Abstract
Abstract Arithmetic sequence is used in this study as a means to explore pre‐service elementary school teachers’ connections between additive and multiplicative structures as well as several concepts related to introductory number theory. Vergnaud's theory of conceptual fields is used and refined to analyze students’ attempts to test membership of given numbers and to generate elements that are members of a given infinite arithmetic sequence. Our results indicate that participants made a strong distinction between two types of arithmetic sequences: sequences of multiples (e.g., 7, 14, 21, 28,…) and sequences of ‘non‐multiples,’ (e.g., 8, 15, 22, 29,…). Students were more successful in recognizing the underlying structure of elements in sequences of multiples, whereas for sequences of non‐multiples students often preferred algebraic computations and were mostly unaware of the invariant structure linking the two types. We examine the development of students’ schemes as they identify differences and similari...
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