Skip to main content

The Curricular Geometries of *SAMBA* Schools: Fractal Dimensions, Surface, Depth, and Recursion

  • Chapter
  • First Online:
Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches
  • 315 Accesses


A collaboration between academics and a community arts group leads to a new geometry of curriculum development, implementation, and evaluation. The new concepts are fractal dimension, surface, depth, and recursion. Interweaving interdisciplinary curriculum and taking action projects, in and out of school, looks like recursive fractals where the surface contains its own depth when interpreted in terms of Euclidean geometry. Important characteristics include dimensional flow (the changing dimensionality in fractal space time) and the ease of recognizing the depth of hegemonic commonsense.

SAMBA, SAMBA SAMBA, Do you know what it means?

It’s not your favorite toothpaste; it’s not your favorite jeans.

SAMBA, SAMBA, SAMBA: DO YOU know what it means??








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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 59.99
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

Similar content being viewed by others


  1. 1.

    Regime shifts typically happen when a smooth change in an internal process (feedback) or a single disturbance (external shocks) triggers a significantly different system behavior. Although such nonlinear changes have been widely studied in different disciplines, ranging from atoms to climate dynamics, regime shifts have gained particular power in ecology, because they can dramatically impact the flow of ecosystem services that societies depend on, such as food distribution, clean water, or climate regulation. Indeed, regime shifts are expected to increase as human influence on the planet increases (the ‘Anthropocene’), including human induced climate change and decreases in biodiversity.

  2. 2.

    An unfortunate word choice that is demonstrative in two ways: (1) as an example of how the language of curriculum indicates a hegemonic depth of Euclidean geometry—even our way of conceiving of theory is steeped in images that place our thinking and being in a Euclidean space time field. We are approaching an object, the curriculum, located in our view from another point in space, our position. (2) The words we are using, the surface of curriculum theory and practice, contains within itself its own depth.


  • Appelbaum, P. (2009). Taking action—Mathematics curricular organization for effective teaching and learning. For the Learning of Mathematics, 29(2), 38–43.

    Google Scholar 

  • Appelbaum, P. (2010). Retrodictive curriculum reform. Journal for the American Association for the Advancement of Curriculum Reform, 6. Retrieved from

  • Appelbaum, P. (2014). Liminal, permeable regions and metaphoric scale: Strategies for avoiding orientalism and reification in trans-national curriculum studies. Journal of the American Association for the Advancement of Curriculum Studies. 10(1). Retrieved from

  • Appelbaum, P. (2016). Disordered order, ordered disorder: Threads, folds and artistic action. In H. Straehler-Pohl, A. Pais, & N. Bohlman (Eds.), The disorder of mathematics education (pp. 273–290). Berlin: Springer.

    Google Scholar 

  • Appelbaum, P. (In press). How to be a political social change mathematics education activist. In M. Jurdak, & R. Vithal (Eds.), Socio-political dimensions of mathematics education: Voices from margin to mainstream. Monograph of the International Conference on Mathematics Education Topic Study Group on Social and Political Dimensions of Mathematics Education. New York: Springer.

    Google Scholar 

  • Boal, A. (2006). The aesthetics of the oppressed. New York: Routledge.

    Google Scholar 

  • Calcagni, G. (2012). Geometry of fractional spaces. Advanced Theoretical Mathematical Physics, 16, 549–644.

    Article  Google Scholar 

  • Goldby, M. (1994). William Kentridge, painter. Revue Noire, 11(December, January/February), 20–23.

    Google Scholar 

  • Illich, I. (1980). Vernacular values. Philosophica, 26(2), 47–102.

    Google Scholar 

  • Kentridge, W. (2014). Six drawing lessons. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Macalalag, A., & Parker, K. (2016). Graduate education course for elementary school teachers: Fostering knowledge of science and the engineering design process. Pennsylvania Teacher Educator, 15, 109–131.

    Google Scholar 

  • Magill, M. (2000). Vik Muniz. Bomb, 73(fall). Retrieved from

  • Muniz, V. (1996). Surface tension. Parkett, 46. Retrieved from

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.

    Google Scholar 

  • Peterson, K., Crow, M., & Macalalag, A. (2016). Uncovering elementary teachers’ notions of engineering design practices using video-captured instruction. Pennsylvania Teacher Educator, 15, 133–150.

    Google Scholar 

  • Rancière, J. (2009). The emancipated spectator. London: Verso.

    Google Scholar 

  • Stathopoulou, C., & Appelbaum, P. (2017). Polysemic provocations of border negotiation. Provocaçôes polissêmicas da negociação fronteiriça. Las provocaciones polisémicas de la negociación fronteriza. Educação Temática Digital. 3(July–September). Retrieved from

  • Walker, L., Harley, K., & Jardim, J. (2010). Wasteland. London: Almega Projects.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Peter Appelbaum .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 The Author(s)

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Appelbaum, P. (2018). The Curricular Geometries of *SAMBA* Schools: Fractal Dimensions, Surface, Depth, and Recursion. In: Gerofsky, S. (eds) Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches. Palgrave Pivot, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Palgrave Pivot, Cham

  • Print ISBN: 978-3-319-72522-2

  • Online ISBN: 978-3-319-72523-9

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics