I've always wanted to write my own textbook/guide for mathematics.  I'm not the biggest fan of classroom textbooks and I never have been.  Over the past few years, I've often started to write one and then I always end up stopping for one reason or the other.  If I started re-writing here, would anyone be interested in reading it and leaving comments about things I could clear up? I could post a little each day. Knowing that others were expecting me to post would help encourage me, and I would also feel motivated by the possibility of receiving feedback.

My book would be focused on Algebra II, with some focus on re-learning basic Algebra I skills needed for Algebra II.  Please don't say taht you'd be interested in reviewing what I write if you honesty would not commit to it.  Math is not a subject that most people find riveting, and I do tend to ramble when I'm excited about a subject.

I like the idea of writing a better textbook or guide, seeing as all the ones that I've seen or used the teacher or the students have complained about because they're generally old and outdated, or would never work to begin with, also because I'm going to be taking Algebra II soon, it could kind of help out, but as for reviewing it, I'm not a reliable source, because I'm more of the type to read something and keep my opinions on it to myself, but if you feel like going for it, go ahead.

I remember way back when, when I was in middle school my math teacher always said the same thing. She absolutely hated our math textbook and constantly said that she could do it better. I also think she was probably one of my best math teachers ever, so I don't doubt her, but I don't know if she ever even tried.

Anyway, to keep this post on topic at all, I'd be willing to try to read anything you post and give my opinion. I won't make any promises, because I'm gonna be fairly busy with schoolwork, but I'd love to try to help.

Awesome!  I probably won't start on it tonight because I also have tons to do...*groans*  LOL.  But I'll get started tomorrow then.  Every time I start, I've always enjoyed it.  I just never keep up with it is all.  I'll piece meal it between my busy work schedule, and every time I post a piece, I'll tag your name in it.

I think that's a great idea.  I agree the school textbooks are garbage.  They are horrible in the ways and methods they go about teaching.  I would read it though I wouldn't have a reason due to my current status.

Would you like me to tag you too Mr. Pace?  I might do a small piece each week, and progress through the whole subject would be slow.  I believe in describing things in great detail, which is probably why I'd never get a textbook posted.

I do use images a lot when typing math notes.  So maybe I should just do it as a google doc and then link it here every time  write a new piece?

I went ahead and favorited this thread, so every time someone posts in it I'll get a notification. I don't favorite a whole lot of threads, so I should be able to keep up with it if you forget to tag me or something. But do feel free to take your time on this first part. I work this weekend and then I have an exam or a project due every day next week. Of course I'd still probably check out what you post, but it would be time that I should definitely spend elsewhere.

I don't think i will read all your posts . Because i hate math ..! Not a big MATH hater but i don't like math .

EDIT: *GRUMBLES REALLY LOUDLY* I hate it when editing the post for a grammatical error spaces it out like this.  I apologize for the horrid spacing.  O.o  I anyone knows how to fix it, I'd love to be told how.

I almost completely forgot about this thread.  With such a busy year, it was easy to do since I am always grading or writing tests or creating lesson plans.  I HAVE started writing the mathematics portion (once again), but I also took some time today to write a letter of introduction and a quick 'how to' on studying more effectively. Hopefully there are enough people that will read this and give some feedback.  Of course, I don't really need feedback on the letter to the readers unless something is worded horribly or it's just plain old boring (I always have hated writing things like that), but I'd like some feedback on the part about taking better notes. If you have some strategies that I haven't considered... by all means, let me know!  I'd love to add more to what I've written.

Also, just fyi, I'm not a fan of big blocks of text... especially when you are trying to keep the attention of teenagers or young adults.  Therefore, if I ever do complete this project, I'd definitely make an effort to re-format it so that it's more aesthetically pleasing. Whether that'd be through bullet points, sub-titles, or graphics, it would happen.

Without further ado, the first few pages (un-proofread or edited) of my 'textbook':

A Letter to Any Readers:

Another textbook? Say it ain't so!  Well, readers, I'm sorry to say that it is.  This is something I've been writing for years, and like every author out there, I'm going to be brazen enough to state that my book is different from the others you've seen.  I'm not going to claim it's more interesting since I'm not very creative, but I will say that it's effective.

