Today I would like to introduce you to Murray Bourne, an Australian who lives in Singapore. I recently became aware of his squareCircleZ blog, browsed through it a bit, then couldn’t stop!
Actually, his blog is only one piece of a larger web presence – Interactive Mathematics (IntMath.com) – a great resource for everyone interested in learning math.
As I used to be the type of student who struggled with math (I preferred languages as a student), Murray’s website would have been a goldmine for me! Fortunately, as an adult, technology has helped me to value math so much more than I was able to as a child. Blogs like Murray’s always entice me to learn about mathematics.
So I reached out to Murray to learn more about him and ask him to share his expertise!
Bettina: Murray, you have a very impressive story to tell. Not only have you taught math (and other subjects) at a number of different institutions, you have also done so in various countries.
On top of this, you are running an extremely popular website visited by several thousand people per day. So I guess it is safe to call you a math enthusiast
How did it all start – have you always been “a math-guy”?
Murray: I was the youngest in the family and would hear my 2 brothers learning their multiplication tables, Euclidean geometry proofs, algebra rules, and so on. Later, when these things came up in my own lessons, I had some sense of what it was about and was fairly comfortable with it.
I had some excellent teachers at primary school, and I learned a lot of positive attitudes through that, including attitudes towards math.
Over time, I developed a broad range of interests (including music), but when choosing my eventual career pathway, mathematics won.
Bettina: Was math always easy for you then?
Murray: No, not always. I remember I really struggled with the concept of functions and only realized later that it was because of the terrible notation that’s used. I wrote an article about this issue, Towards more meaningful math notation.
Bettina: I think your website is a great resource. It must really help to ignite a spark in young people. For someone like me, your website could have been a great help. If something like it had been around at the time, it might have encouraged me to invest more time and effort into my math lessons and homework.
Murray: I’ve always tried to engage those who feel they are non-mathematical types. I find it sad that many math teachers get totally engrossed in algebraic symbols and cannot understand why their students can’t grasp the underlying concepts, or worse, don’t even want to grasp them! I’ve always felt that we need to put more effort into inspiring students to learn math.
In this regard I found Gardner’s work on multiple intelligences to be quite interesting. Based on his ideas, I have aimed to increase interest in math via music, art, language, and sociology (see below this article for some suggested reading!).
Bettina: Murray, I am sure you have worked with a huge variety of different math tools over time – when did you get started with Mathcad?
Murray: Mathcad was the first computer algebra system I’d ever come across, sometime in the early 1990s. It blew me away – here was the tool that I had been looking for. Finally there was something that could remove the tedium of algebra and calculation; a tool that allowed you to explore math and communicate it clearly.
It also allowed you to spend more time on thinking about applications and the meaning of mathematical processes – and my favorite area, graph drawing.
Bettina: Murray, having worked with so many different tools, you really know what to look for in math software – especially from an educator’s perspective. I think our readers might find it interesting to hear your thoughts on what they should look for when evaluating math software for their classes or their children.
Murray: Sure – I’m happy to share my thoughts on this.
Top 5 list of what to look for in math software:
- It must be easy to enter math, both with a GUI (graphical user interface) and with keyboard short cuts. It also must be intuitive and have a good Help system, with plenty of examples that can be re-used and modified.
- The resulting math must look like “text book” math, so it is easy to read. Notation should be consistent with most text books in common use.
- You should be able to export the document in many formats (including as images, and as LaTeX and MathML). It is a plus if it can produce interactive animations for the Web (and for mobile devices), without the need for extra plugins.
- It must produce attractive graphs that are interactive (easy to zoom, drag, 3D rotations, etc), and with good options for placing axes, changing font sizes and so on.
- It must be easy for students to pick up and use, and have well-priced student editions. The emphasis should be on putting powerful tools in the students’ hands so they can explore math, rather than seeing it as a tool for the lecturer.
Bettina: Murray, this is a great list! Fortunately for us, Mathcad holds up well when measured against your high standards.
We have listed a few interesting articles below, if you want to learn more about Murray’s thoughts.
Here are some suggested links to learn how math relates to the “real world”.
- Trigonometric graphs and music
- Music and transformation geometry (this contains one of Murray’s own compositions)
- Music and Fast Fourier Transforms (warning – high level math!)
(b) Dance, kinesthetic
(c) Art, beauty
Here are some tips that may be helpful for our younger readers: