Calculus limits involving infinity: the role of students’ informal dynamic reasoning

Jones, Steven

doi:10.1080/0020739x.2014.941427

Cited by 13 publications

(4 citation statements)

References 30 publications

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“…While we found this approach not applicable to our group, but it was an inspiration for the preparation of small software environments for PMTs. Jones [22] focused on students' understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). We implemented this kind of task in PMTs preparation and also into the tests.…”

Section: Theoretical Subject In Preparation Pmtsmentioning

confidence: 99%

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Slavíčková

2021

Mathematics

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This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs’ preparation is also discussed.

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Section: Theoretical Subject In Preparation Pmtsmentioning

confidence: 99%

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Slavíčková

2021

Mathematics

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“…Many studies showed significant improvement in students' performance in calculus by using nonconventional teaching strategies, which highlights the importance of mathematics teachers being able to implement varied teaching strategies in teaching calculus. Abdullah et al (2020) on the use of experiential learning to develop the critical thinking of students in calculus Chen and Chen (2017) investigated the use of differentiated instruction in teaching calculus; Galia (2016) examined the use of a constructivist approach in teaching calculus; Hernandez et al (2021) studied on the utilization of social media-based learning materials in basic calculus; and Jones (2015) explored dynamic reasoning as a tool in teaching limits at infinity and infinite limits.…”

Section: Least Taught Topics In Basic Calculusmentioning

confidence: 99%

Enhancing students’ performance on least taught topics in basic calculus through Moodle-based courseware package

Evardo Jr,

Itaas

2024

Journal of Mathematics and Science Teacher

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This study utilized the developmental research design to identify the least taught topics in basic calculus and design and investigate the effectiveness of a Moodle-based courseware package. Data were collected from seven basic calculus teachers and five academic administrators through survey questionnaires, interviews, and validation sheets. The quasi-experimental phase of the study used a pre-/post-test control group design with a sample of 69 students, 34 students in the experimental group and 35 students in the control group. The experimental group received instruction using an asynchronous Moodle-based courseware package, while the control group received instruction through lecture notes. Results showed that the least taught topics include infinite limits, limits at infinity, and limits of trigonometric, exponential, and logarithmic functions. These topics were least taught due to time constraints, students’ capacity, scheduling, complexity, and relatability. Validation of the courseware package showed a very high validity. It was found that the use of Moodle-based courseware package and lecture notes effectively increased the students’ performance. However, one-way analysis of covariance results showed that the experimental group gained considerably greater than those in the control group. It was recommended that teachers continue to update their knowledge of different teaching methodologies to develop an encouraging and dynamic learning environment.

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“…Two main aspect are notable: 1) There is a significant number of studies (ELIA et al, 2009;PARAMESWARAN, 2007;JONES, 2014; FERNÁNDEZ-PLAZA; RUIZ-HIDALGO; RICO, 2015) that use task design to enhance the learning of limits or to examine students' ideas on limits; however, there are no studies that propose criteria to design tasks that consider the rich and complex nature of limits on a real variable function. 2) Some methodologies provide guidelines to design tasks, but they fall short in including criteria for both the complexity and diversity of meanings.…”

Section: Introductionmentioning

confidence: 99%

Epistemic Criteria for Designing Limit Tasks on a Real Variable Function

Bastias

Pino-Fan

Medrano

et al. 2021

Bolema

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This article aims at presenting the results of a historical-epistemological study conducted to identify criteria for designing tasks that promote the understanding of the limit notion on a real variable function. As a theoretical framework, we used the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction, to identify the regulatory elements of mathematical practices developed throughout history, and that gave way to the emergence, evolution, and formalization of limit. As a result, we present a proposal of criteria that summarizes fundamental epistemic aspects, which could be considered when designing tasks that allow the promotion of each of the six meanings identified for the limit notion. The criteria presented allow us to highlight not only the mathematical complexity underlying the study of limit on a real variable function but also the richness of meanings that could be developed to help understand this notion.

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Calculus limits involving infinity: the role of students’ informal dynamic reasoning

Cited by 13 publications

References 30 publications

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Enhancing students’ performance on least taught topics in basic calculus through Moodle-based courseware package

Epistemic Criteria for Designing Limit Tasks on a Real Variable Function

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