It's 11:13 at night. My bedtime has slumped over in the corner somewhere, too tired to continue begging me to sleep. My cousin and I are working through her math homework. We've just encountered an equation with imaginary numbers.

"Do you remember going over imaginary numbers in class?" I ask.

She shakes her head dubiously. I'm pretty sure she's never even heard of imaginary numbers before now. Calvin and Hobbes had, thankfully, introduced me to them years ago. It's been awhile, but I think I'm up for it.

"What number times itself equals -1?" I ask.

Her blank stare continues.

Five minutes later she's at least giving me a halfhearted nod when I show her the square root of negative one squared. And as we finally head off to bed -- her promising to visit her math teacher so she can explain the math problems that I couldn't figure out as the clock nudged itself toward midnight -- I realize that math is yet another reason to homeschool.

**Imaginary Numbers**

With math, you can teach it the first time.

As homeschoolers, we can camp on or return to a topic as long and often as a student needs. The classroom requires that we waste students' time. Incomprehensible homework is the embodiment of this inefficiency. I have to learn this content anyway so I can teach it to my student. It would have been better to just teach her math from the start.

Plus, I could have purchased a math curriculum that actually solves each problem for me, step by step. Instead, my tax dollars purchased this pathetic textbook that provides zero explanation for the majority of the problems in the chapter. It's maddening.

I've had people ask me how homeschoolers teach advanced subjects like Calculus. Jill has a great response to new homeschoolers who know they don't know everything. But for the incredulous toward home education, let me say this: I have to teach my student many of her math lessons because the teacher failed to do so. I'm not saying her teacher is bad at her job. But whatever the cause -- lack of time, resources, opportunity, skill, or observation -- students all over this great country are required to learn this stuff at home. I think they'd have a higher success rate if you were there to help them.

Enter homeschooling.

~Luke Holzmann

Filmmaker, Writer, Guardian

## About Luke

Filmmaker, Writer, Pseudo-Dad

My son is a fifth grader in a very good private classical school, 10 students in a class. And I still "afterschool" math, because this is his least favorite subject, which we both know means he isn't spending the time he needs to be really good at it. I love math and really want to show him it doesn't have to be boring. I have used Life of Fred and Teaching Textbooks as an occasional supplemental curriculum. Oh, and I hate imaginary numbers!

Talk about camping out. The other day my daughter came across a hard algebra problem. So I helped her. We worked the problem 6 different ways before we relented and watched the solution. Love Teaching Textbooks and so happy we can get it from Sonlight. We had so much fun!

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Jennifer, that is a great point: We often need to spend more time with the subjects with which we struggle. I'm glad you're able to do that for your son. Keep up the good work, even if you do no like imaginary numbers <smile>.

Vicki, I'm really glad when there are resources that walk you through the problems. I really dislike the textbook to school gave my student because it does not have any explanation for how they arrived at their answer. It's infuriating!

~Luke