Algebra isn't hard. You've been doing it from the beginning. So why is it that math is so difficult for some students?

I firmly believe it's because they haven't learned the language of math. Even babies know that if you put one teddy bear next to another teddy bear, close the door and open it again, there should be two teddy bears there. The difficulty is teaching a child that it can also be expressed in the language of math as 1+1=2.

1+1=2

Does the image above look like an equation to you? No, because it's not. But it could be if we translated it into one, or made it a word problem: How many bears are in the picture above? Show all work.

All of math is the same way, you just keep learning more and more vocabulary as you progress. Addition means "put them together/find the total." Factor means "break them into smaller numbers with division." The problem is that we can forget our vocabulary (much like I've forgotten almost all the Spanish I learned in high school). ∃ π ∀ {1:3} are all just as foreign as + - x ÷ to a new student.

So really, when you're teaching a student math, you're teaching them a language. You're training them to read this foreign script. You're conveying the meaning behind the symbols and sounds. And that is why I find we teach the same concept over and over again in the MathTacular DVDs: We teaching them that writing the equation this way ultimately means the same thing as the other.

1 + 1 = ?
2(1 + x) = 4

Bob saw Jill.
Jill's beautiful features were all Bob could think about as he attempted to soak up every aspect of this moment.

Same meaning... one just has more depth.

Math is easy. Learning the language can be tough. And, unfortunately, I still struggle with English sometimes too. Clever and cleaver are far too similar.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

We all wear a lot of hats. Granted, there may not be 500 that ultimately threaten our lives, but sometimes it can feel like they do.

Wearing this many hats may be easy for you if you're one of those super amazing multi-tasker types. Change a diaper, fold laundry, cook a meal, teach math, mow the lawn, pay bills, drive someone to soccer practice, plant a garden, and maintain a cheery disposition all the same time? You've got it.

Me? Not so much.

I'm a one-at-a-time kind of guy.

That's not to say I can't stop in the middle of something at any moment and do something else entirely. But I have to do them one at a time (I can't even listen to music while reading). So today, one by one, I fixed some typos on the web, added some new content, talked over a few marketing ideas, discussed how our navigation system could be improved--and why it hasn't been yet, worked on explaining the order of operations in an Algebraic equation, briefly explained DVD copyright law, hashed out some design ideas for a new purchasing work flow, read about how well the Forum changes have been going (everyone seems to be very happy, which is great news!), after I read a couple hundred blog posts this morning.

My days are normally a tad more focused than that, so my head's spinning a little right now.

All that to say: I salute you! And today, I empathize with your many jobs. Continue to wear those many hats with joy, and may you have the grace you need to keep your head on when you can't take them all off.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

P.S. Just a reminder: As usual, some good stuff in the Other Posts of Note, like Mary Grace's latest which--as her posts often do--brought tears to my eyes.

One of the many things I love about blogging is how posts can help hone my thinking. As one wise guy called it: iron sharpening iron. I am consistently impressed with your insights and wisdom. You bloggers are just so great!

The most recent example is brief exchange I had with Ann on her blog, starting with this post and ending in the comments of this one. She took an idea that has been lightly tugging at the back of my mind for a while and gave it clarity. I think she is right on.

And, because I'm out here on the blogosphere, I get to read these gems.

<contented sigh>

It's good here.

Want a little more good stuff? Check out this post--NB: mild expletive--that does a fantastic job of describing the nostalgia we have for school and how that is quickly overshadowed by the joys of homeschooling.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

Mass Media Law. Not only is it a class you take on your way to a degree in Motion Picture Production, but it's also something you have to consider when you make media.

Unfortunately, there are tons of lawyers who do nothing but tweak with mass media law, so it's a little difficult for someone like me to keep up. And some laws are just plain crazy, like many of the ones surrounding "intellectual property" rights.

When you go on vacation and you wander through a museum and snap some pictures, do you ever think, "Can I do this?" No, you probably don't because the only signs say that you can't use a flash--implying photos a totally cool.

When hiking through the forest filming your children running down the path, do you ever wonder, "What permit do I need for this?" No. Because, somehow, media law doesn't apply to you because you're an individual and you'll, at most, post it to YouTube (which has amazingly dodged many intellectual property issues. Guess that's what happens when you're backed by Google's money and lawyers).

But me, when I walk through a museum or forest, I do think about those kinds of things. Because I deal with those questions from time to time.

Like today.

What kind of permission do you need to shoot an educational clip in a national forest? Well, it looks like you need something like this.

Fun.

We may end up in my back yard again <smile>.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

Normally, we mean "a hat to help us better think" when we talk about thinking caps.

But all too often, I find that something in my assumptions or preconceptions limits my ability to really consider an idea. And thus, my thinking is capped by how much I'm willing to consider another perspective. So, no matter what hat I'm wearing, I find that a "thinking proof" cap is clamped down around me.

Thinking Cap

I think that's what my dad is referring to in his latest post on the biblical nature of "randomness". It appears that some thinkers have gotten themselves stuck on particular words and missed the actual ideas. In trying to debunk evolution, they have capped their thinking at "God's design" and never got any further. At the same time, as my dad points out, "the Christian evolutionary community" needs to consider some ideas they've never gotten to either.

Granted, our own biases will always blind us and we can't get ourselves to see more clearly by simply wanting it to be so. But, by truly listening to those who disagree with us, we have the opportunity to remove the thinking cap. And that's why I love homeschooling: Despite the labels of "brainwashing," we have the unique opportunity to explore the various sides of a debate. We can tackle tough issues with our families as they arise and our children are ready for them. And while we will never escape our assumptions, we can safely look at challenges to our presuppositions and consider...

So, are you ready for another discussion of something "biblical"? It's a video on "biblical marriage"--though, I would argue, is more an excellent summary of "biblical methods of procuring a wife" than "marriage" per se ...hence why it completely falls apart at the end. It's supposed to be funny. For some, it will be. For you, I'm guessing less so.

And it is not suitable for children.

But it is interesting and, I think, provides an excellent opportunity to shed your thinking cap and consider the ideas. If nothing else, it will challenge your biblical knowledge [smile].

Okay, you've been warned. Ready? Jump in. The water's not too hot yet. If you can't get beyond your own thinking cap--not sure I did--can you spot her assumptions that are limiting her thinking (besides the one I gave you for free)?

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father

One of the beauties of creating educational materials is that you get to relearn everything. And you get to learn it better than you did when you learned it the first time because this time you have to teach it.

So, sure, we all know--if we reach back in our minds far enough--that (1/2)² = 1/4 ...right? One half squared equals a quarter because the exponent is applied to both the numerator and the denominator.

But why? And how would you show that? I mean, when you square, say, a half meter to make a box it doesn't really feel right that it would only be a quarter of a meter squared inside.

My brain started hurting. We'd been thinking these kinds of things through for many hours already, and I was fried. So were Justin and Amber.

This was crazy.

Why couldn't I figure it out? I mean, I did well in math back in the day but I was suck on cubing a half meter into a box that would only be 1/8th meter cubed in size and couldn't, for the life of me figure out how to tell someone that was true.

Then Amber held up a quick sketch, and everything was okay.

We could do this.

Children would be safe trusting us to teach them math. We've got their backs and will be able to demonstrate why a fraction to an exponent is the way it is:

(1/2)²=1/4

And I had one of those light bulb/a-ha! moments myself.

Homeschooling: It's a beautiful thing.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father