Novel Investigation of Multivariable Conformable Calculus for Modeling Scientific Phenomena

New investigation on the conformable version (CoV) of multivariable calculus is proposed. The conformable derivative (CoD) of a real-valued function (RVF) of several variables (SVs) and all related properties are investigated. An extension to vector-valued functions (VVFs) of several real variables (SRVs) is studied in this work. The CoV of chain rule (CR) for functions of SVs is also introduced. At the end, the CoV of implicit function theorem (IFThm) for SVs is established. All results in this work can be potentially applied in studying various modeling scenarios in physical oceanography such as Stommel’s box model of thermohaline circulation and other related models where all our results can provide a new analysis and computational tool to investigate these models or their modified formulations.

Calculus and Digital Natives in Rendezvous: wxMaxima Impact

This article covers how a computer algebra system (CAS) wxMaxima can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where wxMaxima can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and unsuccessfully. By soliciting qualitative feedback on students’ experience in exploiting the CAS, we gathered a mixed reaction. Although some students commented positively, the majority seemed to be resistant to embracing a new technological tool.

Mathematical Refractive Thinking Ability in Multivariable Calculus: Instrument Design and Quality of Use

<p><em>Mathematical refractive thinking ability</em><em> must </em><em>be given in every lecture because it is needed in decision making. This study aims to produce a quality mathematical refractive thinking ability instrument, especially for calculus material. Instrument quality is measured in terms of validity and reliability. Content validity, con</em><em>s</em><em>tr</em><em>u</em><em>ct validity and face validity were assessed by three material experts. The instrument was tested </em><em>by</em><em> 32 mathematics education students to measure empirical validity and reliability. This research resulted in three items of mathematical refractive thinking ability tests that are valid and have instrument reliability in the medium category.</em><em></em></p>

Kemampuan Berpikir Refraktif Matematis Mahasiswa melalui Pembelajaran Peer-Assited Reflection

Refractive thinking needs to be developed in lectures because it has an essential role in decision-making. However, so far, there has not been found any relevant research that develops refractive thinking through applying a learning strategy. The purpose of this study was to obtain an overview of the enhancement of students' mathematical refractive thinking ability based on prior mathematical knowledge through the application of Peer-Assisted Reflection learning and the influence of the interaction of learning factors and the level of prior mathematical knowledge on enhancing mathematical refractive thinking ability. This research is a quantitative study with a quasi-experimental design. Using the purposive sampling technique, 73 students were selected to take the Multivariable Calculus course. The research sample was students who took the Multivariable Calculus course. The instrument used was a prior mathematical knowledge test and a mathematical refractive thinking ability test. Data analysis used t-test, t’-test, Mann-Whitney U test, Aligned Rank Transform, and two-way ANOVA. The findings of this study are: (1) The enhancement of students' mathematical refractive thinking ability who got Peer-Assisted Reflection learning is better than those who got conventional learning for all levels of prior mathematical knowledge; and (2) There is no significant effect on the interaction between learning and prior mathematical knowledge on improving mathematical refractive thinking ability.

STUDENTS’ PERCEPTIONS ABOUT THE IMPLEMENTATION OF PEER-ASSISTED REFLECTION LEARNING IN MULTIVARIABLE CALCULUS LECTURES

A large class can be a problem source in learning Calculus. Peer-Assisted Reflection learning,as the solution, is a learning that combines peer analysis and self-reflection. The purpose of this study was to describe the implementation of Peer-Assisted Reflection learning based on Students’ opinions in Multivariable Calculus lecture. The research design used was pre-experimental with a one-shot case study design. The data obtained from questionnaire responses were analyzed by using descriptive statistics. The result of this study shows that thePeer-Assisted Reflection learning help Students’s carry out activities: reflecting the result of their own work, commenting on the friend’s work, and increasing understanding of the material after revising their work. On contrary, the Peer-Assisted Reflection learning has not been able to carry out the following activities: determining concepts, understanding problems in a short time, understanding the work of colleagues, and finding doubts about the correctness of the answers.

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments.