Is this a motion?

When a school board member says, "I would like to make a motion that ...", is that a motion?

It is not. 

The board member is expressing her desire to make a motion. That doesn't not call for a Second. No action can be taken by the board on a member's expression of a desire for something. Are they going to vote on allowing the member to make a motion?

What should the Chair say? "Thank you. Will you make the motion?"

The board member should say: "I move that ...[announcing what he proposes in a wording intended to become the assembly's official statement of the action taken]." Robert's Rules of Order §4:4.

Far too much time is wasted by the Board when voting on student matters and district personnel matters. There are long lapses while the staffer types up the Motion. The Chair should tell the superintendent to place someone with high, accurate typing speed at the keyboard for typing motions.

This board desperately needs parliamentary training. And it needs an independent Parliamentarian. The Parliamentarian must be independent and not an employee. Correcting the Chair and the superintendent often would not be good for employment security.