As a math teacher, one of the first things I tell my students is that math is not about numbers, formulas, or equations.  It's not about memorizing steps and performing calculations.  Shocking?  Although I imagine you are giving the same look my students do, I stick by my statement. Mathematics is the study of logic, critical thinking, and thought processes in general.  Studying mathematics is how we train ourselves, for example, to better outweigh pros and cons... and to make a final decision on what is best based off of that list.  Studying mathematics allows us to troubleshoot and consider possible solutions.  It also helps us be more inventive if we have a problem we don't know how to solve. Mathematics helps us look at the world with an inquisitive eye, and to seek the reasons behind the way the world works as it does.

If more teachers weren't afraid to teach math with this in mind, I am positive we'd have better math students, and the fear of math classes wouldn't be an epidemic sweeping our country off its feet.  Unfortunately, there's not much I can do to change what's already happened in the past, and all I can do is move forward.

It's part of the reason I wrote this text.  For years, God blessed me with the ability to teach math.  Although I haven't been teaching in the public school system for long, I spent many, many years as a personal or group tutor. No teacher can claim success with every student, but I feel comfortable in stating that I've been successful with most.  The credit certainly isn't on my shoulders though, and I give the glory to God.  This is the gift He gave me and it's only through His grace that I can share my blessing.

To any students reading this text?  I can only advice that you don't give up.  As cliché as that might sound, it's a piece of advice which is always very applicable to mathematics.  It's not easy to train your brain to think a certain way... especially after years of being told the wrong things, or being told the right things in the wrong manner.  The good news is that the effects of bad teaching -are- fixable!  You've simply got to find the initiative to go back and do things the right way.  If you ever feel frustrated to the point of giving up, close your book and step away.  Find something relaxing to do for 15-20 minutes, and then come back to your studies.  If your heart and mind are only focused on your level of struggle, you will never be able to productively study.  Pace yourself and understand that you are bright and motivated, and you'll go far!  I wish you the best of luck in your endeavors, and I hope that my writing is able to help you in some way!


A Prologue, of Sorts:  HOW TO STUDY

Something I've discovered over the years, and something I'm sure most of you know, is that students today don't know how to study.  Students time and time again take a test exclaiming "You've never taught this!" or "I've never seen this in my life!"  However, in my case at least, I'm always able to pull out a student's notes and find the exact location of where such problems WERE taught, studied, and practiced.

Thus, the first issue of course, is that most students don't understand how to take effective notes.  This isn't an easy habit to break or form, unfortunately.  Students, you simply need to realize this:  Your notes are for YOU. Your teacher isn't going home, pouring over your notes, and then shedding a tear because you didn't copy exactly what he or she wrote down.  How many times do you get home and look at your notes.. and feel like you are reading foreign languages?

Newsflash:  Taking notes is pointless if you aren't going to understand what you've written.  Keep this in mind WHILE you are taking your notes during class.  With every letter you write down, ask yourself if you will understand what you have written when you get home.  If the answer is no, jot something down that will help you remember!  For example, if your teacher is going over addition of like terms, and you write 3x - (-2x) = 5x, that might not make any sense to you.  Take the time to make a note to yourself even though your teacher doesn't.  "Subtracting a negative number is the same as adding."

That's so time consuming!  I can hear you yelling it already.  It is indeed, and this is EXACTLY why you need to come up with your own short hand.. a language you can understand when you get home to look at it.  This note, luckily, would have been all too easy to write in short hand.  I would have drawn an arrow to the problem and written "-(-) = +!".  Even if other students or my teacher didn't know what the little blurb meant, -I- would, and that is what's important here.  This of course, was a really simple example.  You've got to learn how to shorten other words though, and how to eliminate unnecessary words like 'the', 'a', and 'then'.  All of these are time and space wasters when you're trying to take quick and additional notes.  Start writing 'w' for the word 'with', or 'bc' for the word 'because'.  Whatever works for you.... do it.  This is not only a useful skill in high school, but in college and careers also.

