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This blog is no longer active. Please see my website http://www.mymathspace.net 
The older material will still be here, because of web searches.

Web based Excel

It is now possible to run a limited version of Excel completely on the web. Below is an Excel web app that I created. It's interactive - you can change numbers and the results will change. More Excel material can be found at my website, http://www.mymathspace.net

MOOCs as course supplements

I'm teaching an Intro to Proofs course this Fall, and am planning to have students also sign up  online for a course called Introduction to Mathematical thinking, a free massively open online course (MOOC) offered by  coursera . The course will be delivered by Stanford professor Keith Devlin, and looking at the online course outline, it looks like a perfect supplement for my transitions course.

This will be the first time I am trying this, and I myself have not taken any coursera course. Looking forward to this experiment. It can only enhance the students' learning experience, and it doesn't cost anything.

Interactive math demonstrations from Wolfram

The following is one of literally thousands of interactive demonstrations in the Wolfram Demonstrations web site. You will need the free CDF player to run the demonstration. A small collection of these can be posted on a class web site for students to explore and then answer questions interactively, perhaps using Google forms, or as a hand-in assignment. Formulating good questions to go along with these demonstartions is a necessity if students are to comprehend the concepts. Otherwise, it may just seem to them like a dumbed down video game!

Quadratic in Vertex Form (or Turning Point Form) from the Wolfram Demonstrations Project by Rod Bate

Google and other online graphers

You can enter an expression like sin(x),cos(x) into the Google search box, and it will give you a graph that you can zoom in on and trace! Pretty simple - nothing to download! Can ditch the graphing calculator for just plain graphing.

You can also check out the Desmos online calculator, which has many features. I  found out about it recently,  from Maria Andersen's blog.

Math Jax

MathJax is a web-based JavaScript application that you can use to include LaTeX in your web pages, like the following.
\[ \cos^2x+\sin^2x=1 \]
\[ \int x \, dx = \frac{x^2}{2}+C \]
No GIF's to export, no complex, additional markups to learn etc. It just works!
If you want to use it in Blogger, click here. Planning to use it to create more math pages with interactive features, using Wolfram Alpha widgets and GeoGebra.

Quick quizzes for fun

A fun quiz to put on your web site can be created easily at xat.com. This one's for a mini review for calculus class I'm teaching in the summer.


Get Your Own Quiz!, More Quizzes

Some thoughts on math videos online

By now, most folks in the math teaching world have heard of Khan Academy. Other free video sites for math include Math TV and Brightstorm. I do refer students to these sites for review and reinforcement. In YouTube, these types of instructional math videos get a large number of views, and so they  obviously address a need out there.

However, I am not convinced that these types of videos actually illustrate concepts very well. There are now a wide variety of technologies that can illustrate math concepts and can be interactive. GeoGebra, graphing calculators, Microsoft Math, OCW applets in math (from  MIT), and lots of applets spread throughout the Internet do a great job of illustrating ideas that are hard to do with just chalk and talk (or their video counterparts). But a simple survey of YouTube videos describing their capabilities showed that they attracted far fewer viewers.

Is it just that students are used to wanting something reinforced the same way they've seen it in their lectures? Do they just want to get their (online) homework done? Are these types of resources used often enough in classrooms to illustrate ideas? 

I don't think any of these technologies takes away from basic skills. I think they make conceptual understanding easier  for many students - if they are guided along those lines. Not everyone can make abstract connections solely on the basis of processing symbolic notation. If one wishes to progress to higher level math or use math in other subjects, it is necessary to be able to think about math in addition to the skills, whether at the beginning algebra level or at the calculus level.And many of these technologies that have been around for a while now can make that task a little simpler.

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.)

Online LaTeX Editors

Although my primary word processor is MS Word 2007 for class materials, I use LaTeX for assignments in my upper level courses. Many of the assignments I create are not too lengthy and so I started searching for a quick browser-based online LaTeX compiler. Here are three I am experimenting with. The first one is totally free. The other two offer a free limited version.

• latexlab.org : works with your Google account sign-in, but it's not affiliated with Google. Advantage is that your tex files are in the Google docs folder. I found the previewer to be somewhat clunky and it seemed to run the slowest of the three I found. But it is free and has no restrictions.
• scribtex : worked very quickly on my sample latex file and rendered a nice PDF file in a separate tab. The interface is very minimalist, though. The free account has restrictions, but will be fine for my use of creating assignments
• verbosus: Has a nicer interface than scribtex, with the tex file and pdf file side by side, but a lot of the window's real estate was taken up with file and project windows. Maybe there is a way to customize it, but I didn't check it out. The free account has restrictions as well.

 I think I'll work with latexlabs and scribtex for now. But I thought verbosus was worth checking out.

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.