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I teach middle school math - 8th Standard and honors algebra this year, but I've also done 6th and 7th in the past.

I really struggled with behavior management when I started out. I really found [ http://www.fredjones.com/books-video/Positive-Discipline-book.html](Positive Classroom Discipline by Fred Jones) to be extremely helpful in practical advice that I could use immediately. I discovered that I was not utilizing body language effectively. Now I don't speak as much, am so much more effective, and students see me as more empathetic.

Two other books I found particularly helpful were [ http://www.amazon.com/gp/aw/d/0470550473?pc_redir=1407308994&robot_redir=1](Teacher Like a Champion by Doug Lemov), [ http://www.amazon.com/gp/aw/d/1416612947?pc_redir=1407558335&robot_redir=1](Total Participation Techniques by Pérsida Himmele & William Himmele).

Get to know your co-workers in your building and district.
-Within my department we plan together, slit the creating materials workload, and discussed what did/didn't work. For honors algebra there is only one teacher at each building so we get together once or twice a month at Starbucks to catch up and plan.
-Beyond your department it's nice to know others that work with your student so you are able to get a more complete picture of that student. In my building we frequently seek out a teacher that has a good connection with a kid to informally mentor him/her in other areas. Also you are then able to share accomplishments to other teachers; they are so excited when another teacher comments about something awesome that happened in a different class.

Kids are less likely to misbehave when they are constantly engaged. Choose activities that put the work burden on them and allow for movement/discussion.
-There are a ton of excellent, free resources out there. Some of my favorites are MARS tasks, NCTM Illuminations, and the Engage NY curriculum.
-Kagan Cooperative Learning (website and books) are easy to implement activities that turn any worksheet into a game and kids love it.

Don't forget to take some time for yourself. I used to eat lunch at my desk so I would have less work to take home. Now I find I'm more productive when working if I take a break and socialize with the other grownups for 20 minutes.

Good luck!

OH YES! All great advice (I'm a math teacher also). Let me also suggest that you immediately get David R. Johnson's three books: Every Minute Counts; Making Minutes Count Even More; and Motivation Counts. The books clearly were written some years ago, but his advice is still relevant, as he speaks from experience.


The big thing that needs to happen these days is to teach the students how to learn and how to study!
With that in mind, let me recommend:

Make Just One Change: Teach Students to Ask Their Own Questions
Method for getting students to engaged in their own education and owning their own learning - through questions on the material that THEY generate.



Make It Stick: The Science of Successful Learning

Oh, I wish I had this book years ago. I've been harping on the research that formed this book (which was just published) ever since I read about the findings in a New York Times article in 2010. It basically says that most of what people believe about learning is wrong and ineffective (Ok, one exception: flashcards (and Quizlet) work). The book then details what you can do in your classroom and what you can teach students to do that will increase their learning effectiveness and retention of the material. This truly is THAT BOOK that I wish every teacher and administrator in the U.S. would read and implement. The nice thing shown in some of their studies is that you can introduce just one or two of these strategies and get improvements - a complete overhaul of our system is not required [although let me do my "Carthago delenda est" and say that I wouldn't shed a tear if NCLB were dismantled tomorrow!]. Inspiring, hopeful, and practical - read it as soon as you can.

By the way, I got the Kindle version and I echo one of the reviewers who said it's perfectly fine. I love a paper version more than the next person, believe me, but the price difference was enough for me to go Kindle, and I'm satisfied.


If you have the money to spare, this is a fun one:
100 Commonly Asked Questions in Math Class: Answers That Promote Mathematical Understanding, Grades 6-12

Things I keep on hand (we have the exact same problem in my school):

1. Story of Maths video and/or Story of 1. Both are a history of math, the Story of 1 is a bit more accessible, a bit sillier, but also shorter. The Story of Maths has several one-hour episodes covering different cultures. I have them both on DVD, but last I checked Story of Maths was on Netflix.
   
   
2. Chapters from the book Crossing the River with Dogs. I actually have the 1st edition, and it's findable online if you're okay with some flexible ethics of piracy. The chapters walk students through some example problems with specific strategies (solve by drawing a picture, solve by making a list, etc), and analyze what went well and what went wrong. I've had great success with kids doing the problems together. It's all accessible to a non-mathy sub (How many games will be played in this tournament? type questions).
   
   
3. Review worksheets! We have the Infinite Algebra software, but you can find some generic ones by the publishers of the software here. Answers are included I think, so kids/sub can check the work.
   
   
4. Logic puzzles and sudoku. I've used this site for free puzzles. Caution, some are more challenging than a lot of kids have patience for. My students also love KenKen (it's similar to Sudoku, but with actual arithmetic involved) as well.
   
