Final Project:
Series worksheets with Wolfram|Alpha.
Activity: "Integral Test" and "Series Review" worksheets.
Technology used: Wolfram|Alpha
Author: Jane Butterfield
Summary: "Integral Test" is a worksheet intended to be worked on in groups. It introduces the integral test, and then has students use Wolfram|Alpha to apply the test (or explain why it cannot be applied) to several series. Total time: about two 50 minute sections. "Series Review" is a take-home review assignment that uses Wolfram|Alpha to get through a lot of practice quickly. Class: BC Calculus or Calculus II.
Integral Test Worksheet
Series Review Worksheet
Notes to Instructor
Technology used: Wolfram|Alpha
Author: Jane Butterfield
Summary: "Integral Test" is a worksheet intended to be worked on in groups. It introduces the integral test, and then has students use Wolfram|Alpha to apply the test (or explain why it cannot be applied) to several series. Total time: about two 50 minute sections. "Series Review" is a take-home review assignment that uses Wolfram|Alpha to get through a lot of practice quickly. Class: BC Calculus or Calculus II.
Integral Test Worksheet
Series Review Worksheet
Notes to Instructor
Comments on this project.
Taylor, inventor of the Taylor Series
Wolfram|Alpha is a great tool. It is readily available to anyone with access to a web browser, which for a university is everybody. It is very easy to share your finds with others--you can just cut-and-paste a link . This makes collaboration between students easy.
While tutoring this semester, I have recommended Wolfram|Alpha to two students. The first was for a Math 220 student who I felt needed lots of practice with the substitution method. At first I told him to email me if he wasn't sure he'd gotten the right answer--and then I realized that he could instead just check his answer with W|A. This would allow him to get through a lot of practice without supervision and without wasting time.
That got me thinking about other places where practice is especially important, but time is lacking. I tutored for Math 231 last summer; this is a particularly tough class to take during summer term, because there is so little time--and the Sequences and Series section always gives students trouble, even during a normal semester. During summer, students have even less time to do enough homework to build up a good intuition for which Series Test to use.
I decided to write a review worksheet that would help students get a lot of practice with series in a short amount of time (that led to my second recommendation--to a student who was preparing for a BC Calculus exam and clearly needed some practice with Series Tests). While writing that worksheet, I realized that Wolfram|Alpha was also well-suited to teaching the Integral Test. The problem there is not that students need more practice--but that no one remembers to check the hypotheses. This is mostly because checking the hypotheses is a drag, and even instructors skip it as much as possible; it occurred to me that Wolfram|Alpha could make it easy, which means we could do lots of examples, which means students might remember that it's important.
While tutoring this semester, I have recommended Wolfram|Alpha to two students. The first was for a Math 220 student who I felt needed lots of practice with the substitution method. At first I told him to email me if he wasn't sure he'd gotten the right answer--and then I realized that he could instead just check his answer with W|A. This would allow him to get through a lot of practice without supervision and without wasting time.
That got me thinking about other places where practice is especially important, but time is lacking. I tutored for Math 231 last summer; this is a particularly tough class to take during summer term, because there is so little time--and the Sequences and Series section always gives students trouble, even during a normal semester. During summer, students have even less time to do enough homework to build up a good intuition for which Series Test to use.
I decided to write a review worksheet that would help students get a lot of practice with series in a short amount of time (that led to my second recommendation--to a student who was preparing for a BC Calculus exam and clearly needed some practice with Series Tests). While writing that worksheet, I realized that Wolfram|Alpha was also well-suited to teaching the Integral Test. The problem there is not that students need more practice--but that no one remembers to check the hypotheses. This is mostly because checking the hypotheses is a drag, and even instructors skip it as much as possible; it occurred to me that Wolfram|Alpha could make it easy, which means we could do lots of examples, which means students might remember that it's important.
