Why Math? Why Physics? Why Science? Why Care? This is why.
Every math teacher has heard it, "Why should I care about math?" I've talked with numerous students and shared with them a value I've always seen in mathematics that few address when asked this question. Math engages the brain in critical thinking and problem solving. Perhaps most students will not need to know how to multiply matrices when they reach their actual job, but that job will ask them to follow a set of rules (row times column) and to think about how they can use those rules or tools to solve a problem (solving a system of equations). That's what I tell people and for the most part I think it's pretty correct, but in the deepest corners of my heart, it's not the number one reason why I think math is important.
What I truly believe is this:
I love math, and believe most students would too (If presented correctly), because it is an art form in-and-of-itself. It is a game, a puzzle, and we as humans are naturally curious. Consider the following example, motivated by Paul Lockhart's A Mathematician's Lament.
I have supplied two figures below, where a triangle is contained in a box.
QUESTION: How much of that box does the triangle take up? Two-thirds? Three-fifths? Four-ninths? Does it matter where the tip is placed?
What I truly believe is this:
I love math, and believe most students would too (If presented correctly), because it is an art form in-and-of-itself. It is a game, a puzzle, and we as humans are naturally curious. Consider the following example, motivated by Paul Lockhart's A Mathematician's Lament.
I have supplied two figures below, where a triangle is contained in a box.
QUESTION: How much of that box does the triangle take up? Two-thirds? Three-fifths? Four-ninths? Does it matter where the tip is placed?
Once you've played with this question for a moment, click on the button below and see what you think of ONE possible solution.
Most of education isn't what you learn, it's how you learn it. If I can show students how they can look at a problem critically or mathematically when they leave my classroom, I'll consider it a success.
If that reasoning isn't enough, there's always these below.
If that reasoning isn't enough, there's always these below.
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Start Brachistocrone at 4:45.
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Twelve Days of Christmas Song
Although it is possible to answer many of the questions connected to this holiday song by hand (in math we call this the brute force method), what we really care about in mathematics is noticing the patterns and then generalizing to describe the actual mathematics that is going on behind the scene.
Did you know there is a connection between this song, Pascal's triangle, tetrahedral numbers and pyramids?
http://math.la.asu.edu/~rich/puzzles/prob015s.html
http://dimacs.rutgers.edu/~judyann/LP/lessons/12.days.pascal.html
Did you know there is a connection between this song, Pascal's triangle, tetrahedral numbers and pyramids?
http://math.la.asu.edu/~rich/puzzles/prob015s.html
http://dimacs.rutgers.edu/~judyann/LP/lessons/12.days.pascal.html
The Office Math
Below are a few clips. If you haven't seen the original scene from the Office, it can be found here. The second and third videos are detailed clips of what you have to work with to solve when the box will hit a corner. I've also included a picture of the grid. Your job is to tell me when and in what corner the box will hit. Can you do it???
DVD Screensaver — Plain from Dan Meyer on Vimeo.