Abstract
The likelihood of misunderstanding and misrepresenting trigonometric ideas motivated an investigation of implicit misconceptions in prospective mathematics teachers’ reasoning about particular trigonometric concepts. To access the participants’ implicit misconceptions, a qualitative approach and case study design in particular were employed. Three prospective teachers chosen purposefully composed the sample. The student teachers majored in mathematics and were in the final year of training. Four diagnostic questions based on trigonometry were administered followed by semi-structured interviews. Qualitative analyses of calculations and interview transcripts revealed implicit misconceptions in participants’ reasoning. The prospective teachers reasoned that trigonometric equations can be resolved in the same way as conventional algebraic equations. Likewise, they demonstrated an erroneous notion that inverse trigonometric functions are evaluated just like indices. Besides, the participants incorrectly considered elements of domains of trigonometric functions to be synonymous with such functions’ extreme values. Overall, prospective teachers’ reasoning demonstrated didactical obstacles. It is therefore proposed that mathematics teacher education should include opportunities for prospective teachers to reason about mathematics concepts in a manner that prevents didactical obstacles. Furthermore, mathematics educators should engage in instructional practices which facilitate prospective teachers’ acquisition of in-depth understanding of mathematics conceptual relationships and differences.
Highlights
Mathematics is a core subject in most countries’ secondary education curricula
The sample consisted of three prospective teachers who majored in mathematics and were in their final year of study at a Zambian university
Subject matter knowledge was categorized as Common Content Knowledge (CCK), and Specialized Content Knowledge (SCK) (Ball et al, 2008)
Summary
Mathematics is a core subject in most countries’ secondary education curricula. This could be due to the subject’s presumed benefits to learners and nations at large. The mathematics concepts as learned in school cannot be relied upon to equip teachers with the kind of understanding required for them to be effective teachers of the same concepts. This view is persuasive because the teaching that goes on in school mathematics classrooms has objectives which are not directly linked to a goal of training would be teachers of mathematics. Teachers’ meaningful understanding of mathematics concepts should be developed during their training as teachers of mathematics (Malambo, 2020) In this vein, mathematics teacher education affords an appropriate platform to begin to strengthen prospective teachers’ mathematics subject matter knowledge coupled with how they could unpack the mathematics concepts for pupils’ conceptual understanding
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