COLOR CODE your notes.  This might sound nuts, but it's one of the best things you could do for a math class.  Pick about three colors you can use in class, and always have them with you, on your desk and ready to use.  Let me give you an example of how color coding can help you better read your notes.  Consider, for example, the difference between the two problems below:

[[insert two pictures, one monochrome, and the other with various colors for the differing steps in the problem. I apologize to vizzed for not having those images ready yet.  I know exactly what problems I want to use though, so the next part may be hard for you to make any sense of until I can garnish the images]]

If you were to glance through the problem at the left, you'd most likely have a hard time distinguishing what was inserted when, or even perhaps what the original problem was.  This is because while you are sitting in class, your mind is following each problem step by step and it makes sense.  Your teacher isn't going to rewrite the whole entire problem each time they add a new step, and rewrite all of the previous steps.  It's too time consuming and would not benefit anyone.  Thus, this is what your teacher's notes would look like, which most students would copy directly as is.  When you get home however, you're not listening to the lesson or watching the problem unfold.  The worked problem looks like a block of numbers and letters and it's difficult to pick out one step from another.

Now consider instead the problem to the right.  In the problem to the right, each part is clearly distinct.  The problem is in one color, and the square root... the second step, is in a different color to help the reader determine that the square root was not a part of the original problem.  Further more, each distinctive step is in a new color.  You don't even have to use more than two colors, though I suggest at least three.  If you have them ready and at hand, you can easily and quickly swap colors when adding the next step to the problem.  If you'd like to be MORE specific, you could even put a key on the top of your notes which reads something like "blue=step 1, red =step 2" etc.  Think about what you see -this- time when you go home.  You still have a block of letters and numbers, but now you have a little more focus.  You can tell which parts go together and which don't.... which parts of the problem were things you added, and which were originally there.

Another good note- taking strategy, and one I hardly ever seen students utilizing, is to take notes about things that go WRONG.  As strange as it sounds, this is probably one of the best pre- emptive strikes you can make on making your own mistakes.  Most students who struggle with math think alike, and so if a peer makes a mistake when they go to the board,it's not all that unlikely that you will make the same mistake.  Much of the time, it's not enough JUST to write the correct way of doing things.  Math is a very fluid subject, in which there are an infinite number of ways to find a solution.  Most students (of any age) recognize at least this fact when it comes to math, and this leads to some very inventive strategies.  You can nod your head in class when you understand that what someone did is wrong, but it doesn't keep you from making the same mistake at home.  You learn a LOT in one day and it's hard to keep track of every small detail.  Your mind is bound to pick up on subconscious hints and when you make the same mistake your classmate did, you might simply think "Oh yes, I saw this today!  I must be doing something right!"

Instead, any time you see a classmate making a mistake, jot it down!  You don't even have to write down WHY it is wrong, though if you have the time, I would suggest it.  If you label it VERY clearly "WRONG WAY", you will at least see that you are making a mistake if you repeat that same method while working your own problems. You'll have that little reminder to the side of your notes, which should unmistakably warn you about dangerous waters.

So now that you have a few tips on better note- taking, how can you utilize those notes from home?  Well, part of the problem I've noticed with most students is that they are TOO reliant on their notes.  Notes are great and all, but they're only a hindrance if you're using them to complete every single problem you work through. Notes should be a guidance, but they shouldn't hold your hand every step of the way.

Here is the advice I usually give to my own students:

Before you attempt any problems, read through all of your notes.  Don't just skip over the problems with a 'yeah, yeah', either.  Instead, mentally go through each step and try to tell yourself WHY each step took place. Pay attention to key words and vocabulary, and look through all those notes you made to yourself on what is wrong and what is not.  Then, and only then, work a few problems.  Use your notes and your memory as a reference if you need to, but make sure you work out each problem ALL the way through.  Too many times, students 'feel' like the answer can't possibly be right, and they toss up their hands without finishing. This is one of the worst things you can do  when studying math. You didn't get any practice, you have nothing to go by when you ask your teacher for help, and more than likely... you were on the right track anyways.  If you're un- confident enough that you 'feel' a problem might be wrong, you're probably not confident enough to make a judgement about what feels right or wrong about the problem.

After you've completed a few problems, close your notes.  Do just as many without looking at your notes or even the other problems you've completed.  You won't be able to look at previously finished problems when taking a test, so why do it when you're trying to learn how to work them?  Practice working the problems without having any visual aide, and this will truly let you know if you understand the problem well enough to be tested on it or not.  Many students are able to complete homework successfully without ever actually learning the material because they merely 'copy' what they did in other problems.  This leaves them with a feeling of success and victory, but does little for them in the long run.

