The cognitive process of students understanding quadratic equations

Abstract

Algebra is mandatory learning in junior high school. That is a continuation of arithmetic with the bridge being variable. Students often have difficulty in understanding it, especially quadratic equations. The purpose of this study is how students’ cognitive processes in understanding the principles of quadratic equations. It was an exploratory study conducted on research subjects. The subjects were junior high school students selected based on their ability to understand concepts and principles about quadratic equations. That’s done through tests about understanding quadratic equations. There were 16 selected research subjects. They were interviewed in-depth by researchers using interview guides. Interview data were analyzed qualitatively based on genetic decomposition. The results of this study are that students can use square, rectangular and unit square cards to determine the principle of factorization of quadratic equations. Students can generalize until completing a perfect quadratic equation. The conclusion is that the cognitive process of students who learn to use learning media based on square and rectangular able to reach a high level (trans-level).

The resolution of quadratic inequality problems in mathematics: Discrepancies between thought and action

“…In this research, algebraic manipulations and visual representations denote the essential connection between symbolic mathematical operations and graphical depictions within quadratic inequalities. In quadratic functions, algebraic manipulations involve the mathematical processes and transformations applied to equations, such as factoring, completing the square, or manipulating coefficients (Herawaty et al, 2021;Hoan et al, 2022;Weiss, 2016). On the other hand, visual representations pertain to the graphical depiction of these equations, particularly the parabolic graphs associated with quadratic inequalities.…”

Development of Higher-Order Thinking Skills test instrument on Quadratic Equation (HOTS-QE) for secondary school students

“…Among the contributing factor to such weakness is that students find it difficult to give meaning or understand the terms used to represent the roots of the quadratic equations (Thomas & Mahmud, 2021). They also often make mistakes when solving quadratic equations, especially in the process of conducting operations to reach the solutions and finding the possible values for substitute variables along with the lack of understanding about fractions, integers, linear equations, negative numbers, and basic mathematical properties such as algebraic expansion (Herawaty et al, 2021). The study by Vaiyavutjamai et al (2005) also reported that many students do not know that quadratic equations have more than one root.…”