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我是通过解决我私人导师给我的max box问题(见附录A)开始我的自主学习的。这个问题是关于有A面纸的问题,然后我被要求从四个角的每一个角用x面切出一个正方形来做一个box。我要找到x的值这样我才能做出最大的盒子。我试着通过一些代数方程来求出创建最大方框的x值,最后,我得到了求x值的模式。找到答案让我有机会把它和差异化的概念联系起来。这对我来说是一件新鲜的事情,当我在网上搜索时,我发现它在与微积分相关的数学教学中很流行。然而,我不知道为什么我发现印尼的数学老师在教授区分概念的时候很少使用这个实用的问题。接下来,我将介绍如何从函数f(x)引入第一个微分原理f'(x)我先画一个函数的图形,然后用直线的梯度和极限的概念来表示两个相邻点的梯度(见附录B),最后我发现一阶导数等于函数中一个点的梯度。然后,我对一些不同的函数进行了类似的计算,最后,我建立了一阶导数的模式。在做这个的时候,我在想我应该先教哪个,梯度还是微分,以便让学生理解一阶导数的来源。此外,通过解决这个问题,我意识到作为一名教师,我可以通过使用算法/代数/分析/计算、视觉(图像/图形)和归纳(模式)思维来教数学。例如,在查找函数的最大值时,我使用了两种不同的方法获得了相同的答案,即绘图和计算。


I started my independent learning by solving the max box problem given by my personal tutor (see Appendix A). This problem about the paper which has side a, then I was instructed to make a box by cutting a square with side x from each of the four corners. I have to find the value of x so that I can make the biggest box. I tried to find the x value for creating the biggest box by doing some algebraic equations and finally, I obtained the pattern for finding the x value. Finding out the answer gave me an opportunity to relate it to the concept of differentiation. It was a new thing for me and when I searched on the internet, found it was popular in teaching and learning mathematics related to the calculus topic. However, I did not know why I found Indonesian mathematics teachers rarely used this practical question while teaching the concept of differentiation.Next, I moved to how to introduce the first principle of differentiation, f'(x), from function f(x). I started by drawing a graph of the function, then formulated gradient of two adjacent points using the gradient of a straight line and limit concept (see Appendix B). Finally, I found that the first derivative equals with the gradients of a point from the function. Then, I tried similar calculations for some different functions, and finally, I established the pattern of the first derivative. While doing this, I was thinking which I should teach first, gradient or differentiation, in order to make students understand where the first derivative comes. Furthermore, a noticeable point for me by solving this problem, I was aware that as a teacher I can teach mathematics through using algorithmic/algebraic/analytic/calculating, visual (image/graph), and inductive (pattern) thinking. For example, when finding the maximum value of the function, I acquired the same answer by using two different methods, graphing and calculating.


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