Skip to main content
Log in

On forests, trees, elephants, and classrooms: a brief for the study of learning ecologies

  • Commentary Paper
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

The classroom intervention studies in this volume, ranging from the study of gestures to that of systemic implementation, are at very different grain sizes. A challenge is to see the forest for the trees – to see how these studies, focusing on different aspects of mathematical activity at different grain sizes, can be seen as aspects of a coherent whole.

I propose an ecological metaphor for the study of mathematical activity. In ecological terms, the biosphere is comprised of interconnected and interrelated ecosystems. I argue that, analogously, there are nested and interrelated mathematical activity systems and structures in which “mathematical sense-making” plays the role of “health” in ecosystems. Moreover, what happens in the classroom environment shapes and is shaped by what happens in sub-ecologies of the classroom (e.g., sociomathematical norms, participation structures, communicational forms such as gesture, and representational tools and their use) and the larger social and organizational ecologies of which it is a part (building culture, support structures for teachers and teaching, external pressures such as testing and accountability systems etc).

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Alibali, M. W., Nathan, M. J., Church, R. B., Wolfgram, M. S., Kim, S., & Knuth, E. J. (2013). Teachers’ gestures and speech in mathematics lessons: forging common ground by resolving trouble spots. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0476-0 (this issue).

  • Harel, G. (2013) Classroom-based interventions in mathematics education: relevance, significance, and applicability. ZDM—The International Journal on Mathematics Education, 45(3) (this issue).

  • Jahnke, H. N., & Wambach, R. (2013). Understanding what a proof is: a classroom-based approach. ZDM—The International Journal on Mathematics Education, 45(3) (this issue).

  • Lehrer, R., Kobiela, M., & Weinberg, P. J. (2013). Cultivating inquiry about space in a middle school mathematics classroom. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0479-x (this issue).

  • Mariotti, M. A. (2013). Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-013-0495-5 (this issue).

  • National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington DC: National Academy Press.

    Google Scholar 

  • Roberts, N., & Stylianides, A. J. (2013). Telling and illustrating stories of parity: a classroom-based design experiment on young children’s use of narrative in mathematics. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0474-2 (this issue).

  • Ruthven, K., & Hofmann, R. (2013). Chance by design: devising an introductory probability module for implementation at scale in English early-secondary education. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0470-6 (this issue).

  • Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: a study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0466-2 (this issue).

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  • Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications (p. 2010). New York: Routledge.

    Google Scholar 

  • Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM Online. http://link.springer.com/content/pdf/10.1007%2Fs11858-012-0483-1.

  • Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education. Tools and processes in mathematics teacher education (Vol. 2, pp. 321–354). Rotterdam, Netherlands: Sense Publishers.

  • Shilling-Traina, L. N., & Stylianides, G. J. (2013). Impacting prospective teachers’ beliefs about mathematics. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0461-7 (this issue).

  • Stylianides, A. J., & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDM—The International Journal on Mathematics Education, 45(3) (this issue).

  • Tabach, M., Hershkowitz, R., & Dreyfus, T. (2013). Learning beginning algebra in a computer-intensive environment. ZDM—The International Journal on Mathematics Education, 45(3). doi:10.1007/s11858-012-0458-2 (this issue).

  • Wood, T., Cobb, P., Yackel, D., & Dillion D. (Eds.) (1992). Rethinking elementary school mathematics: Insights and issues. Journal for Research in Mathematics Education Monograph Number 6. Reston, VA: NCTM.

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alan H. Schoenfeld.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schoenfeld, A.H. On forests, trees, elephants, and classrooms: a brief for the study of learning ecologies. ZDM Mathematics Education 45, 491–495 (2013). https://doi.org/10.1007/s11858-013-0504-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-013-0504-8

Keywords

Navigation