Differential instructional effectiveness: overcoming the challenge of learning to solve trigonometry problems that involved algebraic transformation skills

Abstract

The design principles of cognitive load theory and learning by analogy has independently contributed to our understanding why an instruction will or will not work. In an experimental study involving 97 Year 9 Australian students conducted in regular classrooms, we evaluated the effect of the unguided problem-solving approach, worked examples approach and analogy approach on learning to solve two types of trigonometry problem. These trigonometry problems (sin40° = $$\frac{x}{6}$$ x 6 vs. cos50° = $$\frac{14}{x}$$ 14 x ) exhibited two levels of complexity owing to the location of the pronumeral (numerator vs. denominator). The solution procedure of worked examples provided guidance, whereas the unguided problem-solving was without any guidance. Analogical learning placed emphasis on comparing a pair of isomorphic examples to facilitate transfer. Across the three approaches, solving practice problems contributed towards performance on the post-test. However, the worked examples approach and analogy approach were more efficient than the unguided problem-solving approach for acquiring skills to solve practice problems regardless of their complexity. Therefore, the worked examples approach and analogy approach that emphasizes algebraic transformation skills have the potential to reform instructional efficiency for learning to solve trigonometry problems.

Implementing blended learning to enhance the teaching of 3-dimensional trigonometry

“…In addition, trigonometry is used in calculating the speed and direction of the wind. In geology, structural geologists, seismologists and paleontologists also apply trigonometry in their computations (Ngu & Phan, 2023 ). Similarly, in criminology, trigonometry is useful when investigating a crime scene.…”

“…Similarly, in criminology, trigonometry is useful when investigating a crime scene. The functions of trigonometry are vital in calculating the trajectory of a projectile and estimating the causes of a collision in a car accident (Ngu & Phan, 2023;Sholihah & Firdaus, 2023).…”

“…Previous studies revealed that students have preconceptions about comprehending mathematical subjects like trigonometry despite the fact that trigonometry is essential knowledge for many important functions, physics and construction (Asomah, Agyei, & Ntow, 2023;Ngu & Phan, 2023). The numerous misunderstandings shown in the learners' responses are frequently a sign of these challenges with high school mathematics (Egodawatte, 2011;Luneta & Makonye, 2010).…”

“…Previous research has highlighted the prevalence of errors and misconceptions among learners and identified the need for innovative instructional strategies to address this issue effectively (Baidoo, 2019;Luneta, 2015). Additionally, it has emphasized the growing role of blended teaching methods combining traditional face-to-face instruction with technology-based resources in modern education (Chowdhury, 2020;Ngu & Phan, 2023). This study poses a fundamental research question in light of this context: What are the significant differences in performance and exhibition of errors and misconceptions between grade 12 learners taught 3D trigonometry using blended teaching and those taught using traditional instructional methods?…”