Exploring Grade 10 learner's spatial skills of computing sides and angles figures using trigonometric ratios

Abstract

In Grade 10, learners are facing challenges to compute sides and angles using trigonometric ratios. This is a result of accessing inappropriate and fragmented trigonometric concepts which complicates their computational procedures. The purpose of this study was to explore Grade 10 learners’ spatial skills when computing sides and angles in figures using trigonometric ratios. This was achieved by adhering to the elements of an exploratory case study. The qualitative study was underpinned by the three principles of semantic tenets, conceptual structures, system representation and sense. Grade 10 learners were purposively sampled to explore their spatial skills exhibited whilst computing sides and angles using the three basic ratios. Data were collected in three phases from 22 purposively sampled Grade 10 learners using three mathematical tasks and semi-structured interviews. The two sets of data were analysed thematically. In summary, the textual data from the three mathematical tasks were read critically and the audio data was transcribed. Both sets of data were categorised using axial coding and four themes emerged. The major findings revealed that learners who leave blank spaces have spatial skills that can be expressed verbally. This was shown as learners exhibited appropriate spatial skills during semi-structured interviews. Moreover, learners utilised improper properties of a right-angled triangle during computations of sides and angles using trigonometric ratios. On the other hand, some learners struggled to relate concepts used within the given questions. This resulted from a lack of prerequisite trigonometric concepts to comprehend what the question requires. Based on the findings of the study, the recommendation is that the learning of trigonometry should be based on developing spatial skills that permit the exploitation of relevant properties during the computations of sides and angles using ratios. This should be followed by inclusive formative assessment and verbal assessment to accommodate learners struggling to achieve in written assessment.