International Electronic Journal of Mathematics Education

A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2009 - Volume 4 Issue 3, pp. 195-226
  • Published Online: 12 Dec 2009
  • Article Views: 482 | Article Download: 497
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Abrahamson D. A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory. Int Elect J Math Ed. 2009;4(3), 195-226.
APA 6th edition
In-text citation: (Abrahamson, 2009)
Reference: Abrahamson, D. (2009). A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory. International Electronic Journal of Mathematics Education, 4(3), 195-226.
Chicago
In-text citation: (Abrahamson, 2009)
Reference: Abrahamson, Dor. "A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory". International Electronic Journal of Mathematics Education 2009 4 no. 3 (2009): 195-226.
Harvard
In-text citation: (Abrahamson, 2009)
Reference: Abrahamson, D. (2009). A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory. International Electronic Journal of Mathematics Education, 4(3), pp. 195-226.
MLA
In-text citation: (Abrahamson, 2009)
Reference: Abrahamson, Dor "A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory". International Electronic Journal of Mathematics Education, vol. 4, no. 3, 2009, pp. 195-226.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Abrahamson D. A Student’s Synthesis of Tacit and Mathematical Knowledge as a Researcher’s Lens on Bridging Learning Theory. Int Elect J Math Ed. 2009;4(3):195-226.

Abstract

What instructional materials and practices will help students make sense of probability notions? Li (11 years) participated in an interview-based implementation of a design for the binomial. The design was centered around an innovative urn-like random generator, creating opportunities to reconcile two mental constructions of anticipated outcome distributions: (a) holistic perceptual judgments based in tacit knowledge of population-to-sample relations and implicitly couched in terms of the aggregate events with no attention to permutations on these combinations; and (b) classicist-probability analytic treatment of ratios between the subset of favorable to all elemental events with attention to the permutations. We argue that constructivist and sociocultural perspectives on mathematics learning can be reconciled by revealing interactions of intuitive and formal resources in individual development of deep conceptual understanding. Learning is the guided process of blending two constructions of problematized situations: the phenomenologically immediate and the semiotically mediated.

References

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