Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

Biza, Irene; Christou, Constantinos; Zachariades, Theodossios

doi:10.1080/14794800801916457

Cited by 34 publications

(47 citation statements)

References 7 publications

(6 reference statements)

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“…The problem occurring here is that the student hereby can make an unintentionally distorted interpretation. This is also confirmed by more recent reports, e.g., Biza, Christou and Zachariades who describe students' perspectives and thinking about tangent lines [15], Rösken and Rolka who analyze students' conceptual learning regarding the notion of the definite integral [18].…”

Section: Introductionsupporting

confidence: 62%

“…Students either support a concept or reject it and their interpretation of this concept, as well as their capacity of understanding, can also be affected by their intuition [12][13][14]. The way the student adopts and interprets a mathematical concept also depends on influential factors that characterize students' thinking, like earlier achieved knowledge and experience as well as the situation where the concept occurs [15]. This means that the student visualizes the concept and creates a symbol or a mental model accordingly.…”

Section: Introductionmentioning

confidence: 99%

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On the concept image of complex numbers

Nordlander

2011

International Journal of Mathematical Education in Science and

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A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified in four categories in order to clarify the learning situation. Furthermore, this study also revealed a variety of misconceptions regarding this concept, and most of the misconceptions were also possible to refer to the classification system. In addition, results from an identification test show that students have difficulties discerning the basic property of complex numbers, i.e., that any number is a complex number.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

On the concept image of complex numbers

Nordlander

2011

International Journal of Mathematical Education in Science and

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“…Such misclassifications and related misinterpretations are prevalent in the cases involving functions and graphs (Vinner, 1991), limits (Davis & Vinner, ibid. ), derivatives (Zandieh, 2000), tangents (Biza, Christou & Zachariades, 2008) etc. One could argue that classifying according to a concept image amounts to using natural classification in a mathematical context; concept images might be similar in structure to natural categories while mathematical judgements need to be based on (or at least accord with) formal, agreed definitions.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Classification and Concept Consistency

Alcock

Simpson

2011

Canadian Journal of Science, Mathematics and Technology Educati

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This paper investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accepted definition, but does not necessarily capture the more basic notion that there should be a fixed basis for classification. We examine students' classification of real sequences before and after exposure to definitions of 'increasing' and 'decreasing'; we develop an abductive 'plausible explanations' method to estimate the consistency within the participants' responses and suggest that this provides evidence that many students may lack what we call 'concept consistency'.Running head: Classification and Concept Consistency

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“…For example, when students try to sketch the graph of the derived function they have difficulties relating the graph of the function with the analytical expression, and relating the idea of the tangent line with the derived function (Asiala, Cottrill, Dubinsky & Schwingendorf, 1997;Biza, Christou & Zachariades, 2008;Ferrini-Mundy & Graham, 1994). Achieving the relation between the analytical and graphical modes is gradual and depends on some characteristics of the functions, such as the existence of the cusp point (Baker, Cooley & Trigueros, 2000).…”

Section: Understanding the Derivative Conceptmentioning

confidence: 99%

Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

Sánchez-Matamoros

Fernández

2014

Int J of Sci and Math Educ

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Abstract. This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses pre-service teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers' progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

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Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

Cited by 34 publications

References 7 publications

On the concept image of complex numbers

On the concept image of complex numbers

Classification and Concept Consistency

Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

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