Photos source: Wikipedia
You may recall the strange markings on the Katakana chart in the last lesson. I've reposted it above. Notice how there are numbers and arrows. The numbers tell you which stroke to write first, and the arrows tell you in which direction.
You're probably thinking, can't I just cheat and write it however I want? Yes, you can. In fact, when it comes to Kanji, new learners of Japanese often write how they want. I've had a Japanese friend tell me that not writing with the correct stroke order makes the character wrong. I've also had another Japanese friend tell me that it doesn't really matter.
So what's the point of stroke order? Regardless of it being "more work" and "more memorization," there are benefits to running that extra mile. For one, you'll be able to write characters more easily and fluidly because that's how they are supposed to be written. Also, you won't forget the character as easily because writing it over and over develops muscle memory. There have been many instances when I've managed to write a Kanji that I've forgotten, all because my hands were familiar with the stroke order. It's saved my life many times over countless Kanji quizzes and lesson exams in school.
I can give you one more reason, and this one is a personal one I can relate to. Ever get called on in class to write something on the board? Or how about just writing while someone is watching you? Yeah. Too many times I've been embarrassed because I write with incorrect stroke orders in front of a whole class, or having my teacher look over my shoulder to see that I've wrote a Kanji wrong.
And so because I try to write with the correct stroke orders, I generally have less issues with writing a character incorrectly. Some of my friends on the other hand aren't so fortunate. Believe me, sometimes it's just not cool to get points off a problem just because you missed one little stroke on a character. But whether or not you'll be learning Japanese in a classroom setting or on your own, in the long run, committing to stroke orders will very likely do you a lot of good.
I suggest practicing stroke orders now with Hiragana and Katakana. From now on, I also suggest that when you learn a new Kanji, make sure that you learn its stroke order. (Don't be intimidated though, once you start practicing Kanji you'll find that you can get used to it and stroke orders will become second nature).