Trigonometry learning

Abstract

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their learning of trigonometry matters. Aims: In this study, particular types of errors, underlying misconceptions, and obstacles that occur in trigonometry lessons are described. Sample: 140 tenth grade high-school students participated in the study. 6 tenth grade mathematics teachers were observed. Method: A diagnostic test that consists of seven trigonometric questions was prepared and carried out. The students’ responses to the test were analyzed and categorized. Observations notes were considered. Results: The most common errors that the students made in questions were selected. Several problematic areas have been identified such as improper use of equation, order of operations, and value and place of sin, cosine, misused data, misinterpreted language, logically invalid inference, distorted definition, and technical mechanical errors. This paper gives some valuable suggestion (Possible treatment of students’ error obstacles, and misconceptions) in trigonometric teaching for frontline teachers. Conclusion: The study found students have errors, misconceptions, and obstacles in trigonometry lessons.背景：比較其他數學的主題，三角學是學生認為特別困難和抽象的。學生通常在第八年級開始接觸三 角學，傳統上多數課本以介紹直角三角形的邊作開始。學生需要瞭解他們為什麼要學三角學。 目的：這項研究觸及有關三角學習特殊錯誤的類型、其蘊含的誤解和在課堂上發生的障礙。 樣本： 140名第十年級高中學生和六位有關的數學教師参加了本研究。 方法：學生們參加了一次包括七個三角問題的診斷測試，其反應和觀察筆記被分類分析。 結果： 列出了學生答題時的通病，像誤用方程式、運算程序、正弦和餘弦的數值和位置、誤用數據、 解錯題、錯誤邏輯推理、曲解定義、及技術運算錯誤等。本文給前線老師在教授三角學時可貴的建議 [學生 的錯誤障礙和誤解可能的治療]。 結論： 本研究找出了學生在學習三角課時所犯的錯謬、誤解、和障礙。