Big Myth:- If you have low back pain that means your "core is weak" and a "core strengthening" program would help you.
Sometimes the above statement is true, but just as often it is absolutely not. There is not a direct correlation between low back pain and core strength. In fact, many people that have incredibly strong "core" muscles suffer from regular low back pain, which is because strength is only one element of having good posture, alignment and movement. It is the overall muscle balance in your body and your relative ability at controlling movement that is the true sign of good core stability and a preventative factor to low back pain.
Many, many, many people are stiff as hell, many of these people have low back pain and many of these people think that their planks, crunches and strength program will make them better. Well I am here to tell you that there is a good chance it will make them worse. Granted some will get better, but the most efficient way to improve your strength, flexibility, alignment and pain is to first learn a bit about your body type before pursuing any type of new program.
From a very young age, as you were learning to function in the vertical position, you have been developing strategies for how your body deals with gravity. You picked up some by watching how your parents stand, walk and move. You picked up others from your gymnastics classes and soccer practices when you were six. The hard fall you had on your butt 20 years ago likely altered things and that car accident 5 years ago probably created some compensations. Long story short, your posture, flexibility, movement and breathing patterns are a cumulative product of everything you have done up until today.
You have strongly engrained movement patterns for how you balance and stabilize which typically result in one type of imbalance or another and form a variety of bracing strategies. Instead of equally using your whole body to move and balance, you will immediately migrate to what you are good at. Some people subconsciously brace the heck out of their butt to hold themselves up, others their mid back and still others their chest. Some people just brace everything. When you encourage someone that uses a variety of bracing strategies to do MORE, you will likely further strengthen their imbalance. The trouble is the person will likely see some good results initially because he/she does become physically stronger, but quite often hits a plateau and/or starts developing pain and injuries.
The best core program for bracers and grippers is one that focuses on movement awareness and focuses on everything the person is bad at. It is way harder to unlearn a movement strategy than it is to learn a new one. The people that are used to using rigidity as their stabilizing strategy need to be introduced to mobility and once they can learn to let their bracing go then starting a strengthening program is appropriate. One-on-one Pilates, Feldenkrais training and many of the WTH videos are good examples of movement leading to strength.
I was first introduced to the term butt gripper when I worked with Diane Lee and discovered that I am one. As I became more body aware I realized just how much I actually clench my butt, it blew me away. The more I assertively attempt to not clench, the better my back and hips feel. Diane has a good article on Butt Grippers, Back Grippers and Chest Grippers here (see if any of these look familiar).Also watch my video titled Everything your mother taught you about posture is WRONG
In summary, some people can very much benefit from pure core strengthening programs, but others should stay away. You are best to learn about your body type and posture first, then learn to build targeted strength and practice movements that you are bad at. Try not to just stick to your favorite exercises that you are good at because you will likely just be feeding into your imbalances.
Please refer to the movement exercise progressions found in my video playlists to work through things in an appropriate order.