Elearning on a shoestring

Once again, I'm teaching an online statistics class this Fall. While the online materials that come with the text are really superior, I still needed a platform for my virtual lectures every week. I have used VYEW in the past, but that has a maximum capacity of 20 students for the free version.

I an now using Wiziq, which allows many more students, even for the free version. The interface is much improved compared to what it was in the past. Since many of my students wanted the recordings of the lecture, I upgraded to their premium version (just $50/ year) to get the ability to store the recordings. And students don't have to register to view the lecture.

I have also used Jing in the past, but upgraded that one too (for a whopping $15/ year). Now, I can publish my videos directly to YouTube, which is a big plus for me.

Colleges without a large budget for online learning and/or just a few online courses can use tools like WizIq or VYEW as opposed to enterprise level software such as Elluminate or WebEx.

Wolfram Alpha Widgets

You can now customize your Wolfram Alpha (W|A) queries using a W|A widget right on your web site. It's currently in the Beta stage. You'll see a widget,which I cooked up in a few minutes, below this post. I was able to control the output to just what I wanted. I did not need all sorts of complex number representations and other stuff that comes with the standard W|A query for a simple derivative. Also, with the widget, you don't leave the web site you're on. I plan to put some of these on my class web pages.


Here's another one.

Writing Math in Word 2007

In the past, I have not required my students to typeset math in their homework. They had the option of using Equation Editor or doing it by hand within their word processed documents. I have also encouraged them to use Google Docs, which has a TeX-like interface for math equations.

I recently started using the MS Word 2007 equation editor, which is quite different from the MathType editor they had before. For one thing, you type everything in-line, not in a separate window. You can also use a TeX like syntax to build up your equations, although the point and click feature is what is on the menu. The syntax is not documented  within Word 2007, though, and I suspect most people will simply use point and click. You can find more about the Unicode syntax for building up equations here. It's still a much better equation editor, and next time my students have an assignment using the word processor,  I will require that they use some type of equation editor.

"No Excuses" Software for Math

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...

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

expand((9q+r)^3) for r from 0 to 8

The 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.

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.

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:

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.

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.

Academic Integrity in Online Courses

View more presentations from Judy Baker.

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.

Counterexamples in Calculus

One way I motivate critical thinking in my Intro to Proofs class is by using counterexamples. The book, Using Counter-examples in Calculus by Mason and Klymchuk, provides an accessible set of ideas to think about. Producing counterexamples is an important step to thinking about proofs in general, especially for students who are used to computations. What I really liked about the book were the graphs that accompanied many of the counterexamples. Here is one statement to think about:

True or false: The tangent to a curve at a point is the line which touches the curve at that point but does not cross it there.

The book is actually intended for first year calculus students and could work in that context if the course emphasizes concepts along with the standard skill set.

 

And the counterexample for the statement quoted above is x cubed at the origin.

Are some online math homework systems frozen in time?

I'm teaching an online math course this semester on liberal arts math. I taught it online three years ago, and since then, a lot of innovative technologies have sprung up on the web. However, when I opened up the learning management system (LMS) associated with the textbook, I didn't find any incorporation of any of the new technologies that could streamline my teaching. Rather than rant about its limitations, I have simply chosen to add on the new technologies on my own.

The main reasons for using the LMS from the textbook publisher are the ebook and algorithmic homework. But online learning ought to be more than just text and worksheets on the web!  So here are a few of the free tools I'm using on top of the usual stuff you get with the LMS that comes with a textbook.

• vyew.com   This is a free online meeting tool where I schedule my "virtual lectures" with audio and Powerpoint slides. Students can interact via a chat column on the left of the screen. The students need not register, and the presenter registers for free. I used it during Fall 2009 and it worked quite well.  By the way, check out Maria Andersen's  tips for effective webinars .
• Google docs  Aside from the automated homework, I also have students hand in exercises that they have to write up. In the past, I had them email them to me or drop it in a "digital dropbox" within the LMS. Either way, I had to do the open-edit-save cycle for each document.  With google docs, the student creates a file on the web and simply sends me the link as a collaborator. I just click, edit and save in the same location and I'm done! No attachments to email back and forth. This is the first semester I'm implementing this. Our university's email system is through Google, and so all students already have access to Google docs. Even otherwise, they can create one for free.
• Wolfram Alpha This computational engine not only solves equations, but also has access to many data sets. I am planning to use it for students to make specific queries and write up the implications of what they find.
  

Hopefully, the publisher issued LMS's will evolve to include tools such as these. My virtual lectures especially have tended to create a lot of interaction among the students and myself. It can really help reduce a feeling of isolation in an online course.And Google docs and Wolfram Alpha are technologies our 21'st century students should become familiar with anyway.

The paradox of higher math standards in high school

Those of us who regularly deal  with entering college freshmen are all too familiar with their inadequate math preparation. But in fact, high school mathematics has been ramped up quite a bit in terms of content. What happened? An article in the American Physical Society discusses this paradox. The author of the article, Dr. Joseph Ganem,  is a professor of physics at Loyola University, Maryland. He is also a parent of children in high school. He  noticed that over the years, the math homework his children were assigned required his frequent intervention. Since this is a parent with a Ph.D. in physics, he had no trouble helping them. But what about the many other students who do not have such an educated parent or access to tutoring services?  Sounds like many students are just muddling through their jr. high and high school math without retaining much of anything.  He points to two major flaws in the high school curriculum:

1. Confusing difficulty with rigor. It appears to me that the creators of the grade school math curricula believe that “rigor” means pushing students to do ever more difficult problems at a younger age. It’s like teaching difficult concerti to novice musicians before they master the basics of their instruments. Rigor–defined by the dictionary in the context of mathematics as a “scrupulous or inflexible accuracy”–is best obtained by learning age-appropriate concepts and techniques. Attempting difficult problems without the proper foundation is actually an impediment to developing rigor.  (emphasis mine)
[....]

2. Mistaking process for understanding. Just because a student can perform a technique that solves a difficult problem doesn’t mean that he or she understands the problem. ...

Pushing students too early to do algebra is not really the answer to our perennial problem of students being noncompetitive in the global mathematical landscape. We ought to invest in better teacher prep programs in colleges and provide better incentives for pursuing a career in K-12 teaching. And the math that is taught should be focused and connected, not just a drill based collection of disconnected topics, nor the latest reform program designed by math educators from the education college.