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Student‐Invented Numeration Systems: Pattern‐Analysis and Mathematical Understanding
Author(s) -
Senger Elizabeth S.
Publication year - 1997
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/j.1949-8594.1997.tb17357.x
Subject(s) - task (project management) , consistency (knowledge bases) , computer science , base (topology) , mathematics education , arithmetic , perception , cognitive science , artificial intelligence , psychology , mathematics , engineering , mathematical analysis , systems engineering , neuroscience
Thirteen fifth graders were given an assignment to invent their own numeration systems, following a unit on bases and a look at early events in the history of numbers. The task presented options that required the students to make decisions (such as whether to use a base, which base to use, design of symbols, etc.), and build a rationale for the elements of their system. Analyses of patterns embedded in their invented systems provided an assessment of student understanding of numeration. The progression of more and less complex thinking related to the student's choice of a base other than 10, consistency of logic throughout the system in words and symbols, rationale for change, and perception of real life examples that would change if the system was adopted. The invention task is presented as another way to make connections.