Visual Roots of Mathematical Symbols

  • Ferdinand D. Rivera
Part of the Mathematics Education Library book series (MELI, volume 49)


In my Algebra 1 class, solving for the unknown in a linear equation occurred when they had to deal with reversal tasks in patterning situations such as item 4 in Fig. 4.1. Figure 4.2 shows the written work of Dung (eighth grader, Cohort 1), who understood the process of solving for the unknown in the context of finding a particular stage number p whose total number of objects is known. As shown in the figure, he initially took 1 away from 73 and then divided the result by 3. For Dung and his classmates, this particular process of undoing has been drawn from their everyday experiences in which doing and undoing form a natural and intuitive action pair. When my Cohort 1 participated in a teaching experiment on patterning and generalization in sixth grade, the first time I saw them use the undoing strategy occurred in the context of the patterning activity shown in Fig. 4.3. When they were confronted with the situation in item 21, the first thought that came to them was to take away the height of the original cup hold and then divide the result by 3.


Teaching Experiment Number Line Seventh Grade Stage Number Mathematical Symbol 
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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsSan Jose State UniversitySan Jose CaliforniaUSA

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