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Social science students’ concept images and concept definitions of anti-derivatives
Pythagoras ( IF 0.3 ) Pub Date : 2019-11-13 , DOI: 10.4102/pythagoras.v40i1.484
Eunice K. Moru , Makomosela Qhobela

Calculus is an important branch of mathematics in a number of social and natural science disciplines. In the social sciences anti-derivatives are required in tackling problems in marginal analysis and optimisation problems. In the natural sciences students need to understand antiderivatives to deal with rates of change for concepts such as velocity, acceleration and rate of flow. However, students fail to understand some of the basic concepts of calculus (Brijlall & Ndlazi, 2019; Maharaj, 2014; Metaxas, 2007; Grundmeier, Hansen & Sousa, 2006). For example, students have problems in relating fundamental concepts and their definitions with associated procedures. This disconnect suggests that students have difficulties understanding functional and operational relationships between the mathematical notations and the calculus concepts they represent. What is desirable is that mathematical procedures be understood conceptually, but this is not necessarily the case since many students continue to learn mathematical procedures by rote application of an algorithm (Moru & Qhobela, 2013). A general anti-derivative, which is sometimes referred to as an indefinite integral, is an essential concept in calculus because it serves as a basis for many reallife problems and when students continue further into calculus courses, they frequently encounter anti-derivatives more than derivatives (Jones, 2013).

中文翻译:

社会科学专业学生的概念形象和反导的概念定义

微积分是许多社会和自然科学学科中数学的重要分支。在社会科学中,在处理边际分析和优化问题时需要使用反导数。在自然科学中,学生需要了解反导数以处理诸如速度,加速度和流速之类的概念的变化率。但是,学生无法理解微积分的一些基本概念(Brijlall&Ndlazi,2019; Maharaj,2014; Metaxas,2007; Grundmeier,Hansen&Sousa,2006)。例如,学生在将基本概念及其定义与相关程序相关联时遇到问题。这种脱节表明学生很难理解数学符号和他们所表示的微积分概念之间的功能和操作关系。理想的是从概念上理解数学程序,但这不是必然的情况,因为许多学生继续通过死记硬背应用算法来学习数学程序(Moru&Qhobela,2013)。通用反导数(有时称为不定积分)是微积分中的基本概念,因为它是许多现实生活中问题的基础,并且当学生继续学习微积分课程时,他们遇到反导数多于导数(琼斯,2013年)。但这并非一定如此,因为许多学生继续通过死记硬背应用算法来学习数学程序(Moru&Qhobela,2013)。通用反导数(有时称为不定积分)是微积分中的基本概念,因为它是许多现实生活中问题的基础,并且当学生继续学习微积分课程时,他们遇到反导数多于导数(琼斯,2013年)。但这并非一定如此,因为许多学生继续通过死记硬背应用算法来学习数学程序(Moru&Qhobela,2013)。通用反导数(有时称为不定积分)是微积分中的基本概念,因为它是许多现实生活中问题的基础,并且当学生继续学习微积分课程时,他们遇到反导数多于导数(琼斯,2013年)。
更新日期:2019-11-13
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