Does it really matter if you train your core before, during, or after your training session? Actually, yes; and I’ll tell you why. Many back injuries occur when the muscles of the core become fatigued, and fail to maintain stability. So, it would be risky to target and fatigue those core muscles before calling on them to keep your back safe during the rest of your workout. That means lots of core training before squats, deadlifts, and other heavy or complex movements is probably a bad idea.
Instead, your warm-ups should include just a few core activation movements. This way, you’ll fire up your nervous system to recruit the correct muscles for safe and efficient movement, but won’t fatigue those muscles with lots of reps or weight.
During your workouts, focus your effort on safe, effective training. Your core will work hard to stabilize your spine and assist in movement, without any targeted training. Heavy compound lifts, like squats or power cleans, can generate far more core engagement than crunches. So, remember to take good posture, brace, and stabilize your spine. Your whole workout is core training.
At the end of your workout, when the rest of the job is done, it’s safe to do more core specific training. An added bonus of organizing your training this way, is that training your now pre-fatigued core may lead to additional core-muscle endurance. More core endurance equals more spinal stability and less injuries.
As always, progress your core training slowly. Start with static holds, like planks. Work your way up to flexion and extension, then onto rotation; all with controlled tempos. Ballistic movements like medicine ball tosses come last, after you’ve developed a solid base of trunk strength, pelvic stability, and hip mobility. The workout below is an example of core training for an advanced athlete. Below that, I’ve also linked to an (old) exercise demo I did for one of the exercises in that program.