Author: Dahlia

Textbooks have a tough job. One on hand, all they really have to do is explain stuff in a way people can understand. On the other, they don’t have the tools we do when we engage in classroom, person-to-person, or even YouTube learning! There’s no mix of sound and writing to time the visual cues just right. There’s no space for waiting to see if someone has a question before proceeding. There’s no visible writing process that the reader can see as their mind tries to capture the new concepts.

There are just words. And there are just images.

Maybe, when I know a little more computer programming than I do right now, I would be able to make animations that could accompany each explanation. But would that really help? I wouldn’t be able to correlate the animation with the exact verbal cues that could really bring the message home unless I just made it a video.

I’ve thought of doing videos for this project instead of written explanations. But I’ve decided to focus on writing. Why? First, because a large part of my motivation for creating these pages is to one day compile them and make an honest-to-goodness bound book out of them. How could I say I’m writing a non-textbook and not even have a book to show for it! That would be like a bird having wings and not even being able to fly! (sorry, penguins.)

The second reason is that I feel like there are already amazing video resources out there for the same kinds of content that I’ll be writing about. I don’t need to do videos–those websites are just as much on the Internet as this website is, and are much better known. And maybe you could argue that there are also already good websites with math content on them. And I would agree with you! Maybe I just think that fun colors and different font sizes will win people over. I don’t know. I just feel like the Internet is a little more in need of written explanations than it is videos right now. Maybe I’m wrong.

What I mean to say is, I hope this project ends up as more than just me typing up random math symbols in my basement. I hope my explanations make sense to both the students and non-students who want to learn.

I think the biggest downside to a written explanation versus a face-to-face interaction is that there isn’t a good way to check for misconceptions, and then correct them before teaching important points. You can try to explain the best you can, you can write side note after side note explaining common misconceptions and why they are incorrect, you can put big warning headers “warning: you probably have a misconception about this topic!” on everything. But it just isn’t as effective as talking about it in person. The student can’t talk to the page and the page can’t talk back! (I mean, I suppose they could do the first one….)

I do the best I can, but I just can’t write a textbook that private tutors you.

All I can do is hope my basement skills are enough to get the message across.

I’ve been going to school now for almost 17 years, and Math has been a required subject since kindergarten. Fortunately for me, I’ve always really enjoyed math. Doing math problems helps me calm down when I feel stressed, and stretching my mind to understand new mathematical concepts is something that feels like coming home.

But I know most people don’t feel this way. I read somewhere that more than 10% of schoolchildren experience pretty bad math anxiety (I know, Wikipedia readers, “[citation needed]”). But that’s a lot of students. And those are only the ones who can give it a label. Based on my experience tutoring, I would say more than half of people feel stressed out at the idea of doing math problems.

I don’t think math is the problem. I think something I call the “methodology mindset” is. And I think textbooks are.

Ever opened up a math textbook? Some people don’t open up their first math textbook until college. When they do, they are likely to see something like this:

Then they throw up.

What’s written above isn’t the kind of thing written for students to understand math. It’s written for mathematicians.

But mathematicians aren’t the ones reading Calculus textbooks! They are too busy reading books on analytic geometry or number theory. The only people who read textbooks are teachers and students. And the teachers don’t need them either, at least not for learning the material (we hope). So why don’t mathematicians write textbooks for students?

Math, especially the post-college kind of math, is a major language. And it’s the language mathematicians speak most of the time. If you’ve ever met someone who has trouble speaking their native language after spending a lot of time in a foreign country, then you can understand. A mathematician spends so much time thinking and writing in mathspeak (probably in their basement, which is where all respectable mathematicians spend the majority of their time, scribbling down numbers and letters and muttering under their breath) that when they start writing a textbook for students, they might forget to use normal human languages. And maybe we can cut them a break. Would you be able to teach a kindergartener to tie their shoes with a knot you DON’T usually use?

The problem is, we rely on these mathematicians to pass our classes and do our jobs. There are plenty of translation agencies–teachers, websites, youtube videos, books, etc. But why not just make understandable material in the first place?

That’s my goal, with NotATextbook. I want to write a textbook that students can actually use. One without proofs and formal language and weird symbols that no one really understands and fewer people use. I’ll start with Calculus, as it lends itself very easily to a conceptual explanation, and because it’s my favorite of the maths. Hopefully, when I finally publish it, it can be a resource written in a language students can understand. Everyone can understand math with enough mental effort and a good enough explanation. Students, you’re responsible for the mental effort. I’ll do my best to give a good explanation.

Even if I write it in my basement.