A Conceptual Approach to Calculus Made Possible by Technology

Thompson, Patrick W; Byerley, Cameron; Hatfield, Neil

doi:10.1080/07380569.2013.768941

Cited by 67 publications

(20 citation statements)

References 17 publications

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“…Researchers such as Thompson et al (2013) suggest the use of a conceptual approach to teach calculus as a better option compared to the traditional approach. The traditional approach commonly known as the procedural approach may be defined as lecturer-led with direct instruction of rules or procedures for solving problems (Peal, 2010).…”

Section: Errors In Trigonometrymentioning

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: Errors In Trigonometrymentioning

confidence: 99%

Analysis of errors in derivatives of trigonometric functions

Siyepu

2015

IJ STEM Ed

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“…The definite integral is interpreted as Riemann sums in numerical terms and also means the area limited by curves in graphical terms. From an algebraic perspective, the Fundamental Theorem of Calculus or the operation of taking the integral is in the foreground (Thompson, Byerley, & Hatfield, 2013). Making connections using numerical, graphical, and algebraic representations, and helping students to understand the definite integral concept, are among the basic targets of calculus (Goerdt, 2007).…”

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confidence: 99%

Conceptual Understanding of Definite Integral with GeoGebra

Tatar

Zengin

2016

Computers in the Schools

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“…Thompson et al (2013) emphasise an approach that allows students to explore variation and covariation in a technological environment, prior to leading up to the study of the FTC. They designed a digital environment that simulates the 'bottle problem', in which water accumulates in a bottle: the participants were asked to graph the volume of water in the bottle as a function of its height.…”

Section: The Learning Of Calculus In Dynamic Environmentsmentioning

confidence: 99%

Comparing Calculus Communication across Static and Dynamic Environments Using a Multimodal Approach

2016

Digit Exp Math Educ

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In this article, a thinking-as-communicating approach is used to analyse calculus students' thinking in two environments. The first is a 'static' environment in the sense of static visual representations, such as those found in textbook diagrams, while the second is a dynamic environment as exploited by the use of dynamic geometry environments (DGEs). The purpose of the article is to compare calculus students' communication as it is facilitated by each of these two environments, and to explore the role of paper-and digital-mediated representations for positioning certain ways of thinking about calculus. The analysis provides evidence that the participants employed different modes of communicationutterances, gestures and touchscreen-dragging -and they communicated about fundamental calculus ideas differently when prompted by different types of representations. The study presents implications for teaching dynamic aspects of functions and calculus, and argues for a multimodal view of communication to capture the use of gestures and dragging for communicating dynamic and temporal mathematical relationships.

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A Conceptual Approach to Calculus Made Possible by Technology

Cited by 67 publications

References 17 publications

Analysis of errors in derivatives of trigonometric functions

Analysis of errors in derivatives of trigonometric functions

Conceptual Understanding of Definite Integral with GeoGebra

Comparing Calculus Communication across Static and Dynamic Environments Using a Multimodal Approach

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