Solving Problem Types Contextualized to the Quadratic Function and Error Analysis: A Case Study

Abstract

The article aims to determine the academic performance and errors in the resolution of types of problems of application of the quadratic function, of high school students from the Los Lagos Region and Los Rios Region in Chile. The approach is qualitative and descriptive with case studies. A math test with open response problems and an opinion questionnaire were developed and applied. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context and fantasist context, but with difficulty in the resolution of non-routine problems. In addition, errors originating in affective and emotional attitudes associated with blockages at the time of initiating the resolution, forgetfulness at the time of posing the quadratic function, prevail over cognitive errors originating in an obstacle and errors originating in the absence of meaning.

Analyzing Students’ Thinking in Mathematical Problem Solving Using Vygotskian Sociocultural Theory

“…SCT concepts have been the subject of an investigation by researchers in mathematics education. These researchers have explored several ways in which the principles of SCT might potentially enhance students' ability to solve mathematical problems (Campbell et al, 2022;Chalkiadaki, 2018;Díaz et al, 2020;Kerrigan et al, 2021). Researchers Windsor (2010) and Bature and Atweh (2019) discovered that students' conceptual understanding and algebraic thinking improved when they collaborated and interacted with one another to find solutions to difficulties.…”

“…A good communication and collaboration is influenced by student awareness, and the given problems must include problem solving (Campbell et al, 2022). Also, communication and collaboration is useful for completing, exploring, and investigating ideas and opinions, and sharpening ideas to persuade other (Díaz et al, 2020;Hidayat & Aripin, 2023).…”

Difficulties and Errors of Grade 9 Learners in Solving Quadratic Equation: Input to the Development of Strategic Intervention Material

“…Agustyaningrum et al (2018) note that these types of errors are manifested by both theoretical and conceptual content. To address these errors, teachers need to implement an intervention for learners to learn subsequent concepts (Díaz et al, 2020). In addition, Thomas and Mahmud (2021) used a diagnostic test with 30 Form 4 learners to diagnose errors they commit when solving QE.…”

Peer assessment processes in a problem-solving activity with future teachers

“…We chose an open-ended problem because the variety of results and ways of solving, together with the lack of Open-ended problems can be classified as nonroutine problems in the sense that solvers do not know a previously established procedure to solve them (Díaz et al, 2020), so it was likely to encounter difficulties finding solutions and its assessment would be a greater challenge for the future teachers.…”

“…In the same vein of making the evaluation a challenge, we chose a problem with a topic in which students usually present difficulties, the functions, specifically, involving a quadratic function (Amaya & Medina, 2013;Díaz et al, 2020). Facing an answer with different mathematical characteristics to those given by themselves and involving a topic generally problematic, would force them to reflect on its evaluation, allowing us to notice these aspects of the resolution to which they give more importance or how attached they are to their own resolution when evaluating.…”