   
5. If you have access to computers, desmos activities are great. There are a variety of Marbleslides for various levels, and the Water Line activity works well for almost any level. I make Polygraphs for my students (it's like a math version of Guess Who?), and it keeps them occupied for easily a whole class period (usually, I intend it for only 15-20 minutes, but they get sucked in). You can definitely use the Activity Builder to do something more related to the specific curriculum for each class, but use the search function...there are tons of great activities that folks have made and shared that are ready to go or need minimal tweaking.
   
   Good luck!

Math

• Multivariable Calculus
  
  
• Differential Equations
  
  
• Linear Algebra
  
  You have to know those three pretty well to start. You pick up some more math along the way as needed, but that's the bulk of it.
  
  Physics
  
  
• Classical Mechanics (basic, Newtonian)
  
  
• Electrostatics
  
  
• Electrodynamics
  
  
• Basic Quantum maybe. It's not necessiry for Lagrangians/Hamitonians but it's very cool stuff and you get to see Lagrangians/Hamiltonians in more action (oops, I made a pun...).
  
  
• Special Relativity
  
  More Math
  
  
• "Old school" differential geometry and Reimannian geometry. They both show up a lot, but Reimannian is more common in more advanced stuff. And notation starts to become more important
  
  
• Tensors (which comes with Reimannian geometry, but they're worth mentioning by themselves cuz they're important)
  
  
• Calculus of Variations
  
  
• Misc: Taylor Series, Taylor Series, Taylor Series. Basic Fourier Analysis and complex numbers.
  More physics
  
  
• Analytic Mechanics ("advanced" class mech/Lagrangian & Hamiltonian dynamics)
  
  
• General Relativity
  
  Some books
  
  
• Class Mech: Kleppner/Kolenkow for Newtonian stuff, Marian&Thornten for more basics and a pretty good intro to calculus of variations and Lagrangians/Hamiltonians. Both these have chapters on Special Relativity too.
  
  
• Griffiths E&M for E&M (first half of book is statics, second half is dynamics)
  
  
• Quantum: J.S. Townsend's A Modern Approach to QM
  
  
• General Relativity: I used Hartle's Gravity. It's good, but I had two or three major beefs with it. I've also heard Sean Carrol's book is good.
  
  
• This series. Fair warning though, those are very advanced and are more of a reference for professors than an actual book to learn by.
  
  
• This Math Methods in physics book is very nice.
  
  I come from a physics background so I'm familiar with a lot of this stuff. I'll let people better in the know suggest the relevant math books.
  
  It's a long road but well worth it in my opinion. Good luck.

The Grapes of Math and the other books in that series are pretty good. Kind of a mix of numeracy and recreational math, but for kids.

There's a good book called Innumeracy, but that may be over the head of a child that young.

Once he's had a bit of algebra, A Long Way From Euclid is an excellent book. Even without the algebra, he might benefit by reading it together with someone.

You may also want to look at the library for introductory material on Euclidean geometric constructions, orgami, tessellations, fractals, topology (Flatland?), stereograms, Logo ("turtle graphics"), combinatorics, celestial mechanics.

Or for more hand-on stuff: play with Newtonian physics - build stuff with catapults, marbles, etc. The Art of the Catapult is a good book with plans for various machines.

Also, building kites, or paper airplanes:

The Paper Airplane Book

Paper Airplanes and Other Super Flyers

The Great Kite Book

25 Kites That Fly

Kites For Everyone

When do you realize that they are not learning? Is it when you get the test? Do you notice this earlier?

What is the structure of your class like? What techniques do you use to have the students doing more of the thinking and you doing less of it? Do the students collaborate or do they work independently?

Do you have manipulatives? Do you use pictures or models to help with their thinking to break up the thinking?

I teach at a much more priveledged school, but a class can be apathetic anywhere if the environment is off. There are plenty of teachers that don't have as much success as others because of their environment and their attitude in class. The major bits in that regard that I can offer is to structure the class around the student doing as much as possible and giving time for thinking, and time for sharing, and time for discussion, then with a quick follow up.

Whiteboarding is awesome. Look into a book called 5 Practices ... (long title) link here:

https://www.amazon.com/Practices-Orchestrating-Productive-Mathematics-Discussions/dp/0873536770

Focus on building up their ability to explain themselves by discussing how to explain how you know something using definitions or shared experiences / methods, and then implementing them relentlessly in class.

When it comes to technology, I prefer pencil and paper for most tasks and teacher led activities using electronics to prevent distraction and from them getting into pitfalls.

Also, some simple physics or probability stuff is always good to do in a lab setting to see how some math concepts show up in the real world (having 5 people measure someone's arm length as precisely as possible and averaging them, etc).

