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.
