Wolfram|Alpha widgets for an online course

I've blogged about using Wolfram|Alpha (W|A) widgets for general use. Since I teach an online intro stats course every year, I thought it be handy to embed the widgets right in the topics section within the course management system. W|A widgets can fetch some data distributions - it's a lot easier to insert these types things at point of use rather than to send students to web sites all over the Internet. Also, I do not have to type extra instructions so that students can obtain the proper data. Here is the one I plan to use for some health statistics. ( I noticed that the units on the plot for height and weight seem to be inconsistent with the text - puzzled by that one, since W|A is usually pretty accurate.)

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.

"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.

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.

Efficient Math Commands for Wolfram Alpha

Wolfram Alpha is a free, online, computational engine. It provides some of the power of a computational algebra system (CAS) such as Maple or Mathematica without having to learn the proper syntax. However, it takes a little bit of practice to get WA to give exactly what you want.

Here, I'll give a list of queries that are commonly used in math classes:

• Solving an equation in one variable:  solve 3x^2-1=0 
  
• Solving an equation for one variable in terms of another:  solve 3x+2y=-8 for y
• Factor an expression: factor (4x^2-16y^2) 
• Simplify an expression: simplify (x+3(x+2)^2-2(x-y)) 
  
• Plot a function:  plot x^3-x^2
  
• Plotting a function on a given interval:  plot sin(x), x=-pi..pi
• Take the derivative of a function: derivative of (x^3+sin(x))
  
• Higher derivatives: second derivative of (x^3+sin(x)) 
• Higher derivatives, symbolic:  d^2/dx^2(x^3+sin(x))
• Integration:  integrate (x^3+sin (x))
• Definite Integrals: integrate (x^3+sin (x)), x=-2..3 

There are many, many more cool things you can do with Wolfram Alpha and I have only scratched the surface here. But the commands above should take care of most of the solving equations and graphing chapters in algebra, and the differentiation and integration material in calculus. I've told my students about it so that they can check their homework.

One thing to note is that WA will often give both graphical and algebraic representations for solutions of equations. It really helps students to connect those concepts.  However, it is not going to help a student set up and solve a word problem or help them to interpret a solution or a graph. If you're interested in teaching or learning both math concepts and skills, then WA is an extremely useful tool.

 

Wolfram Alpha

There has already been a lot of buzz about the online computational engine called Wolfram Alpha (WA). You can check out this article in the Wall Street Journal, for instance.

My main interest in WA is to figure out how to integrate it into the classes that I teach, which range from developmental mathematics to graduate level numerical analysis.
In a summer 09 class I taught in Intermediate Algebra, I told all my students about WA and encouraged them to check their homework answers using it. Here's a worksheet on lines that I wrote using WA.



The answers are already given by WA - I'd like the students to figure out how they were arrived at. Also, WA automatically ties in the algebraic and graphical perspectives. This makes connecting concepts much easier. I plan to do more worksheets of this sort in the future for material in precalculus and calculus and will be posting them here.