#MathEd – Math for My Nephew

A while ago I was asked to provide some resources I use to teach math for my nephew (well, nephew-in-law). I decided to gather them together into a blog post and thus get a two-fer.


Mathematical Association of America (http://www.maa.org/) – Their stated mission is “to advance the mathematical sciences, especially at the collegiate level.” Membership is open to students and teachers (K-12 and college), starting at $35/year (student with proof of status) and going up to $249/year (Member Plus). I’m a member and for me the real value of membership is access to a wide range of publications plus discounts on books, both e-book and printed. (Disclaimer: I currently write book reviews for the MAA web site but I am not compensated.) You can follow them on Twitter at @maanow and on Facebook as maanews.

National Council of Teachers of Mathematics (http://www.nctm.org/) – Like the MAA, the NCTM offers memberships to students, teachers (primary through college) and to organizations. They also offer the option of an ‘e-membership’ at each level for a slight discount. Membership annual dues range from $44 (Student and Emeritus) to $144 (Full Individual Membership). Membership gives you access to a host of instructional materials, NCTM’s ‘e-standards’ and NCTM’s E-Seminars, 60 minute on-demand video presentations on a variety of math education topics. You can follow them on Twitter at @NCTM or on Facebook as NCTM Illuminations.


Math with Bad Drawings – This is one of my favorite sites. Ben Orlin provides an entertaining and educational view of math from a teachers perspective. The title comes from each post being illustrated by a series of stick drawings on a whiteboard. I wrote a review of his site here. I’ve used some of his posts as jumping-off points for discussions in my math class. You can follow Ben on Twitter as @benorlin. He’s also on Facebook but doesn’t appear to be too active.

MathBabe – Cathy O’Neil is a former Wall Street quantitative analyst who left for the wilds of higher education. She mainly blogs about Big Data and math education in higher ed. I wrote a review of her site here. A smart, interesting, fun site. You can also follow Cathy on Twitter.

Finding Ways to Nguyen Students Over – Fawn Nguyen is a California math teacher who has one of the best math blogs I’ve seen for primary and secondary educators. She clearly works hard to present math to her students in innovative and entertaining ways and she shares these techniques on her blog. (I wrote a review of her site here.) However, the real hidden gems of her site for educators are the affiliated sites like Visual Patterns, Math Munch and Would You Rather. These sites are a treasure trove of fun math problems and exercises you can share with your students or work on your own.

The NRICH Project – Not a blog per se, but The NRICH Project was started by the University of Cambridge, according to their “About” page:

“to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.”

(More here.) The content is divided into material for teachers and students. Each category is further divided into primary and secondary education. The idea is to present tasks that target multiple learning styles. These are known as “rich tasks” and you can get more information about them from this article.  Teaching materials are printable and downloadable for ease of use. You can also follow the NRICH project on Twitter  and on Facebook. You can sign up on their mailing list to get updates. They also provide a guide for parents and caregivers.

Project Euler – Also not a blog but a cool site for more advanced math fans. (Yes, there are some of us out there.) It’s a collection of almost 500 math problems, some of which may require basic programming skills. Each problem builds on insights gained solving previous problems so I advise doing them in order. I’ve posted a few of the problems on my site. Working on the problems presents interesting insights and is definitely mind-expanding.


NumberPhile – This is a nice resource of short, entertaining videos about specific math concepts. I do a short segment at the beginning of my classes called “Math Minute” and I’ve used several of these as inspiration for material. You can also follow them on Twitter and Facebook.

ComputerPhile – Not strictly related to math, but computer science is based on math. Similar to NumberPhile, ComputerPhile provides short videos about topics like undecidability, cryptography and how computers use math to do animation. You can follow them on Twitter or on Facebook.

I’m always looking for good math resources, both for my classroom and this blog. If you have any interesting leads, post them in comments!

#WeHateMath Apples v. Oranges

Recently I was asked to briefly explain the difference between math and arithmetic.  Here’s what I came up with:


Arithmetic can answer the question:

“What is 3 plus 2?”

