Errors In Using Convergence Tests In Infinite Series

Abstract

The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven open-ended questions. The data analysis was done using descriptive and content analysis techniques. Findings were presented as follows: inappropriate test selections; failure to check convergence criteria; incorrect use of a comparison test; limit comparison test error; re-test convergence test results; considering ∑ as a multiplicative function; misunderstanding of special series; considering that series has no character when the convergence test is inconclusive; confusing sequences with series; misunderstanding of the nth-term test; misinterpretation of convergence test results. Findings showed that students with insufficient procedural knowledge had difficulty in solving the given problem even if they understood it, whereas those with insufficient conceptual knowledge could not literally understand what they did even if they solved the problem. Therefore, the establishment of a moderate balance between procedural and conceptual knowledge in the learning of the convergence of series is essential in reducing the errors or learning difficulties for developing deep mathematical understanding

İlköğretim Matematik Öğretmenlerinin Kanıt Şemalarının İncelenmesi

“…Örneğin p ⇒ q şeklinde bir önermenin hükmünden yola çıkarak kanıtlarını yapılandırmaya çalışmışlar bunun doğruluğunu savunmuşlardır. p ⇒ q koşullu önermesinin doğrulanmasının istendiği durumlarda öğrencilerin q ⇒ p işe koşarak doğrulama yaptıkları (Genç & Akıncı, 2020;Laudien, 1999) veya p' ⇒ q' işe koşarak doğrulama yaptıkları (Antonini & Mariotti, 2007;Stylianides, Stylianides & Philippou, 2004) görülmüştür.…”