Tag Archives: math

On Truth and Freedom (or, Math as a Liberal Art)

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“Mr. Faulkner, I really struggled with this problem.  I knew I was somewhat on the right track but I just could not figure out how to get to the answer.  So I started to get frustrated, but I kept working.  Then finally I figured it out and I was so excited that I shouted, ‘Yes, I’ve got it!’ so loudly that my mom heard me from the next room.”

“And how did you feel when you finally found the way to the answer?”

“I felt . . . I felt free.”

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“For now we see in a mirror dimly, but then face to face; now I know in part, but then I will know fully just as I also have been fully known.”  1 Corinthians 13:12

“And you will know the truth, and the truth will set you free.”  John 8:32

“Do Your Math!”

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Many students “don’t like” math because they “can’t do” math.  Many students “can’t do” math because math has only ever been presented to them as something “to do.”  Rarely is math presented as something “to understand,” even less often something “to contemplate,” and hardly ever something “to love.”

Why is that?  We know why.  Math is the lowest hanging fruit (science is a close second) for the “practical” utilitarian agendas of modern education reformers nationwide.

Math tutors everywhere make money hand over foot showing kids how to use shortcuts so that they can “do math.”  “Don’t worry about understanding this concept, just learn the trick!”  Besides, parents aren’t going to pay a tutor to help their child love math; the expected return on their investment is quite simply a solid “A” in the class.

Or a high score on the SAT (don’t get me started).

So we’re left with students (and I was one of them!) who can find the area of a circle, but can tell you nothing about Pi except that it can be approximated as 3.14.

Big deal, you say.  Does a carpenter need to understand the elegant beauty of the design of a screw if he can use screws effectively and efficiently to build a beautiful house?

Maybe not.

But if we decide that math is for doing, not for knowing (much less for loving), then we are withholding beauty and truth (and, in my opinion, a piece of God’s glory) from our students.  In other words, we’re cursing them.  And math class will end up being a complete waste of time for all the students who don’t become engineers or accountants.

But no, you say.  For those non-accountants and non-engineers math still teaches them to think logically!  True.  But if that’s the only use of math for those students, we might as well let them drop math and add more Latin classes.  Oh wait; we can’t do that, can we?  I forgot about those darned SATs!!

I have some students who can “do math” better than others.  That will always be a reality.  But you know what else I’ve discovered?  When I walk my students through the exercise of creating the spiral of a nautilus shell by starting with the Fibonacci Sequence, the biggest smiles of pure delight (without fail, almost every time) appear on the faces of those students who are not as good at “doing math.”

I find this fascinating, if not sad (for those students who would rather get back to the business of doing math).

The ability to do math is a useful skill that will prepare our students for the marketplace.  The ability to know and love the divine beauty in math will further conform our students into God’s image.

My encouragement to math teachers (myself included!): Make math a conversation (it is a language, after all).  Insist on understanding, on knowing.  Invite contemplation.  Reveal beauty.  Model curiosity and wonder.  Then, and only then, do math.

You may end up covering less, but you will uncover even more.

I Cannot Give an Answer (Part 2)

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An excerpt from math class today . . .

Me: “Why is four a factor of twenty?”
Student: “Because it goes into twenty.”
Me: “Can’t everything ‘go into’ twenty?”
Student: “Okay, because four times five is twenty.”
Me: “Forty times one-half is twenty.  Is forty a factor of twenty?”
Student: “No.  But I know that four is a factor of twenty.”
Me: “Why?”
Student: ” . . . I don’t know.”
Me: “That’s a beautiful answer.  Now you’re ready to learn.”

Fun with Four Digits

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This could be a fun post if several of you participate – so give this a whirl!

1) Take any four-digit number, using at least two different digits. (eg., 4013)

2) Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary. (eg., 0134 & 4310)

3) Subtract the smaller number from the bigger number. (eg., 4310 – 0134 = 4176)

4) Go back to step 2 with your new number from step 3 above.

Follow these steps in a loop until your answer from step 3 starts to repeat.  Write that repeating number as a comment to this post.

Go!

And Now for Something Mathematical . . .

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Perhaps in this blog so far I have not given much indication that I actually teach math, save the previous post.  Well here’s something a little less philosophical (or is it?).  If any of my past students are still reading my blog (I don’t blame you if you’ve gotten bored), can you tell me what is special about this pattern of numbers?  Hint: It’s a little more odd than what is obvious.

Training the Mathematical Mind

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My good friend and colleague Brett Edwards and I did a seminar together yesterday at the annual Association of Classical Christian Schools Conference, hosted this year here in Atlanta.  A link to the presentation (sadly, absent our humorous commentary) can be found on Brett’s website (a website which I recommend you peruse further, especially if you teach math).