Hi Thermo. Yes, it has to do with how 'k' is determined. The spring constant is equal to force applied divided by the change in length of the spring, where that change has units of distance. Suppose you have a long spring and put a marker at the midpoint, then apply a force at the end. The end will deflect by an amount F/k, but what happens at the midpoint? It deflects only half as much, so effectively the spring constant of one half of the spring is equal to 2k.

Perhaps you are thinking in terms of percentage change of length of the two halves, rather than the absolute change in length? If so, then you would be correct - if the full spring compresses 10% under a certain load, then each half also compresses 10%. In engineering we use the relationship Stress = E times Strain, which is based on this idea. It says that for a given material the force per unit area applied (stress) equals E (which is Young's modulus, and is a characteristic of the stiffness of the material) times change in length per unit length (strain). Using this approach allows the use of a constant value for E regardless of the length of the material.