Abstract
Twenty-three kindergarten and first grade children were asked to articulate the meaning and the need for punctuation marks in a list of numerals showing prices for a list of items. Despite not having been schooled yet formally on the use and roles of numerical punctuation, many children gave similar explanations regarding the purpose of punctuation marks in numerals, including: to separate, to mark the type of number (e.g., price), to denote value, to make it a different number, and to read the number differently. Each of these explanations is a partial description of the conventional use of these marks within written numbers. These findings provide evidence that children are, in fact, creating and recreating ideas about different aspects of written numbers such as the role of punctuation marks before necessarily being able to fully articulate how written numbers work and before being formally taught, though they have obviously been exposed from an early age to these particular aspects of written numbers.
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Notes
Throughout this paper, we will use “written numbers” and “numerals” as synonyms.
Throughout this paper, we will distinguish between “written numbers” and the NWS. Written numbers will be considered elements of the NWS. In turn, the NWS is comprised of those elements as well as the relations among those elements.
Theorems-in-action have been described as “mathematical relationships that are taken into account by students when they choose an operation or a sequence of operations to solve a problem” (Vergnaud 1988, p. 144), which are usually not expressed verbally, most of them are not explicit, and they may even be wrong. Other researchers have referred to these as hypotheses (Ferreiro 1986) or theories (Karmiloff-Smith and Inhelder 1974). Ferreiro (1986) has used the term “hypothesis” to refer broadly to ideas or systems of ideas constructed by children to explain the nature and way of functioning of written language as an object of knowledge.
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In keeping with the context in which the interviews reported in this paper occurred (in the United States of America [USA]), unless otherwise noted, throughout this paper we consider commas as marking place value within whole numbers (in some other countries, this role is taken up by periods) and periods as marking a separation between whole numbers and decimal fractions (in some other countries, this role is taken up by commas). This research was carried out through the support of Tufts University’s Faculty Research Award Committee (FRAC) program. Angie Collins, McKinne Dunn, Anja Pearson, and Patty Chen assisted in the data collection, analysis, and manuscript preparation.
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Brizuela, B.M., Cayton, G.A. The roles of punctuation marks while learning about written numbers. Educ Stud Math 68, 209–225 (2008). https://doi.org/10.1007/s10649-007-9109-x
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DOI: https://doi.org/10.1007/s10649-007-9109-x