First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.

Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:

Geometry and solutions

Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.

A First Course in Calculus

For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.

Some more very good books that should be used more, by Gelfand:

The Method of Coordinates

Functions and Graphs

Algebra

Trigonometry

Lines and Curves: A Practical Geometry Handbook

I think it can be reinforced this way, but I feel that a lot of the asking of "why?" can be important for students, albeit annoying at times for teachers, and that may not come up in the same way with games(Though it also might).

Beyond this, there are students who do desire to continue with mathematics after the basic high school curriculum, and many of them do not really know that until after they complete some higher-level math courses like Calculus. So the math is still important.

That being said, I love bringing games in to the classroom. Though I typically stay away from anything advertised as a "math game." Instead, I bring games that I like, but in which mathematical concepts can be found. Some examples I've used in class include: Set, Mao, The Great Dalmuti, Settlers of Catan, and Formula D.

We often ask our 9th graders to show how to add, multiply, subtract, etc. in more than one way. They often prefer algorithms but they have difficulty making sense with what they actually mean and how they transfer into algebraic thinking. I do have to say over time, they get better at the multiple ways of performing operations.

People who are good at number sense and mental math often don't waste time with algorithms.

I would recommend picking up this book and spending 5-10 minutes a day doing number strings:
http://www.amazon.com/Building-Powerful-Numeracy-Middle-Students/dp/0325026629

You can also pick up "Lessons and Activities for Building Powerful Numeracy" which has handouts/worksheets and sample discussions with students.

You can basically look for anything else that is written by Pamela Weber Harris or Catherine Fosnot.

https://www.amazon.com/Perfect-Compass-Classroom-Geometry-10-Inches-x/dp/B005HYOIUW

​

By far my favorite. I don't love the safe-drawing compasses so much so I make sure to order a class set of these every few years or so. They are sturdy and can be used with any pencil or pen. They can be a little finicky but I think once you get used to them they're great.

​

Some downsides: the point is pretty sharp so there are some worst case scenarios that will go through any teachers mind. I've used them with diverse populations of students - honors kids and then those kids that screw around a lot and have never had any problems.

Math content knowledge on a subject is pre-requisite to pedagogical knowledge. If a teacher can't divide fractions, xe won't be able to effectively teach xir students how to divide fractions either. This point was highlighted in Liping Ma's book that has been making the rounds in math ed community.

You are right that just knowing how to divide fractions doesn't mean that you can effectively teach it; that's where the jingle "ours isn't to ask why/ just invert and multiply" came from: well-meaning teachers who are trying the best they know how to get their students to pass the tests.

"The Number Devil" is a great book, lots of pictures, easy to read, but really has some neat mathematical concepts explained simply.

There are some board games that encourage abstract or mathematical thinking.

I slowly bought 5 decks of the Set card game, which is good for a couple days' distraction (especially if kids shuffle in and out through the week).

Combination finding games like Sushi Go will also get some mileage.

If you have a smaller class and longer periods, 6-player Settles of Catan will lead to a good discussion on probability (and how life isn't fair because no one is rolling 8).

I don't know what age, and students at that age vary wildly in level. However, there are a number of things I might suggest, for different parts of that age range:

The dragonbox app suite.

This link for a list of great toys/physical resources, sortable by age range.

Bedtime Math

Turing Tumble

https://scratch.mit.edu/ (Just let 'em play with making whatever they want to make!)

The book The Number Devil

Use number strings or number talks. These are mental math teaching strategies. In number strings you can talk about rounding to friendlier numbers (like multiples of 10 or doubling) for subtraction and then compensating. You can do the same thing for multiplication. After all, when most of us multiply 17 by 19 we don't use the algorithm, we multiply 17 by 20 then we subtract 17 (or -20 and add 3).


This books are useful
http://www.amazon.com/Building-Powerful-Numeracy-Middle-Students/dp/0325026629

And www.numberstrings.com

We can talk via email if you need more ideas. This has been my pedagogical focus. Incorporating numeracy into algebra.

I think Basic Mathematics is basically a precalculus text. I can't stand normal textbooks, everything is disconnected and done for you. This is written by one of the best mathematicians and will provoke thought and understanding. He knows his audience too, he's good with kids, check out his book Math! Encounters with High School Students. He's also written a 2-volume calculus text that I know has been used well in high school settings.

elementary. I teach high school but read a book knowing and teaching elementary mathematics which contrasts US teachers understanding an teaching with Chinese teachers... it's really interesting.

I've heard good things about: http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773/ref=cm_cr_pr_product_top?ie=UTF8
but I admit I haven't read it.