"Hey, apple, that's your stem lifting that weight, not your core."
Are you using your core muscles to do core strengthening exercises or are other muscles getting in the way?
Let's rephrase that question. Are you allowing your core muscles to work or are other muscles getting in the way?
Your core muscles are really deep. From the perspective of the Alexander Technique, we would call them "postural support" muscles. These are muscles that you don't have a lot of direct control over in terms of using them to mover your self around. If you're staying upright, they are working. They could probably work better.
What's getting in the way?
Habits of overusing more exterior muscles, such as the muscles in the back of the neck, the shoulders, the armpits, and inner parts of the upper arms, and the fronts of the thighs prevent the deep core muscles from doing their job.
Those exterior muscles are better-suited for moving you around and feel strained and sore if they are working all the time to hold you up.
Why would you use those other to hold yourself up then?
Because of what we tend to do when . . .
We sit all day using a computer
Stand all day
Slump over a smart phone
And lot's of other stuff that I'm sure you can add to this list
Then when we go to exercise we bring those habits with us and even if you really want to strengthen your core, you may have a lot of trouble not engaging those habits and overusing those other muscles.
We get used to our habits and it can feel like that's all we know. That's where Alexander Technique lessons can come in really handy. There's a teacher guiding you to feel something new. To experience being in your body, standing, sitting, moving around, and doing the things you like to do in a way that feels different.
You'll learn to sense what you learn in lessons more and more on your own, so that when you want to strengthen your core through exercise, you know how to get out of it's way and let it work and the icing on the cake is that if you are using your body in a more natural way, you'll also strengthen your core just by going about your day.