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Okay, I know it’s been a LONG time, since I’ve posted, but I just haven’t had the time. Even today’s [...]
Aug 02 2005 |
tech
- Cover of Is God a Mathematician?
I’m reading a great book right now called “Is God A Mathematician?” by Mario Livio. It’s a fascinating book about whether mathematics is discovered or invented. It’s a really interesting book (so far) and has really gotten me excited about math, again.
It got me thinking about how I was taught math and why I disliked math so much. I remembered some of the things I learned and, for whatever reason, focused on the formula for the area of a circle: (A = ?r2).
What I asked myself was, “why is that the formula of a circle? Why, if you multiply the radius times itself and then times pi, some constant, do you get the area of the circle?” After digging into this, I realized why I didn’t like math in school.
Pi
Pi is a constant, meaning the number never changes. But, as I learned reading this book, it represents something. Pi is equal to the ratio of the circumference (C) of a circle to its diameter (D). No matter what the size of the circle, this ratio is always the same, 3.14159…it goes on, literally, forever.
I never knew that! Well, to be fair, maybe I did and just forgot. But I certainly didn’t remember it. That’s really interesting. But what does that do for our formula?
Maybe we can substitute (C/D) for pi into our formula to help it make more sense?
Area of a Circle
Now the formula for the area of a circle is A = (C/D) r2. Well, the diameter of a circle is twice the radius, right? If we substitute 2r for D, we get A = (C/2r) r2. We can cancel out the r in 2r because of r2 on top, and we’re left with A = (C/2)r.
The area of a circle is equal to its circumference times its radius, divided by 2.
But, does this make sense? Kind of. Here’s how I understand it. Take a circle, like this one:
Now, let’s show the radius:
The radius has a length of r (of course) and a width of 1 unit. If we show the radius x times, it might look like this:
The formula, again, says we should show the radius C/2 times, though, right? (C/2) * r means show r (C/2) times:
Now, here’s where it breaks down for me. Doesn’t that just give you half the area? Why divide by 2? Isn’t this what we’re looking for?
Anyway, the point is this: this formula (C/2)r makes so much more intuitive sense to me. To understand the area, just draw the radius as many times as the circumference is long. Pretty soon, you’ll fill up the circle. Count the number of radii you had to draw to get there, multiply by the length of the radius and you’ve got the area. In that sense, it’s no different from the area of a square.
Back to Teaching
Which brings me to my point. When we teach math, why aren’t we teaching this way? The way I learned math (rote memorization and application) only taught me to memorize. When it came to word problems, I was abysmal because I didn’t know why I should be using which formula.
I suspect that same problem is found in every subject. My goal is to help my kids learn to find out why what they’re doing works. I want them to understand the mechanics and inner workings of everything they do so they can manipulate it, change it and use it anyway they need to, in order to solve whatever problem they’re having.
What do you think? Is this a worthwhile endeavor or just unnecessarily confusing?
My favorite quote is this one:
“Mothers, cherish that role that is so uniquely yours and for which heaven itself sends angels to watch over you and your little ones. Yours is the work of salvation, and therefore you will be magnified, compensated, made more than you are, better than you are, and better than you have ever been.”
Read the full text here.
I recently took down a blog post for the first time ever. If I thought the post were merely poorly-written or I was wrong about my position, I wouldn’t have taken it down.
But I draw the line at hurting people who are genuinely doing their best.
The post tackled the very sensitive subject of mothers working while raising children. I don’t feel I gave the proper context around my opinions and beliefs and a close friend told me the post hurt her feelings. I spent a good deal of time thinking about it and talking it over with Heidi. In the end, I decided to take it down and give myself some time to think about how I wanted to approach this subject that I feel very strongly about.
Instead of tackling just the subject of working mothers, I’ll step back a little and start with a broader context: families. Because my opinion on mothers working stems from my feelings about the family.
Okay, down to brass tacks. Why do I think families are so important?
“You want to have how many kids?”
That’s the typical (and understandable) reaction I get from people when I tell them my wife and I would like to have 7 kids (or more, if we can). I admit, it is a lot of kids. And, with two kids now, I can’t fathom handling five more. Not to mention how expensive it is to raise kids.
Additionally, some people think the world is overcrowded and that bringing lots of kids into it is irresponsible. There are two problems with that:
- The purpose of the Earth is to give God’s children a place to go through the mortal experience. The statement above counteracts that purpose.
- The fact is, the Earth is not overcrowded. There are more than enough resources to go around, if they’re used and distributed efficiently. Did you know only 7% of the land in the US is developed?
And there are a number of reasons why we feel comfortable with having a big family.
First, we take it one kid at a time. It’s not a goal or something we absolutely have to have. We just want to have as many kids as we can support. Seven just happens to be our guess as to how many we can biologically have before time runs out.
Second, our family brings us more joy than anything else on the planet. I’m never happier than when we’re all together and that joy does not diminish with more kids (or at least from 1 to 2 kids).
Third, there are scale advantages (so we’re told). Once the first kid gets old enough to help with the second, we expect that things will get a little easier. Plus, we’ll already have all the clothes, beds, toys, etc., so it won’t be as expensive, initially.
Fourth, the purpose of this life is for us to become as much like God as possible. You know what God’s purpose of existence is? To have kids and help them become like Him:
“For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man.”
Immortality means living forever and eternal life means becoming like God and living like God lives. One way we can become like Him is to do His work, the most important part of which is to help “bring to pass the immortality and eternal life of man” by bringing more of His spirits to Earth to go through the required mortal experience or by taking care of the kids who have already come to Earth who have been left behind by their parents here, for one reason or another.
And finally, a big reason I want to have lots of kids is this: when I see my two sons playing or pushing each other or crying or just sleeping in their cribs, the thought that there might be 2,3,4 or more other kids waiting to join our family fills me with love, excitement and anticipation.
And the thought of leaving them behind brings tears to my eyes.
