I am a big fan of integrated abdominal training. I believe most of the "core training" should be done in a standing position with a combination of vertical and horizontal forms of resistance.
However, sometimes you might have to start with exercises that will help the abdominal muscles to fire properly before moving into more integrated movement patterns. Here is an example of a core control exercise from Bill Hartmann's blog. I especially like the idea of the arms overhead pushing against the wall. This will reflexively activate the abdominal wall and teach subconscious muscle recruitment.
Progression towards the standing and more integrated position could go in the following way:
Think of the stages of early child development: from the back to the belly to more upright into eventually standing. This will help the adbominal wall and the "pillar" of core to become and effective and participating member of the total movement system. We don't do this progression with everyone, but for some who have trouble initiating the core control activity.
Here is another potential stage of the progression: Kneeling with horizontal resistance. This phase already requires a great team-work capacity between the hip (glutes/hip flexors) and the adbominal wall. As you already know so well, this exercise is for demonstrational purposes only.
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