IntMath Newsletter: Resources, inspiring teachers, KaTeX
By Murray Bourne, 30 Sep 2014
30 Sep 2014
In this Newsletter:
1. 20 Gifs That Teach You Science Concepts
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)
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:
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:
[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.
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.
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).
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;
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:
Until next time, enjoy whatever you learn.
See the 9 Comments below.
30 Sep 2014 at 8:37 am [Comment permalink]
The pattern alternates between closed shape and open. It also alternates between symmetry along the diagonal and rotational symmetry. The next shape should be closed and have diagonal symmetry, so the answer is B.
30 Sep 2014 at 3:37 pm [Comment permalink]
I would like to ask you to add an article bout rubix cube solving in future. And let me say I enjoy your stuff very much. Thanks.
30 Sep 2014 at 4:04 pm [Comment permalink]
@Dineth: Thanks for the suggestion. I used to play with Rubik's Cube many years ago. I don't know that much about solving it, but this article has some interesting information: The Mathematics of the Rubik’s Cube.
30 Sep 2014 at 4:08 pm [Comment permalink]
I cannot do these whats next in the pattern problems. What I think should be next is b) and here are the reasons:
The pattern seems to be alternating slopes, positive, negative
There's a pattern of number of end points, 0, 2, 0, 2 so 0 next right?
But then number of pieces 3, 2, 2, 3...2?
And angles, curves, curves, angles... curves?
And the slopes seem to suggest d)
So in a test I'd go for a) which seems least likely to me.
1 Oct 2014 at 12:41 am [Comment permalink]
Very interesting and useful articles.
I am going to use most of them in my classrooms.
(I am teaching math online from USA to three schools in India, one started by Gandhi, 100 years ago).
1 Oct 2014 at 2:19 am [Comment permalink]
Choice D. The pictures follow a pattern where the first is made with 3 parts, the second is 2 parts, the third is one twisted part. Now the pictures repeat with 3 parts, so I picked D, made with two parts.
9 Oct 2014 at 1:33 pm [Comment permalink]
Ans is (b) as given sequence is mirror image about alternate diagonal of the square.
9 Oct 2014 at 4:29 pm [Comment permalink]
Blondes (the puzzle from Oldaque P. de Freitas)
Two blondes are sitting in a street cafe, talking about the children. One says that she has three daughters. The product of their ages equals 36 and the sum of the ages coincides with the number of the house across the street. The second blonde replies that this information is not enough to figure out the age of each child. The first agrees and adds that the oldest daughter has the beautiful blue eyes. Then the second solves the puzzle. You might solve it too!
16 Oct 2014 at 2:54 am [Comment permalink]
The 1st and the 3rd shapes are "closed", 2nd & 4th are "open". So, there is a sequence closed, open, closed, open,... The 5th member must be "closed". The orientation of 1st & 3rd is up-left (ul) to down-right (dr). The 2nd & 4th are down-left (dl) to up-right (ur). Now, the sequence is ul-dr, dl-ur, ul-dr, dl-ur,... The 5th member must be ul-dr. That means a shape "closed", up-left to down-right oriented. Those criteria suggest figure "b".