Textbooks

(Catching up:

It's interesting that the first textbook I opened (Social Arithmetic) began with an explanation of why a child might want/need to be learning the contents.  In the Math 9 and Pre-Calc 11 workbooks I've looked at in the schools, most of the sections give a similar sort of "where could this math be used" talk.  This textbook is also very much a guide for real life math and has very explicit examples about farming, etc (which makes sense given the title).  This book also opens with a segment about Native Americans that manages to explain how the writers (definitely white) saw the Native Americans' pictorical way of conveying numbers (they saw it as very much inferior) through their explanation of it.  Their own method of explaining math was a lot of sentences.  The book read a lot like an actual book that was telling a story, with questions embedded within the story.

I also took a look at MathQuest8, which has a lot of pictures and a more whimsical feel to it.  There's a lot of different things on each page, although they do pretty well to split it up via lines and boxes.  Each mini-segment does not do a lot of explaining, mostly giving an example and then practice opportunities.  This book is a lot more explicit as compared to Social Arithmetic with mathematical language fully being used.

Personally, I've used Khan Academy a lot in my own learning— it's quite different given that the medium is mostly videos rather than writing, but I think that it allows for a lot more flexibility in what the instructor can explain.  Also, if you have questions, the community might have already asked/answered them.)

While I was in high school, I actually did not use math textbooks in my classes other than to check answers to practice problems we were given.  So I can't say in particular how I was affected as a student then.  I use textbooks much more often in college, although I've never particularly thought about the language they've used.  I believe most that I've seen have used 'we' while writing, which I write as well when I'm writing proofs for homework (I'm not sure if I picked this up from the textbook or from my classes).  I like 'we' because to me it creates a sense that both the author and the reader are involved— you are not being directed to do something by yourself, but to follow along hand-in-hand a path paved for you.

I understand completely why someone would use a textbook, especially as a new teacher, because I think it gives the teacher something clear to follow (you don't have to make it all up).  It can also potentially help you align with other teachers in your school on what you're teaching.  I also think that the workbooks I saw in the schools can help students keep everything in the same place for math class and provide them with structure (explanations, examples, exercises).  On the other hand, I think it can be easy to get stuck in the routine of using the textbook and therefore not do any other sorts of activities.  Not all students learn well from a book.  However, I think it can be helpful at the very least as a reference.

I will say that I talked to a newer math teacher (Max from Hamber) on an observation who did not use the workbook at all; he also did not have students take any notes (and I think he didn't post notes either, but I can't be sure if I'm remembering correctly).  It was a classroom where he had them figure out what they were doing on whiteboards and then gave a quick synthesis at the end of the class.  To be honest, this really threw me for a loop because notes are so fundamentally part of school in my mind.  His argument was that students write notes and then never look at them again, so there was no point.  I personally don't agree with that because I reference my notes (at the very least!) when I do my homework and realize I've forgotten something.  In any case, it was an interesting class to observe.