Arithmetic cannot answer the question:

“What are 3 apples plus 2 oranges?”

Math, on the other hand, can take a higher order look at the problem and answer:

“3 apples plus 2 oranges are 5 pieces of fruit.”

Math is about relationships and patterns.

Math is arithmetic plus context.

#WeHateMath #DIYMath FreeMat

(Cross-posted at Coding4Humans)

Today in DIY Math we’re looking at  FreeMat. As the name suggests It’s modeled after MatLab. FreeMat has been in development for over a decade by a group of volunteers

System Requirements – Specific hardware requirements were not available but the pre-built packages I tested all run on 32 or 64-bit Intel-compatible CPUs. The application itself doesn’t seem to use much memory. As an example, the Mac version uses about 85 MB of real memory on my system. Since Windows XP is supported, we can assume that XP-compatible hardware constitutes the base system.

Installation – The latest version is 4.2 and is available for Windows (XP and up), Linux (various) and Mac OS X. In addition to pre-built packages for the above platforms, the source code is also available and is released under the GPL license. All versions of FreeMat are kept at the same version level and functionality.

Windows: Simply download the 52.5 MB setup file and double-click it. (NOTE: A portable version of Freemat is also available so you can run it from a thumb drive without installation.)

Linux – I installed FreeMat on Debian Linux using APT and on my system it was a 12 MB download, using an additional 22 MB of disk space.

Mac OS X – The installer is a 79.5 MB compressed disk image (DMG) file. Double-click the file to mount it, then drag the program and documentation to your Applications folder. The two files together take up about 250 MB of disk space.

Documentation – The Mac download comes with a PDF manual detailing all of the functions available in FreeMat. (For Windows or Linux, you can download the manual here.) The manual is automatically generated using Doxygen, which scans specially marked comments in the source code and outputs documentation in a variety of file formats.

This is both a good thing and a bad thing. It’s good in that it makes it easy for developers to actually maintain their documentation, assuming they remember to update the comments. It’s a bad thing because there’s no guarantee that the resulting document will be well-written. In fact, the included manual is very sparsely written, despite the 162 page (!) table of contents. It is less a manual than simply an API reference. Each function or class is briefly described and includes one or two usage examples. The target audience for this manual are those who don’t need a manual. It’s comprehensive but very terse.

A much better option to start with is the FreeMat Primer. Who’s the audience? Let the authors (Gary Schafer and Timothy Cyders) tell you:

We assume that you have Freemat properly installed and working. If you have any issues, direct them to the online Freemat group, http://groups.google.com/group/freemat.

This book was originally written for the Windows version. The book now covers more of the Linux and Mac versions, as well. In those cases where there are differences, we’ll point them out.

It’s a much friendlier introduction to the software. It’s very readable, with plenty of screenshots, little tutorials and code examples. With this and the official function reference you have a very good documentation base. In addition, there is also a Google group available for more interactive support. There is another Google community intended to host FreeMat tutorials. (At this time the content is a bit sparse.) You can also type helpwin at the command prompt from within FreeMat.

Compatibility – Based on the scripts I tested, MatLab support is somewhat hit-or-miss. I’ve been able to run scripts with no modifications, minor modifications or not at all. I would suggest that you test your Matlab scripts on a case-by-case basis and then decide whether you want to make the changes or just re-write from scratch. The scripting syntax is similar enough that most of your work will be figuring out equivalent function calls.  (A MatLab to FreeMat translation guide would be a really good project. Better yet, some kind of conversion tool.)

Command Line vs. GUI – The Windows and Mac versions of FreeMat are targeted at a graphical interface so accessing the tool from the command line is at best a non-trivial . The Linux version can be launched from the CLI. With no parameters, the graphical client starts up by default. To use the CLI version only, start the tool with the option -noX or -nogui to suppress the graphical subsystem This will give you a FreeMat command prompt in your terminal window. If you simply wish to run a Freemat command and then exit, use the option -f to run the tool in command mode. (NOTE: if you want to see the output of your command, make sure to specify that as FreeMat will not show any output.)

