer Science & Business Media.

    Chapter  Google Scholar 

  • Kaiser, G., Schwarz, B., & Tiedemann, S. (2013). Future teachers’ professional knowledge on modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies. ICTMA 13 (pp. 433–444). New York, NY: Springer.

    Chapter  Google Scholar 

  • Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100, 716–725. https://doi.org/10.1037/0022-0663.100.3.716

    Article  Google Scholar 

  • LeFevre, J. A., Fast, L., Sowinski, C., Osana, H. P., Skwarchuk, S. L., & Manay Quian, N. (2009). Who’s counting? Numeracy and literacy practices of early learning and child care practitioners. Canadian council on learning final report. Ottawa, ON: Canadian Council on Learning.

    Google Scholar 

  • Lesh, R., English, L. D., Chanda, R., & Serife, S. (2013). Problem solving in the primary school (K-2). The Mathematics Enthusiast, 10, 35–59.

    Article  Google Scholar 

  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 665–708). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5, 109–129. https://doi.org/10.1080/10986065.2003.9679996

    Article  Google Scholar 

  • Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models and modelling perspectives on mathematics problem solving, learning, and teaching? In W. Blum, P. Galbraith, W.-G. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 161–170). New York, NY: Springer Science & Business Media.

    Chapter  Google Scholar 

  • Lingefjärd, T. (2013). Teaching mathematical modeling in teacher education: Efforts and results. In X.-S. Yang (Ed.), Mathematical modeling with multidisciplinary applications (pp. 57–80). Holboken, NJ: Wiley.

    Chapter  Google Scholar 

  • Martin, R. B., Cirino, P. T., Sharp, C., & Barnes, M. (2014). Number and counting skills in kindergarten as predictors of grade 1 mathematical skills. Learning and Individual Differences, 34, 12–23. https://doi.org/10.1016/j.lindif.2014.05.006

    Article  Google Scholar 

  • Mazzocco, M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research & Practice, 20, 142–155. https://doi.org/10.1111/j.1540.5826.2005.00129.x

    Article  Google Scholar 

  • National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, DC: National Academies Press.

    Google Scholar 

  • Paolucci, C., & Wessels, H. (2017). An examination of preservice teachers’ capacity to create mathematical modeling problems for children. Journal of Teacher Education, 68, 330–344. https://doi.org/10.1177/0022487117697636

    Article  Google Scholar 

  • Romano, E., Babchishin, L., & Pagani, L. S. (2010). School readiness and later achievement: Replication and extension using a nationwide Canadian survey. Developmental Psychology, 46, 995–1007. https://doi.org/10.1037/a0018880

    Article  Google Scholar 

  • Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM, 47(7), 1241–1254.

    Article  Google Scholar 

  • Sriraman, B., & Lesh, R. A. (2006). Modeling conceptions revisited. ZDM, 38(3), 247–254.

    Article  Google Scholar 

  • Stender, P., & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM, 47(7), 1255–1267.

    Article  Google Scholar 

  • Stillman, G. A., Blum, W., & Kaiser, G. (Eds.). (2017). Mathematical modelling and applications: Crossing and researching boundaries in mathematics education. New York, NY: Springer.

    Google Scholar 

  • Stipek, D. (2013). Mathematics in early childhood education: Revolution or evolution? Early Education & Development, 24, 431–435. https://doi.org/10.1080/10409289.2013.777285

    Article  Google Scholar 

  • Thomas, K., & Hart, J. (2010). Pre-service teachers’ perceptions of model eliciting activities. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies. ICTMA 13 (pp. 531–530). New York, NY: Springer.

    Chapter  Google Scholar 

  • Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling in the elementary school: A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28, 577–601. https://doi.org/10.2307/749692

    Article  Google Scholar 

  • Watts, T. W., Duncan, G. J., Siegler, R. S., & Davis-Kean, P. E. (2014). What’s past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43, 352–360. https://doi.org/10.3102/0013189X14553660

    Article  Google Scholar 

  • Zawojewski, J. S., Lesh, R. A., & English, L. D. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 337–358). New York, NY: Erlbaum.

    Google Scholar 

Download references

Acknowledgments

This research was made possible by funding from Concordia University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Helena P. Osana .

Editor information

Editors and Affiliations

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

Osana, H.P., Foster, K. (2021). The Genesis of Modeling in Kindergarten. 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_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-63900-6_13

  • 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