which job to find to increase teaching experience If you don't have enough teaching experience, what kind of job you should try to find to increase the teaching experience. Now many jobs have set requirements for teaching experience. It seems contradiction, Without appropriate job we can't increase the teaching experience,but without enough teaching experience we can't find jobs. Thanks for advice!
 A: Here's my American university perspective.  I've been an adjunct instructor at a community college, a TA at a Research I university, a postdoc at a Research I university, and now I have a permanent position at a small liberal arts college.  Each position has been completely different, and nothing has informed my teaching more than making each of these major steps in my career.   
When I was a grad student, teaching at community college was an excellent way to get experience.  You only need a Master's degree, which you can usually pick up on the way to a Ph.D., it usually pays better than TAing, and you have complete responsibility for your courses (which is looked at much more positively than merely being an assistant when you look for a permanent job).  It also might expose you to a wider variety of students than you might see at a typical research I school, especially if you teach a course during the normal semester and not a summer course.
Many hiring committees also want breadth of teaching experience, not just years.  They will want someone comfortable and capable stepping both into a "developmental math" course (i.e., high-school level stuff) and into a variety of advanced courses, including inter-disciplinary and computer-intensive courses. My advice is:  keep trying to expand your experience when you're starting out --- always try to teach something new whenever possible.  Don't turn down a teaching position to research --- do both!  Some graduate programs let a few select students have complete control over a course.  You usually need to prove yourself to get such a job, so you must put your best into your teaching to prove yourself (if you aren't doing this, you might not want to reconsider a teaching path anyway).
Also, explore alternative teaching environments.  You might be qualified to try teaching an online course, a course for a test prep company, to do outreach with high-schools in your area, or to start a "math circle". All of this will show your commitment and your passion for education, which might be what a hiring committee will look for in someone relatively new to teaching rather than just a few semesters of teaching experience.
A: My experience overlaps Barry Smith's some, but this is too long for a comment.
On community colleges: The community college where I taught would hire people with bachelor's degrees in math to teach math courses, but the courses eligible for transfer to a four-year institution (basically, the non-remedial courses) could only be taught by people with master's degrees.  Having a master's degree made you more attractive to the CC folks.  And if you had a PhD, that was even better.  At the CC where I taught for three terms I was the only one on the faculty with a PhD, and so even though I was an adjunct I was handed the most advanced courses they offered (Calculus III and differential equations).  The other thing I will say here is that since I didn't get much teaching experience in graduate school, I don't think I would have been hired for my first tenure-track job at a teaching school without the experience I gained working at the CC.
Depending on the area of math you are studying, don't forget that there are departments outside of math that might be willing to hire you as an adjunct.  My PhD work was in operations research, and because of that I was able to teach some advanced OR-related business classes.  Knowledge of other math-related areas that might get you hired as an adjunct in a business or engineering school are statistics and computer programming.  This is not math, per se, but it would still be teaching experience in a related area.
Finally, there are ways to supplement your experience teaching in the classroom.  Barry Smith mentions some.  If you are a graduate student, here are some more suggestions.  Volunteer to help the undergraduates at your institution prepare for the Putnam or the Mathematical Contest in Modeling, maybe in a weekly seminar format.  Start a journal club for graduate students, where each week one of you teaches the others the content of some journal article.  Some institutions (such as Colorado - see here) have a graduate teacher preparation program.  Take advantage of that.   
