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What are some exercises I can use in my training with 14 year olds to make their core muscles stronger?

According to Steve Pyle on core training:

The intent of core training is to strengthen the muscle groups that stabilize your skeletal structure. These are primarily the muscles in the thoracic area that determine your posture in each sport and in effect link your upper and lower body. The muscle groups that you strengthen with core training generally don't have the range of motion needed to drive you forward, but they are the "platform" from which your arms and legs work. This need for a stable platform clearly applies to proper running posture.

Core training helps get you "in touch" with individual muscles and small groups of muscles. This awareness of specific muscles, or muscle groups is the first step in improving various posture and form issues. For example, many adults (and plenty of athletes) have poor posture stemming from weak mid-back muscles (rhomboids). The first step to improving your posture is getting to know these muscles, then toning them so you can tighten them independently of your lower back's muscles.

Core training focuses on muscular areas of the abdominals including obliques (side muscles), upper and lower back (deltoids, rhomboids), hips (gluteals, hip flexors, psoas), outer and inner thighs (abductors and adductors), hamstrings, even some pectoralis and triceps work.

In running events, you are only as strong as your weakest muscular link. Consider what you felt like during your long run. When you become fatigued, your form falls apart. It's not just because of tired legs, it's tired arms, tired back, everything hurts. Having a strong torso helps hold your form together in the latter stages of an endurance effort or any distance race effort.

The movements below can all be done without any special equipment.

Here is a short sequence of core movements:

Abdominals:
Upper: Crunches, lateral crunches, full sit-up.
Lower: Leg raises, single, "pedaling," double legs.
Side: Bridging on your side, double leg raises.

Back:
Upper: Bridging, hyperextension.
Lower: Bridging, hyperextension.

Hips:
Abductors: Side leg raises.
Adductors: Side double leg raises.