Just finished teaching a short course on software for use in math classes.It's a course required for math majors, and the objective is to familiarize students with the various types of software to do math.
Way back when, like ten years ago, math software was the domain of licensed software housed in college computer labs. The usual stuff happened - the computers got updated, but the software license did not get renewed. And excuses for not using the software abounded - you could only use the software in the labs, students couldn't afford the software for their home, etc. etc.
Fast forward to 2010. Students bring in their own laptop and WiFi is freely available. I built my software course around free or easily available software such as Wolfram|Alpha, Geogebra, and Excel. Of the three, Geogebra was quite a hit. Students could download the software for free on their own laptops or use the web based applet. And they were up and running without mastering any rarefied syntax.
Wolfram|Alpha was a close second. There was some frustration that the "natural language" interpretation of W|A was not so natural! Nevertheless, the students did find W|A to be a good tool for doing math.
Then there is the lowly spreadsheet. Found basically on every desktop, students were quite surprised you could do actual math in Excel. They used it to model data, forecast trends and examine limits and difference quotients.
I put all the course material on our campus Blackboard. I plan to transfer it to my Moodle account so that the course material is accessible to everyone.
Integrating math technology easily - no licenses, no fees, no excuses...
Sunday, May 30, 2010
Friday, March 26, 2010
Proofs and Wolfram Alpha
In my Introduction to Proofs course, I discussed the proof the following: The cube of an integer is of the form 9k, 9k+1, or 9k+8, for some integer k. The problem is from the text I use, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
The big idea here is to to note that any integer can be written as 9q+r, q some integer, r=0,1,2,..,8. Then simply find (9q+r)^3 and examine the form of the expression of the nine different cases for r. The algebra is a bit tedious - and so Wolfram Alpha comes to the rescue in the form of the command
Note that the proof itself consists of the big idea of writing an integer as a multiple of 9 with a remainder. W|A simply did the grunge work for us of expanding the polynomials and substituting the values of r. In a course such as this, W|A can be a great timesaver in doing these types of calculations and students see the value of such software as efficient helpers in solving larger problems.
The big idea here is to to note that any integer can be written as 9q+r, q some integer, r=0,1,2,..,8. Then simply find (9q+r)^3 and examine the form of the expression of the nine different cases for r. The algebra is a bit tedious - and so Wolfram Alpha comes to the rescue in the form of the command
expand((9q+r)^3) for r from 0 to 8The output is here:
Note that the proof itself consists of the big idea of writing an integer as a multiple of 9 with a remainder. W|A simply did the grunge work for us of expanding the polynomials and substituting the values of r. In a course such as this, W|A can be a great timesaver in doing these types of calculations and students see the value of such software as efficient helpers in solving larger problems.
Monday, March 15, 2010
Teaching teachers to teach
An article in last Sunday's New York Times discusses the complex issue of teacher preparation. The writer of the article includes a lengthy discussion of math teaching in particular. I found it to be quite interesting - the work of math educators doesn't usually make it to mainstream media. Hopefully the Times will continue its coverage of key education issues such as this one.
Friday, March 5, 2010
Getting students to be quantitatively literate
One of the main aims in teaching a Math for Liberal Arts course is to get students to have a better appreciation of general mathematics. And what better way to do that than to have them read math articles or blogs aimed at a general audience? Sounds like a good plan, but I needed to make it a graded assignment so it would get done.
In my online course I am now making up questions related to articles in Steven Strogatz's NY Times blog. Steven Strogatz is a mathematics professor at Cornell University. He makes basic math so clear and brings in so many connections that anyone who reads it will get something out of it, no matter what their education level is. Using his post on algebra, I asked my students the following as part of a longer homework assignment:
In my online course I am now making up questions related to articles in Steven Strogatz's NY Times blog. Steven Strogatz is a mathematics professor at Cornell University. He makes basic math so clear and brings in so many connections that anyone who reads it will get something out of it, no matter what their education level is. Using his post on algebra, I asked my students the following as part of a longer homework assignment:
Suppose the length of a hallway is y when measured in yards, and f when measured in feet. Write an equation that relates y to f.I gave them the wrong answer of y=3f and asked them to figure out why it's incorrect. Not exactly rocket science, but having them read something about math other than what's in a textbook is a big thing for many of my students. When we get to the probability and stats part later in the semester, I plan to do something similar with the abcnews.com articles by John Allen Paulos, math professor at Temple University. These articles are not as direct as Strogatz's, but do aim at probabilistic understanding for a general audience.
Wednesday, February 24, 2010
Online math courses and academic integrity
For the past three years, I have been teaching an online math course every semester. To ensure that the students taking the class are really the ones who signed up, I have always used in class midterm and final exams. I check their ID and my grading system system reflects a heavy weighting toward the in-class tests. I encourage students to use whatever resources are available, including Wolfram Alpha, to study and do their online homework. They know that the in class exams are closed book and so the outside resources mainly serve as a study guide. All information about my online classes are publicized well before the class starts, and so the students know what is expected.
I do wish there was a better way to monitor academic integrity other than in-class tests. A presentation by Judy Baker, Dean at Foothill College, CA, discusses many aspects of online learning and academic integrity.
I tend to agree with her that most students are honest. But the anonymity of an online course can certainly tempt students to compromise their sense of ethics, especially those who are math-phobic. High tech security measures are too cost-prohibitive to use in an academic online setting. As online programs and courses are expanding in colleges and universities, there certainly needs to be a discussion on how to check identities of the students in the classes, and to ensure that they are the ones doing the work. One suggestion is to require students to make a presentation using a webcam. Would a one-on-one short oral exam using something like vyew.com and a webcam work for math courses? It is worth thinking about. But I think that an online course with no face to face interaction, either virtual or real, is opening itself to all sorts of compromises.
I do wish there was a better way to monitor academic integrity other than in-class tests. A presentation by Judy Baker, Dean at Foothill College, CA, discusses many aspects of online learning and academic integrity.
I tend to agree with her that most students are honest. But the anonymity of an online course can certainly tempt students to compromise their sense of ethics, especially those who are math-phobic. High tech security measures are too cost-prohibitive to use in an academic online setting. As online programs and courses are expanding in colleges and universities, there certainly needs to be a discussion on how to check identities of the students in the classes, and to ensure that they are the ones doing the work. One suggestion is to require students to make a presentation using a webcam. Would a one-on-one short oral exam using something like vyew.com and a webcam work for math courses? It is worth thinking about. But I think that an online course with no face to face interaction, either virtual or real, is opening itself to all sorts of compromises.
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