Revealing Gaps in Students’ Mathematical Communication and Connection Abilities on Quadratic Functions

Abstract

Mathematical communication and connection abilities are essential competencies for mathematics learning because they help students build meaningful conceptual understanding and solve problems more systematically. This study aims to analyze high school students’ abilities in mathematical communication and connection with quadratic functions. This study employed a descriptive mixed-method approach, combining quantitative analysis of students’ test results with qualitative analysis of their written responses. The research instrument consisted of six open-ended questions, designed around indicators of mathematical communication and connection abilities. Data were collected through written tests. The responses were quantitatively scored and categorized using Arikunto’s criteria, followed by an in-depth qualitative analysis to examine students’ mathematical communication and connection processes.Students’ responses in each category were then analyzed in depth to identify the characteristics of their abilities. The results show that students’ mathematical communication and connection abilities range from low to high, with most students falling into the medium category. Further analysis revealed that students who demonstrated good communication abilities did not always exhibit strong connection abilities, and vice versa These findings are supported by the distribution of students’ abilities, where 66.67% of students were categorized as having moderate mathematical communication ability and 80.56% as having moderate mathematical connection ability. Despite this, a deeper analysis of each indicator reveals that the weakest performance was found in the ability to connect mathematical concepts to real-life contexts, as most students failed to respond to problems requiring contextual explanation. In addition, several common error patterns emerged. Students with low communication ability tended to omit important information, use incorrect mathematical notation, and fail to explain their reasoning. Meanwhile, students with moderate to high communication ability often demonstrated correct procedures but struggled to establish connections between concepts, particularly when applying quadratic functions in different contexts.