Norbert and Errol Answer: Is Addition Really Simple?

Norbert: Yes, it is actually pretty simple. Though, there is some complexity that we don’t always think about.

Errol: Kids have to face these complexities and make sense of them. So, if you are dying to refresh your addition, please watch our newest video in the tutorial section. Enjoy!


The dreaded question: “Will this be on the test?”

“Will this be on the test?”

I doubt there’s a teacher alive who hasn’t heard this one.  I doubt there’s a student alive who hasn’t asked it themselves or been very interested in the answer.

Teachers really don’t know how to answer this question.  If you want to see some of the more creative answers I’ve seen, you can always look at this post at math with bad drawings.  In fact, you should read it no matter what, because it’s great.  It also made me ask a question.

Why don’t teachers like this question?

Because they really, really don’t like it.  I mean, it drives teacher’s bonkers to have to answer this question.  The answers in the post I linked to (written by an actual teacher) should make that clear.  If you really don’t believe it, just ask a few teachers.  You’ll see.

Before we continue, let’s get one thing out of the way:  It’s obvious why students ask the question.  It makes sense to us.  After all, if it’s not on the test, that means that forgetting it won’t get us in any trouble.  And studying is hard and takes time which we could spend doing things which we care about more.  It’s just figuring out how to best use our time, under the assumption that our goal is to pass tests.

So why don’t teacher’s like it?  I suspect that there is no one single reason, but easily the biggest one is that most teachers don’t want to teach their students how to pass tests.  Oh, they want the students to be able to pass tests—they are trying to teach them after all.  But the thing that teachers really dream about is that their students will someday, as adults, be using what they learned to make the world a better place.  They want the students to be expanding our knowledge of the universe, curing cancer, solving social problems, or protecting the innocent.

Being able to take a test has very little to do with most of these.  The real question isn’t whether they can take a test; it’s whether they’ve learned.  Teacher’s try, and how do they try, to make tests which measure how much a student has learned.  When all is said and done, though, the world’s best tests really don’t reach that goal.  There is practically no problem in the real world which is solved by sitting in a room answering questions that somebody else already knows how to do.  And it’s even rarer to have a time limit defined in hours rather than days.  Or weeks.

And this is the heart of the problem.  The students are trying to solve one problem—what do I need to do in order to get out of this class with good grades?  What do I need to do in order for my parents to not get mad at me?  How to I get this requirement taken care of so that I can go work on things I actually care about?

And no wonder teachers can’t get behind that.  They love what they do, and they love the knowledge they are trying to give, hopefully to help a student for a lifetime.  A student asking this question means that they aren’t looking past the end of the semester, and probably will neglect and forget all that information the teacher just taught them. To the teacher, this means that the teacher just wasted their time teaching, and the student wasted their time sitting in a classroom.  And people hate being told that all their hard work is being wasted.

I don’t know what the right answer to this problem is.  After all, it’s important for both students and teachers to know how well both are actually doing, so we need to test somehow.  This all leads in to the eternal debate about the right way to test, which is waaaaay bigger than this post.

My first thought is, can we teach the students to look at the problem this way?  I’m not sure how.  After all, “looking at problems this way” probably isn’t going to be on the test…

Seeing part of the mind of God

I’ve been busy recently working on an introduction for some videos we are putting together for the website.  We hope to re-use it a lot when we start getting really in-depth into some of our tutorials, and so we are spending some real time making it look as good as it needs to be.  We are also going to use these tutorials to introduce you to the actual math dragons.  We’ve named them Norbert and Errol.  The names seemed—appropriate.

All of this has made me think more, though, about something that’s very important to me, personally.

Why am I doing this?  Why?  It takes hours to do this kind of thing, and it can be very slow at times.  I’m having to learn new things and practice with new tools all the time.  I’m not an animator.

Why am I dropping all this time into trying to explain to people what math is?  Why does it matter?

Well, part of it really is all the reasons we give on the introduction page.  Both me and Jason really believe that math education is important for our children’s future.  We both feel like math education can be improved, and that we have the skills to help people understand why.  There’s so much that can be improved, and the world has finally gotten to a place where we can spread the message far and wide.

But that’s only part of it.  There’s another part.  There are ways I’ve always envied Jason.  He likes teaching.  It’s a big part of who he is, and he does a good job of it.  We enjoy talking about ways he can help his class through some of this stuff, which can be really difficult.  I enjoy the challenge, even while knowing he’s better at it than I am.

I’ve have spent some time teaching.  I’ve tutored on and off throughout my life, never for money.  I’ve had mixed success.  With my experience, I can at least consistently get the students to the right answer, but sometimes the students got rather fed up because I kept asking the very simple “Why?” questions which they weren’t really used to.  They just wanted to get the right answers so they could play basketball.  And who can blame them?

In all of this, though, there’s been something very special that has always been treasured.  It’s that moment when a child, or an adult, or even myself, finally understands.  There’s the point where people get it.  Something that was difficult before is—well, still difficult, because math isn’t easy.  But it makes sense.  They now know how to use it.  This is a beautiful moment, like the moment you make it to the end of a hike and see the sun rising over the valley.  Or the moment when you realize that this is finally it, I am really, truly going to graduate.  (I’d add a marriage comparison here, but I’m still single.)

I believe so much that more people can get this kind of moment in mathematics that do right now.  I believe that this clarity is a moment worth striving for in its own right.  In our own little way, we see a very small part of the mind of God.  And the best part is, it’s still useful for all those other things we keep talking about.  In fact, it turns the STEM fields— science, technology, engineering and math—from a high-paying chore to a challenging puzzle.  It’s still not easy, but it is worth it.

And I want so much to give more children and adults the chance to experience that for themselves.  I see so many people who could get it, but have decided they just don’t know how.  Combine this with the practical downsides of innumeracy, and you have a cause I can fully get behind.

Names and programs and politicians and school boards may come and go, but this part of math, I will push for regardless.