Integrating FreeMat with your native scripting environment is problematic (okay, just about impossible),as FreeMat scripts are meant to be run from within the FreeMat interface. You can edit them inside FreeMat or using your favorite text editor but make sure that they are saved to FreeMat’s working directory. (You can set this up by running pathtool from within FreeMat.)


The GUI for each version is comparable in look and feel.

FreeMat Interface

FreeMat GUI

This is from the Mac version of the tool. In addition to the main terminal window, FreeMat also tracks your command history (allowing you to invoke a previous command simply by double-clicking on it), tracks what variables are currently in memory, along with their data types and values if applicable. The Debug window is supposed to show any error or warning messages but on all three platforms I tested, the messages showed up in the main terminal window and the Debug window remained blank.


Pros: Easy installation, all supported platforms are kept current with a common codebase, decent documentation and online support.

Cons: Development progress is a bit slow. The latest release (4.2) was posted in June of 2013 and that was two years after the previous release. CLI support is limited or non-existent in the Windows and Mac versions and all scripts are restricted to running within the FreeMat environment. Third party support is a bit anemic.

Would I use this in my class? – I would feel confident recommending this to my students. The ease of installation and minimal setup are a definite plus, you don’t need the latest hardware to run it and the price fits everyone’s budget. It supports nearly everything we might do in 100- and 200-level math classes with enough overhead room for more advanced work.

#DIYMath – Math Wants to be Free

(Cross-posted at Coding 4 Humans)

As a programming and math nerd, I’ve certainly made good use of Wolfram Alpha. After all, it’s free*, it’s ubiquitous (all you need is a Web browser but there are also apps for both Android and IOS) and it’s natural language interface is very powerful and easy to use.  It’s certainly a cost-effective alternative to commercial math packages like Matlab ($50 – $2,150) or even Wolfram’s own Mathematica. ($139 – $2,495)

However, much as I love the folks at Wolfram, it’s nice to have your own math software that:

  • doesn’t require an Internet connection
  • runs on computers you control
  • still gives you a lot of power and flexibility

It’s even better if the software is:

It turns out that there are several software packages that fit the bill, each with their own strengths and weaknesses but all absolutely free and cross-platform. With that in mind, I’m going to be reviewing each of them from the perspective of a teacher and casual programmer. To keep things consistent, I’ll be looking at the following categories:

System Requirements – Because there’s no point downloading the software unless you can actually run it.

Installation – How easy is it to find and install the software? How big of a download is it and how much disk space and RAM does it need? How does installation compare between platforms? I’ll be installing the software on Windows 7, Debian Linux and Mac OS X Mavericks and comparing the experience.

Documentation – Does the developer offer good documentation and/or tutorials? (By ‘good’, I mean documentation you are actually expected to read**.) Is information available from third parties?

Compatibility – Like it or not, MatLab and Mathematica are the big dogs in the math software field. How easily could a MatLab or Mathematica user transition to this package? How easy is it to port code? The easiest way to test this is to see if scripts designed for MatLab or Mathematica will run with minimal or no modification.

Command Line vs. GUI – Some of these packages allow you to run them from the command line as well as in a graphical interface. This is very useful as it allows you to integrate the software with your native scripting language for easy automation. How do the two compare? Do both offer the same functionality? Does the software operate in the same way on different operating systems?

Summary – Pros, Cons and whether I’d recommend this to my students.

As I’ve said, I’m looking at this from the perspective of a math teacher. Are there other aspects of the software you’d like me to examine?

*for a certain definition of ‘free’

**I’ve noticed that a lot of open source software documentation seems to assume that the target audience are those who don’t need to read it. Yes, poor documentation makes me cranky.

#TheMelvinProject My Apology to Senator Al Melvin

Dear Senator Melvin:

In March of this year, I wrote a post making fun of you and your opinions on the Common Core Standards.

Based on recent events, however, I would like to take this opportunity to apologize.

