Education
p-ISSN: 2162-9463 e-ISSN: 2162-8467
2013; 3(4): 221-230
doi:10.5923/j.edu.20130304.02
Michela Maschietto
Department of Education and Human Sciences, University of Modena e Reggio Emilia, Reggio Emilia, 42121, Italy
Correspondence to: Michela Maschietto, Department of Education and Human Sciences, University of Modena e Reggio Emilia, Reggio Emilia, 42121, Italy.
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Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved.
This paper concerns the use of instruments in teaching and learning mathematics at primary and secondary school levels. It focuses on the introduction and use of the arithmetical machine Zero+1, called pascaline, and its relationships with other instruments used by students to write numbers and make operations, as spike abacus or calculator. The analysis of three teaching experiments shows that the instruments are related with respect to their utilization schemes, but also to their representations.
Keywords: Artifact, Arithmetical Machine, Instrument, Mathematics Laboratory, System of Instruments
Cite this paper: Michela Maschietto, Systems of Instruments for Place Value and Arithmetical Operations: an Exploratory Study with the Pascaline, Education, Vol. 3 No. 4, 2013, pp. 221-230. doi: 10.5923/j.edu.20130304.02.
Figure 1. The arithmetical machine Zero+1 (pascaline). It is produced and sold by the Italian company “Quercetti” (http://www.quercetti.it) |
Figure 2. The pascaline by B.Pascal (1642)[16] |
Figure 3. Graphical representations of a system of artifacts[8] |
Figure 4. Pascaline for base five[8] |
Figure 5. Five-bag |
Figure 6. System of instruments |
Figure 7. Drawing 3 in students’ worksheet |
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