Analysis of the Meanings of the Antiderivative Used by Students of the First Engineering Courses

Pino-Fan, Luis Roberto; Moll, Vicenç Font; Gordillo, Wilson; Larios, Victor M.; Breda, Adriana

doi:10.1007/s10763-017-9826-2

Cited by 26 publications

(28 citation statements)

References 17 publications

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“…Furthermore, teachers and lecturers should be aware of the diversity of representations, especially graphical representation, of the mathematical concepts (Pino-Fan, Font, Gordillo, Larios, & Breda, 2017). The use of different representations (graphical, algebraic, symbolic and etc) in teaching and learning Calculus concepts and transition between these representations will help students to acquire a deeper understanding of the concepts (Breda, PinoFan, & Font, 2017;Mallet, 2007;NCTM, 1989;Park, 2015;Tall, 1996;Tiwari, 2007).…”

Section: Question 4mentioning

confidence: 99%

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Borji

Ahadi

Radmehr

2018

EURASIA J MATH SCI T

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APOS-ACE (Action, Process, Object, and Schema-Activities, Classroom discussion, and Exercises) is applied in this article to explore the teaching and learning of derivative by giving emphasis on its graphical understanding. For this purpose, a Genetic Decomposition is developed based on the outcomes of previous studies and on our personal teaching experiences. An ACE cycle is designed with the help of the Maple software and implemented on a group of freshmen Iranian students (experimental group). The outcomes of this implementation are evaluated by comparing the performance of the experimental group to the performance of another equivalent student group (control group), to which the same subject was taught in the traditional, lecture-based way. Our findings demonstrated students' who were in the experimental group shown a better understanding of the derivate compared to the control group. Therefore, such ACE cycle with Maple could be used more frequently for teaching calculus, especially derivative.

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Section: Question 4mentioning

confidence: 99%

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Borji

Ahadi

Radmehr

2018

EURASIA J MATH SCI T

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“…Recent research papers (Badillo et al, 2011;Drijvers, Godino, Font, & Trouche, 2013;Font, Trigueros, Badillo, & Rubio, 2016;Fuentealba, Sánchez-Matamoros, Badillo, & Trigueros, 2017;Mackie, & Court, 2002;Pino-Fan, Godino & Font, 2011;Pino-Fan, Font, Gordillo, Larios, & Breda, 2017;Robles, Telechea & Font, 2014;Tall, 2013;Tiwari, 2007) on learning and teaching of Calculus have revealed the complexity of the fundamental mathematical objects in this area of mathematics (derivative, integral, etc. ) and the need to teach different partial meanings of these objects and connect them to each other for their understanding.…”

Section: Introductionmentioning

confidence: 99%

Application of the Complementarities of Two Theories, APOS and OSA, for the Analysis of the University Students’ Understanding on the Graph of the Function and its Derivative

Borji

Moll

Ahadi

et al. 2018

EURASIA J MATH SCI T

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The goal of this paper is the combined use of two theories, APOS and OSA, for the analysis of the university students' understanding on the graph of the function and its derivative. For this, we study the students' understanding to solve one graphing problem in relation to the first derivative and characterize their schemas in terms of levels (intra, inter and trans) of development of the schema for sketching ′ when given the graph . We present a multiple case study in which 14 students of the first course of Calculus in one university of Iran participated voluntarily. Results show that most of the students in our study had major problems in developing mental constructions and doing the practical work needed to solve the problem, particularly those mental constructions that have to be made to calculate the derivative at the critical points and to determine the speed of the variation of the inclination of the tangent lines to , which is why most of them have constructed a schema at the intra level of development of the schema for sketching ′ when given the graph . We finish with some final conclusions.

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“…The activating process occurs internally but can be marked when students remember all the ideas learned about inverses. Pino-Fan et al (2017) emphasize that the activation of the scheme involves verbal and symbolic meanings of the structure of the problem. However, schemes that have been formed are sometimes unable to be activated by students and depend on processing information that occurs in long-term memory (LTM) (Sun, 2006).…”

Section: Reversible Reasoning Indication For Inverse Function Problemsmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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Analysis of the Meanings of the Antiderivative Used by Students of the First Engineering Courses

Cited by 26 publications

References 17 publications

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Application of the Complementarities of Two Theories, APOS and OSA, for the Analysis of the University Students’ Understanding on the Graph of the Function and its Derivative

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

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