Sure, you admitted that you hadn’t actually read the standards document and what little you did hear about it, you grossly misunderstood. Certainly it was this lack of understanding that led you to follow your personal beliefs and oppose implementing the standards in your state of Arizona.

However, at least you didn’t say that implementing Common Core would make students gay.

So you’ve got that going for you, anyway.



#WeHateMath Storytelling in Math Education

Recently my math class was studying basic probability and I had one student who was really having a hard time wrapping her head around the topic. One evening I got an email from them, stating that they didn’t understand one of the practice problems:

Given that P(E) = 1/4 find the odds in favor of E.

I replied:

P(E) means the probability of E happening. 1/4 means that there are four possible outcomes and that E (the one we want) is only one of them.

We figure our odds for something by comparing the number of possible things that we want (in this case just one) versus the number of possible things we don’t (in this case the other three).

So the odds are 1 to 3 that our event E will happen because out of four total, only one of them is E.

I hope this helps.

They responded that it didn’t help and that they had read the chapter multiple times and just weren’t getting it.

I gave this some more thought and decided on a different tactic:

Let me give it one more shot:

We’re having a dog race — four beagles: Evelyn, Sam, Henry and Charlie.

All four dogs are evenly matched – same age, physical condition, everything – so each of them is equally likely to win.

However, Evelyn is your favorite and you’d like to know the probability that she’ll win the race.  There is a total of four dogs so she has one chance in four to win.  In math-speak, this is known as :

P(E) = 1/4

What about the odds? Well, It’s Evelyn against the other three dogs so we say that the odds for Evelyn winning are 1 to 3 or 1:3

Once I had expressed it in the form of a story, it clicked. They replied that they now understood what the problem was about and had a better sense of the material.


In my experience, the mere mention of ‘story problems’ (sometimes known as ‘word problems’) is enough to send my students into fits. (Google ‘story problems suck’. This is not an isolated issue.)

But stories are the primary way we humans communicate with each other. I use stories in my classes all the time. Sometimes they’re personal anecdotes (usually of the ‘See what I did there? Don’t do that’ variety), historical references or just something I made up like the example above.

I think that the issue with traditional story problems is that they’re not very interactive. Most seem to be little more than a written statement of the math problem we’re trying to solve.

So maybe we need better stories.

One promising project is Oppia. This is a Google project described as a “Tool for creating interactive educational content”. In other words, you can create a story that guides your student through a topic, periodically asking them to apply what they’ve learned to solve a problem within the context of the story.

You can set up your own copy of Oppia on your own computer to test it, contribute to or browse through the lessons at the official hosted server or just use their test server to see how it works. I played with one of the tutorials and it was very engaging. So head on over there and give it a try, let me know what you think.

#WeHateMath Blog Review – MathFiction

MathFiction is not strictly a blog per se but it’s unique enough that I felt it deserved a shout-out.  From the site description:


Do you like fiction and mathematics? Are you looking for a book or story that might be useful for the students in your math class? Are you interested in what our society thinks about mathematicians? Then you’ve come to the right place. This database lists over one thousand short stories, plays, novels, films, and comic books containing math or mathematicians.


The list is maintained by Alex Kasman, who teaches in the Department of Mathematics at the College of Charleston. I came across this site when I was doing some research for a blog post about using calculators in math class. I was trying to remember an Isaac Asimov short story that I had read which described a future where nobody is taught arithmetic any more since it’s all performed by machines. (“The Feeling of Power” [1957]) A brisk search of the Intertubes brought me to MathFiction and I was so impressed that I bookmarked it for my classroom tool kit.

You can browse through the material at your leisure or, if you have something specific in mind, use the search page, where you can either use the site-specific Google keyword search or power-search by author, title, summary, medium, genre, topic or motif. Entries are also rated by both math content (1 to 4) and literary quality. (You can search on these fields as well.)
As both a nerd and a math teacher, I have a feeling that I’ll be spending a lot of time on this site. So head on over there and tell Alex I sent you. (I’m trying to start a thing.)