Associative and reflective connections between the limit of the difference quotient and limiting process

Hähkiöniemi, Markus

doi:10.1016/j.jmathb.2006.02.002

Cited by 19 publications

(12 citation statements)

References 13 publications

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“…Numerical, graphical and symbolic representation use by computers enables to better understand calculus concepts. [5,9,26,27,28 Barak et al [29] indicated that the use of animated movies promoted students' explanation ability and their understanding of scientific concepts. The findings also indicated that the students who studied science with the use of animated movies developed higher motivation to learn science, in terms of self-efficacy, interest and enjoyment, connection to daily life and importance to their future, compared to the control students.…”

Section: Resultsmentioning

confidence: 99%

“…Representations of a perception may be thought to pieces of procedural and conceptual knowledge. [5] During the last 10 years fast advancement of the computer sector led to discussions among different mathematicians groups. Some mathematicians while defending those technological applications in calculus instruction, shall be more influential in learning others due to the peculiar principals of mathematics concentrated on the disadvantages of computer technology.…”

Section: International Journal Of Mathematical Education In Science Amentioning

confidence: 99%

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Impact of computer animations in cognitive learning: differentiation

Altıparmak

2014

International Journal of Mathematical Education in Science and

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In mathematic courses, construction of some concepts by the students in a meaningful way may be complicated. In such circumstances, to embody the concepts application of the required technologies may reinforce learning process. Onset of learning process over daily life events of the student's environment may lure their attention and may enable them to gain from the preliminary knowledge. Therefore, a good initiation may be realized in the course of meaningful learning. The underlying meaning of the abstract concepts by computer animations may be accomplished in class environments. That study is conducted searching out to discover the effects of animations over the learning process in mathematic courses. The study was performed over the 58 university freshman students selected randomly. Thirty-two students constituted the experiment group and 26 students constituted the control group. Computer animations-aided instruction model in constructive form were applied on the experiment group and non-computer-aided instruction model in constructive form were implemented on the control group. Student academic success via a test method developed by explored group with confidence rate .819 (Cronbach's alpha) revealed that data were evaluated by two-way variance analyses. The findings provided from the final test shows that the experiment group students were significantly higher according to the control group students in terms of academic success average scores. Computer animations were observed to be significant to assimilate the derivative concept in a discrete way over the students, to appeal their attention, animations of real life events observed to transform the abstract meanings in the events to a concrete manner. Students of whom the concrete stage is constructed meaningfully found to be tactful in reaching to semi-abstract and abstract stages.

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Section: Resultsmentioning

confidence: 99%

Section: International Journal Of Mathematical Education In Science Amentioning

confidence: 99%

Impact of computer animations in cognitive learning: differentiation

Altıparmak

2014

International Journal of Mathematical Education in Science and

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“…Other studies reported on students' difficulties in understanding the limiting process from layer 2 to layer 3 (e.g. Hähkiöniemi 2006). Roorda et al (2015) described that student ability to make transitions between representations and layers was an indicator of their conceptual understanding of the derivative.…”

Section: Understanding the Concept Of Derivativementioning

confidence: 99%

Solving Rate of Change Tasks with a Graphing Calculator: a Case Study on Instrumental Genesis

Roorda

Vos

Drijvers

et al. 2016

Digit Exp Math Educ

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In an increasing number of mathematics classes throughout the world, technology is being used for the teaching and learning of mathematics. But knowledge is limited about the long-term development of students' mathematical thinking when learning mathematics with the use of technology. This article reports on the development of a student and the role of the graphing calculator (GC) in his learning about derivatives and instantaneous rate of change. This case is compelling, because the student is an intensive user of the GC and develops flexible problem-solving techniques -techniques which differ from those of his peers and from what he was taught in mathematics class. We used the framework of instrumental genesis to investigate how this student's mathematical thinking was affected by the use of the GC. Over a 2-year period, we administered four task-based interviews involving problems on instantaneous rate of change situated in contexts. We found that the use of the GC may facilitate a learning process in which instrumentation schemes involving symbolical representations develop separately from those for the graphical and numerical use of the GC.

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“…The processes of construction and use of mathematical concepts in calculus have been the focus of numerous analyses (Confrey & Costa, 1996;Zandieth, 1997;Dörfler, 2002;Berry & Nyman, 2003;Meel, 2003;Mason & Jonston-Wilder, 2004;Edwards, Dubinsky & McDonald, 2005;Harel & Sowder, 2005;Habre & Abboud, 2006;Hähkiöniemi, 2006). The cognitive construction is a process that uses symbolic, schematic, and linguistic meanings to express changes in perspective and points of view (Dörfler, 2002;Harel, Selden & Selden, 2006).…”

Section: Introductionmentioning

confidence: 99%

Characterizing Thematized Derivative Schema by the Underlying Emergent Structures

García

Llinares

Sánchez-Matamoros³

2010

Int J of Sci and Math Educ

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This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between a function and its first derivative to the derivative function and the second derivative. This conscious shift of properties of derivatives is differently manifested by the students in the trans level of development of the derivative schema and can be considered evidence of the different characteristics of the thematization of derivative schema. From here we suggest that there are different underlying structures in the constructed schema due to the consciousness in which students use the relations between a function and its derivative.

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Associative and reflective connections between the limit of the difference quotient and limiting process

Cited by 19 publications

References 13 publications

Impact of computer animations in cognitive learning: differentiation

Impact of computer animations in cognitive learning: differentiation

Solving Rate of Change Tasks with a Graphing Calculator: a Case Study on Instrumental Genesis

Characterizing Thematized Derivative Schema by the Underlying Emergent Structures

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