Students' mathematical connections and communication in contextual problems by problem-solving ability

Source abstract

Background–Mathematical connection and communication are central to solving contextual problems, yet they are usually examined separately, so little is known about how they appear together within the same solution process. Objective–This study describes ninth-grade students’ mathematical connections and communication in solving contextual problems on curved-sided solids across low, medium, and high problem-solving ability categories. Method–A descriptive qualitative design was used. Twenty-seven students completed a two-item contextual test scored with a Polya-based rubric, and the two lowest-scoring students in each category were purposively selected for in-depth analysis. Written work and semi-structured interviews were analyzed through data condensation, data display, and conclusion drawing, with credibility established through source and method triangulation. Results–Connection and communication showed different patterns across the problem-solving categories, becoming increasingly comprehensive in the higher categories. Low-category students showed limitations from the problem-understanding stage, whereas medium-category students carried out procedures correctly but stopped at computation without interpreting results in context. High-category students met all indicators, and two profiles emerged from the qualitative analysis, procedural-systematic and visual-representational, each observed in one student. The absence of contextual conclusions was consistent across the low and medium categories. Conclusion–Within the selected cases, connection and communication appeared closely aligned, and interpreting results in context most clearly distinguished high-category students. Teachers may need to support this step explicitly and encourage multiple representations. Given the small single-school sample, the findings describe patterns among the participants rather than generalizable relationships.