Endrayana Putut Laksminto Emanuel, Herfa Maulina Dewi Soewardini, Meilantifa

Commognitive View: Analysis Of Students' Work Results In Using Definite Integrals To Solve Contextual Problems

Introduction

Commognitive view: analysis of students' work results in using definite integrals to solve contextual problems . Explore students' commognitive processes solving definite integral contextual problems (area between curves). Study shows effective translation, symbol use, graphing, and systematic problem-solving skills.

Abstract

The purpose of this study is to describe students’ commognitive processes when solving contextual problems on definite integrals related to the area between curves. The research method was carried out through several stages, namely preparation, data collection, analysis, and drawing conclusions. The research subjects were ten students from a private university in Indonesia who were asked to solve a contextual mathematics problem within 30 minutes, specifically on definite integrals to determine the area bounded by two curves. Based on their work, one student was selected as the main subject to be analyzed using a commognitive approach and interviewed in depth to obtain more detailed information. The results of the study showed that the subject was able to translate the problem statements into mathematical form accurately. The subject was also able to use mathematical terms and symbols correctly (words use), illustrate the given conditions into graphs appropriately (visual mediators), and apply problem-solving steps systematically based on prior knowledge (routines). In addition, the subject was able to draw correct conclusions supported by valid mathematical arguments. Based on these findings, it can be concluded that students are capable of solving contextual mathematics problems successfully. Furthermore, it is expected that students can improve their understanding of course materials so that they are able to solve given problems more optimally and support the achievement of learning objectives.

Review

This study presents an interesting exploration into students' commognitive processes when tackling contextual problems involving definite integrals, specifically related to the area between curves. The use of a commognitive lens offers a valuable framework for understanding the intricate interplay between mathematical discourse, visual representations, routines, and narratives in problem-solving. The research question is clearly stated, aiming to describe these processes, and the structured methodology involving preparation, data collection, analysis, and conclusion drawing is appropriate for a qualitative inquiry. The focus on a specific mathematical topic at the university level makes the study relevant to mathematics education research. While the study's aim is commendable, the methodological choices present a significant limitation regarding the generalizability of its findings. Although ten students initially participated, the in-depth commognitive analysis was ultimately performed on only one selected student. While this allows for rich, detailed insights into that individual's process, it makes the broad conclusion that "students are capable of solving contextual mathematics problems successfully" an overstatement, as it is based on a single successful case. The abstract effectively highlights the application of commognitive elements like "words use," "visual mediators," and "routines" in describing the subject's success, demonstrating the framework's utility in dissecting cognitive actions. However, the subsequent recommendation that students "improve their understanding" feels somewhat generic and disconnected from the specific commognitive insights gained. To strengthen future research building on this foundation, it would be beneficial to either explicitly justify the selection of the single subject (e.g., as an exemplary case, or one demonstrating specific commognitive characteristics), or expand the commognitive analysis to a larger, more diverse group of students to capture a broader spectrum of commognitive processes, including potential struggles or variations. Further detail on the criteria for selecting the main subject would enhance transparency. Additionally, the implications of the findings could be elaborated beyond general improvement, potentially suggesting specific instructional strategies or curriculum adjustments based on the observed successful commognitive patterns or identifying areas where students commonly face commognitive challenges. This study serves as a valuable initial step in applying the commognitive framework to integral calculus, offering foundational insights into individual student problem-solving.

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