On Understanding the Notion of Limits and Infinitesimal Quantities

Parameswaran, Revathy

doi:10.1007/s10763-006-9050-y

Cited by 20 publications

(6 citation statements)

References 23 publications

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“…Calculus requires a high level of conceptual understanding, yet many students struggle to make sense of differentiation (Paramenswaran 2007;Siyepu, 2013a). Some students show an inadequate understanding of the concepts of function and variable (Barnes, 1995;Siyepu, 2013a).…”

Section: Students' Understanding Of First Principles Of Differentiationmentioning

confidence: 99%

Analysis of errors in derivatives of trigonometric functions

Siyepu

2015

IJ STEM Ed

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Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students' understanding of mathematics. The purpose of this study was to identify errors and their origins when students did calculations in derivatives of trigonometric functions. The participants of this study were a group of thirty students who were registered for Mathematics in a university of technology in Western Cape, South Africa. The researcher used a qualitative case study approach and collected data from students' written work. This study used Dubinsky's (1991) APOS Theory (Actions, Processes, Objects, and Schemas) to classify errors into categories and analyse the data collected.Results: Errors displayed by students were conceptual and procedural; there were also errors of interpretation and linear extrapolation. Conceptual errors showed a failure to grasp the concepts in a problem and a failure to appreciate the relationships in a problem. Procedural errors occurred when students failed to carry out manipulations or algorithms, even if concepts were understood. Interpretation errors occurred when students wrongly interpreted a concept due to over-generalisation of the existing schema. Linear extrapolation errors occurred when students over-generalised the property f(a + b) = f(a) + f(b), which applies only when f is a linear function, to the form f(a * b) = f(a) * f(b), where f is any function and * any operation. The findings revealed that the participants were not familiar with basic operational signs such as addition, subtraction, multiplication and division of trigonometric functions. The participants demonstrated poor ability to simplify once they had completed differentiation. Conclusions: This study recommends the strategy of focusing on elimination of errors to develop students' understanding of derivatives of trigonometric functions. This can be done through learning activities that lead to identification and analyses of students' errors in classroom discussions.

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Section: Students' Understanding Of First Principles Of Differentiationmentioning

confidence: 99%

Analysis of errors in derivatives of trigonometric functions

Siyepu

2015

IJ STEM Ed

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“…Several studies (e.g., Bonotto, 2005;Ginsburg & Seo, 1999;Hiebert & Carpenter, 1992;Mack, 1995;Parameswaran, 2007;Raman, 2002) differentiate between informal and formal explanations. Informal explanations refer to explanations based on the informal knowledge that students bring to the classroom from their real-world experiences.…”

Section: Classifying Explanationsmentioning

confidence: 99%

Fifth-grade students’ use and preferences for mathematically and practically based explanations

Levenson

2009

Educ Stud Math

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This paper focuses on fifth-grade students' use and preference for mathematically (MB) and practically based (PB) explanations within two mathematical contexts: parity and equivalent fractions. Preference was evaluated based on three parameters: the explanation (1) was convincing, (2) would be used by the student in class, and (3) was one that the student wanted the teacher to use. Results showed that students generated more MB explanations than PB explanations for both contexts. However, when given a choice between various explanations, PB explanations were preferred in the context of parity, and no preference was shown for either type of explanation in the context of equivalent fractions. Possible bases for students' preferences are discussed.

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“…Çetin, 2009;Kepçeoğlu & Yavuz, 2016;Lee, 1992;N. Çetin, 2009;Parameswaran, 2007;Tall & Vinner, 1981;Williams, 1991, etc.). These studies generally focus on the effect of learning environment design on learning the concept of limit, student understanding of the formal definition of the limit, and misconceptions about the limit and the continuity.…”

Section: Introductionmentioning

confidence: 99%

“…Süreklilik, türev ve integral kavramlarının şekillendirilmesinde de temel teşkil eden önemli kavramlardan biri limittir (Arslan ve Çelik, 2013;Cornu, 2002Cornu, , N. Çetin, 2009. Çember içerisine yerleştirilen düzgün çokgenin kenar sayısının arttırılmasıyla alan hesabının yapılması (Millî Eğitim Bakanlığı [MEB], 2005), fonksiyonların asimptotlarının belirlenmesi, geometrik serilerin toplamının hesaplanması (Parameswaran, 2007), türev ve integral tanımlarının oluşturulması (Cornu, 2002;Denbel, 2014) gibi birçok durumda limit kavramına başvurulmaktadır. Bu bakımdan limit kavramının tam anlamıyla öğrenilmemesi durumunda analiz ya da genel matematik derslerine yönelik yüzeysel bilgiler edinilmesinin kaçınılmaz olacağı söylenebilir (Arslan ve Çelik, 2013; Özmantar ve Yeşildere, 2013; Lee, 1992).…”

Section: Introductionunclassified

“…Çetin, 2009;Kepçeoğlu ve Yavuz, 2016;N. Çetin, 2009;Parameswaran, 2007;Tall ve Vinner, 1981;Williams, 1991 vb.). Bu çalışmalarda genel olarak öğrenme ortamı tasarımının limit kavramının öğrenilmesine etkisi, limitin formal tanımına yönelik öğrenci anlamaları, limit ve süreklilik ile ilgili kavram yanılgılarının incelenmesine odaklanılmıştır.…”

Section: Introductionunclassified

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Investigation of Pre-Service Science Teachers' Graphical and Algebraic Understanding of the Concept of the Limit

Öztürk¹,

Sönmez²

2020

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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The limit, at the center of almost all subjects of analysis and general mathematics, is also covered in science teaching program. Even though the limit is more important for mathematics to be fully acquired in the mind, it has undeniable importance in different fields of science such as physics, chemistry, and biology. The fact that the concept of limit is mostly taught through graphs and algebraic operations in the general mathematics course instructed in the science teaching program renders it significant to examine pre-service teachers' graphical and algebraic understanding levels. Accordingly, the aim of this study is to examine pre-service science teachers' graphical and algebraic understanding levels concerning the concept of limit. The participants of the study are pre-service teachers in the first year of a science teaching program. Data were collected through an open-ended exam. The data were analyzed by graphical and algebraic understanding categorical scoring charts and are presented based on frequencies and percentages for indicators of each understanding level. The study found the pre-service teachers' graphical understanding of the concept of limit to be higher than their algebraic understanding. We think that the results obtained in this study will give faculty members an idea about teaching practices related to the concept of limit.

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On Understanding the Notion of Limits and Infinitesimal Quantities

Cited by 20 publications

References 23 publications

Analysis of errors in derivatives of trigonometric functions

Analysis of errors in derivatives of trigonometric functions

Fifth-grade students’ use and preferences for mathematically and practically based explanations

Investigation of Pre-Service Science Teachers' Graphical and Algebraic Understanding of the Concept of the Limit

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