I thrive on attention-getting techniques, specifically techniques that motivate the students to work together in a cooperative group and create a great finished product. Calculus is a great subject for this. When students first learn what slope is in algebra, they’re given a formula: [slope = m = (y2 – y1)/(x2 – x1)]. In calculus, this formula is expanded upon and the students take to a different view of slope, namely, the derivative of a function. One reason why I’m excited to teach this topic is it opens the door to many activities that the students can actively engage in and get hands-on experience. One of the very last projects that my high school calculus class undertook was surveying different elevations of land around a creek and then determining the slope from the data. I would hope that I can do something very similar with a class of my own.
My second topic is just on the flip side of slope…area. This involves taking the integral (or anti-derivative) of a function. This is expanded from geometric area formulas, such as for circles, triangles, rectangles, and all the other shapes you’re familiar with. Once students can connect the two concepts from geometry and calculus, it should be apparent that calculus is a beautiful mixture of algebra, geometry, trigonometry, and just as much, arithmetic.
FYI: A function is a special relationship between x’s and y’s. Each x coordinates to one and only one y, and vice versa. When put onto paper for a visual effect, this function is called a graph. My math lesson for today… :-)