Once you've finished a few problems on your own, go back and compare them to the ones you did earlier, or to your notes.  If you're working problems where the solutions are in the back of the book, check your work.  Most importantly however, DON'T panic if you did something wrong.  Making mistakes and correcting them is a part of the learning process, and you shouldn't ever shy away from those errors.

What you do from there depends on how you fared.  If you did everything completely incorrectly, try to do a few more using your notes, and repeat the process of setting your notes away and trying them on your own.  If you did well, keep going!  Repeat these steps as often as you need to, but remember... never, EVER let your tension rise to a boiling point.  If you become frustrated, bored, or apathetic about completing the problems, it's time to take a break.  Close everything and walk away, play a game, or have a snack. BE SURE YOU COME BACK though.  If it takes several breaks to get everything done, that is A-okay. There's nothing wrong with taking your time, so long as you have learned something.  Keep in mind that the ultimate goal is the passing of a test.  Completing homework is indicative of monkey -see, monkey- do behavior unless you've actually learned the material and can do it on your own.

There are other strategies you can employ for better note taking and studying habits, but that is not the purpose of this text.  However, I hope these few tips and guidelines will help you along your path to being a more successful math student.  Take them, employ them, and grow!

______________________
Some side notes:

As for the rest of it, I've started off with some basic algebra  review which I would hope to bring in to the topic of algebra II.  Though I love the idea of writing a textbook in all subjects, even one is a huge endeavor to partake on my own.  Thus, I was thinking I should start off with algebra II.  It's not the only thing I've taught, but it's the class I'm teaching right now, and the class I've taught for the longest.  Right now, if I work on it, all the kids' common mistakes and incorrect ways of thinking are fresh in my mind.  Also, if I can complete even a chapter or 2 within the next year, that's just more material I can give my kids to study and learn from, currently.

I do worry though about not being in the same school next year, or not teaching the same classes.  So many changes are going on in our system that I'm not sure I want to be there, and if I am there, I'm not sure any text would be of use to my students.  While I have a small appreciation for the -reasoning- behind the changes, I'm not keen on the actual activities themselves.

For these reasons, I've actually considered starting with the algebra I.  As I began to write the algebra II, I kept thinking of small concepts my students often miss out on, and I actually started writing a few appendixes which cover that material before going any further with the more complex material.  If I wanted to write my text on algebra I, it'd be quite easy to take those appendixes and work with them and expand them.

Due to my indecisiveness on which topic to write for, I've had a hard time continuing with my work.  Every time I feel motivated enough to work on it, I think of something else I could add, or how I could improve one feature, and then I question where I'm heading with it.  Perhaps I just need one big chuck of time in which to sit and write.... whichever my mind desires to focus on.  I can always sort chapters and such later, after all.

In any case, it will probably be a while before I get the actual math portion up here.  I have many images made up in the actual document, and I'd have to copy them into Paint or something in order to upload them here and have the text make sense.  I WANT to do it... never fear, I just need to find the TIME to do it.

Singelli: Like! Don't stop with this, it just might help me! I'm in a 2...

Edit: Stupid autocorrect! I meant Singelli, not Dingell. Lol...

I would look it over if you posted it. Textbooks today aren't really the best.

Singelli :

When you preview an edit, for some reason it posts all
tags into your post wherever there are line breaks. So every time you preview an edit it adds even more line breaks. To fix the spacing, you can delete all of those tags. What I like to do is make the edits I need and then copy my post. If I like what I've done in the preview, I paste the post back into the post box and confirm the edit to do away with the weird spacing. Since your post is exactly the same before you press preview, except without the extra tags, it accomplishes the same thing as going through and deleting the tags yourself. I wouldn't think this issue would be too hard for David to fix, but I don't know if he knows about it.

soxfan849 :  Aaahhhh.... thanks.  I had NO idea that was going on, and no one could ever tell me what was causing it.  Thank you SO much.  I'm going to go back and fix it now, which I believe I do through the old post editor?  ((You don't need to post in the affirmative, but I'd like to know if I'm wrong and don't figure it out after a few minutes))

Since you were one of the ones interested in helping me out (to some extent) with this, do you have any feedback for me?  It needs touching up of course, but I mean over all as a whole?

EDIT: I didn't see the break tags, but I was able to fix it nonetheless using the old post editor. Thanks TONS.