IntMath Newsletter: Resources, inspiring teachers, KaTeX

30 Sep 2014

In this Newsletter:

1. 20 Gifs That Teach You Science Concepts
2. Make!Sense
3. MOOC: Audio Signal Processing for Music Applications
4. Inspiring teachers (8 TED talks)
5. KaTeX - a new way to display math on the Web
6. Math puzzles
7. Final thought - Why I'll never tell my son he's smart

1. 20 Gifs That Teach You Science

If a picture is worth a thousand words, a good animation is probably worth a million. Here's a collection of animations that I hope you find interesting: 20 Gifs That Teach You Science Concepts Better Than Your Teacher Probably Can (this has disappeared)

2. Make!Sense

A lot of math (and science) is text-book driven, whereas it's often better to learn concepts as a result of observing and interacting with actual objects.

Make!Sense is a new product that helps to achieve this goal. Here's the developer's description:

"Make!Sense is a universal interface system that allows you to quickly and easily connect different types of sensors to your computer or smartphone. You can use Make!Sense to observe movement, moisture, light, temperature, even your own heartbeat! If you’re curious about it, you can probably Make!Sense of it."

I've found that students respond well to playing with such data loggers. It's hands-on and usually a lot more meaningful than worksheets.

Here's their KickStarter page:

Make!Sense

[KickStarter is a crowd funding platform.
Disclaimer: I have no connection with this product.]

3. MOOC: Audo Signal Processing and Music

Stanford University is offering a free MOOC starting this week (1st Oct 2014) A MOOC is a "massive online open course". This one promises to be a very interesting application of math to music. Audio Signal Processing for Music Applications

For some background on what this course is about, and to get an idea of the concepts involved, see:

Fast Fourier Transform (on IntMath)

See more Stanford University MOOC offerings.

4. Inspiring teachers: 8 TED talks

Here's some good ideas from great teachers for the start of the school year.

The role of the teacher is crucial in every class, but especially in math. Here's a collection of TED talks by inspiring teachers. All of them are relevant for improving math education. TED talks - Inspiring Teachers

5. KaTeX - a new way to display math on the Web

I think it's important to be able to communicate math concepts easily in online forums and other digital media. KaTeX is similar to MathJax in that it can display math without using images.

KaTeX is a new method for publishing LaTeX-based math on the Web. It's faster than MathJax, but not as robust (yet). KaTeX - a new way to display math on the Web

There's also KaTeX with ASCIIMathML input and MathJax fallback

6. Math puzzles

The puzzle in the last IntMath Newsletter asked about a rectangle whose perimeter equals its area. The correct answer with explanation was approached in 3 different ways by the following respondents:

Algebraic: Francis, Joe, Tomas, Smitha, Francisco, and bahaa;

Tabular: Janet;

Graphical: Nicos and Abby S.

In their answers, Nicos and Abby are talking about the graph of

(where x and y are the side lengths). Here's what it looks like (it's a hyperbola):

We don't use the lower-left arm of the hyperbola (which would give us negative lengths).

The point A on the graph is (4, 4), the solution which gives us a square. (But the question said it cannot be a square.)

The answer has to be near this point on the curve (the further you are away from this point, the bigger the rectangle becomes.)

If we try x = 5, it gives y = 10/3, which isn't an integer.

But x = 6 gives y = 3. Both are integers, their product (the area) is 18 and this equals the perimeter 2(3 + 6) = 18. Hence point B represents the answer. (It's equivalent to (3, 6).)

New math puzzle: Consider the following sequence of images.

Which one of the following represents the next in the series?

Leave your responses here.

7. Final thought - growth mindsets

Salman Khan, well-known creator of the Khan Academy, has some great things to say in his article, "The Learning Myth: Why I'll Never Tell My Son He's Smart".

He talks about 2 ways of approaching learning, with either a fixed or growth mindset. Here's a quote:

Fixed mindsets mistakenly believe that people are either smart or not, that intelligence is fixed by genes.

People with growth mindsets [however], correctly believe that capability and intelligence can be grown through effort, struggle and failure. [They] embrace challenges, and understand that tenacity and effort can change their learning outcomes.

The take-home message is that we should praise effort, diligence and tenacity, not inherent skills.

See the complete article: The Learning Myth: Why I'll never tell my son he's smart

Until next time, enjoy whatever you learn.

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