Bootstrapping mental constructions: a learning system about negative numbers

  • Baruch B. Schwarz
  • Amy S. Kohn
  • Lauren B. Resnick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 608)


In this paper, we propose a new model for learning mathematical concepts which cannot develop informally. This is a “middle-out“ approach in which the objects of the system can be mapped both to formal knowledge and to real-life problems. We hypothesize that the key process which governs the acquisition of knowledge within such learning systems is reasoning with mental models, which we hold to be similar to the acquisition of basic mathematical constructs in non-school settings. The paper reports the development of a system for learning negative numbers and a study in which two pairs of students were exposed to that system.


Word Problem Number Line Negative Number Exemplification Component Planning Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Brown, A. Collins, P. Duguid: Situated cognition and the Culture of Learning. BBN Report No. 6886, BBN Laboratories, Cambridge, MA, 1989Google Scholar
  2. 2.
    J. G. Greeno: Number Sense as Situated Knowing in a Conceptual Domain. Journal for Research in Mathematics Education, 22(3), 170–219, 1991Google Scholar
  3. 3.
    P. Nesher: Microworlds in Education: A Pedagogical Realism. In L. Resnick (Ed.), Knowing, Learning and Instruction, Essays in Honor of Robert Glaser, 187–216, 1989Google Scholar
  4. 4.
    I. Peled, L. B. Resnick: Building semantic computer models for teaching number systems and word problems. In J. C. Bergeron, N. Herskovics & C. Kieran (Eds). Proceedings of the 11th Annual Conference of the Psychology of Mathematics Education, 2, 184–190. Montreal, 1987Google Scholar
  5. 5.
    B. Y. White: Intermediate Causal Models: The Missing Links for Successful Science Education?. In R. Glaser (Ed.), Advances in Instructional Psychology, 4, Lawrence Erlbaum & Associates, Hilldale, NJ, in pressGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Baruch B. Schwarz
    • 1
  • Amy S. Kohn
    • 1
  • Lauren B. Resnick
    • 1
  1. 1.Learning Research and Development CenterUniversity of PittsburghUSA

Personalised recommendations