![]() Technological tools, teaching materials and students’ acceptance are key aspects for online education at current times. Each lab assignment required a written component in which the student would summarize or analyse results instead of simply collecting source code, which often occurs when a full CAS is used. If the student is using their own computer, this is not a problem however, if you are in university lab classroom, there may be some information technology (IT) issues with allowing students to download freely. In order to view the activities listed in the Wolfram Demonstration Project, the student is required to download (at no cost) a Mathematica Player. In the case of approximation techniques, the student can go the MathWorld site, type ‘Riemann Sum’ in the search box and have access to a player that will allow them to input their function, the interval, number of subintervals and select the approximation method ( Figure 5). However, for many of these common calculus concepts, the student can access the link to the Wolfram Demonstration Project from the Wolfram|Alpha site or visit MathWorld, another Wolfram creation. Wolfram|Alpha will not return a numeric or graphical result from a request to approximate an integral using the trapezoid or Simpson’s rule. It should be noted that there are some concepts that Wolfram|Alpha cannot address directly such as approximation techniques for integration. ![]() Questions can address concepts such as signed areas, symmetry and area or absolute value of areas. Once the student has an opportunity to observe examples, then the student will be required to make predictions about the result of other definite integrals. Since Wolfram|Alpha displays both the numeric result and the graphical interpretation, the student is able to see connections in how the integral is set up and how the value of the integral changes based on the limits of integration (Figures 3 and 4). The lab assignment would ask the student to evaluate several definite integrals. One example would be a question about the area under a curve. In most lab assignments, the student was also required to show the simple output so that the professor can ‘see’ what the student used as a reference. Creating lab questions with this in mind provides an opportunity for a knowledge engine such as Wolfram|Alpha to be used as a tool for the student to be able to formulate inferences instead of simply reporting output. Lab questions are formulated so that students are asked to compare, test, synthesize and predict. Hence, the exercises require the student to demonstrate ability beyond the levels of knowledge and comprehension and move towards higher levels of Bloom’s Taxonomy of cognitive thought including analysis and comprehension. The lab assignments created for Calculus Two (in this case that would include integral calculus with applications, sequences and series) were designed with the purpose of using Wolfram|Alpha as a computational tool to enhance conceptual knowledge. ![]() Overall, I feel that using Wolfram|Alpha in Calculus One has immediate advantages over a standard CAS, and as Wolfram|Alpha continues to improve, I only see the advantages increasing. This does not seem possible at the time of writing, even when using exact Mathematica syntax. ![]() The only outstanding issue that I experienced is the issue of controlling aspect ratio and the exact window for certain graphs. ![]()
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