Oddly, there was no actual provision for the calling of a Constitutional Convention (just as there is no such provision in our present constitution), but representatives of the soon-to-be 13 states agreed to convene a convention anyway, with the intent of producing a governing document that would serve the intent of the people more responsively than the Articles had.
Whether or not our federal government in its present form was what those framers had in mind, and whether or not what our federal government has become is what WE want, will be the subject of our next few polite exchanges.
Soon after our present constitution was drafted, but before ratification, an attempt was made to "sell" it to the American people through a series of articles which appeared in selected newspapers. These essays were intended to argue the merits of the new constitution, explain the intent of the new document and sway public opinion in its favor. The letters were all signed by the Latin name Publius, but were in actuality written by three men: Alexander Hamilton, John Jay, and James Madison.
Alexander Hamilton became our country's first Secretary of the Treasury, in the administration of George Washington; John Jay was to be the first Chief Justice of the U.S. Supreme Court; James Madison (who is called the father of the constitution, and was the principal author of it) was a member of the Virginia legislature and later served in the U.S. Congress as a representative of that state. He then became Thomas Jefferson's Secretary of State, and finally he became the 4th President of the United States.
If you have a desire to learn the reasons our constitution was framed the way it is, the thinking that went on in the minds of the men who wrote it and what they were trying to accomplish, read the Federalist Papers. There are 85 essays altogether, most published between October, 1787, and August of 1788. A complete collection of all the essays (including 8 additional essays) was also published in book form in 1788.
One thing that Americans don't often think about, but should realize, is that these men and the rest of the men on your personal list of founding fathers, absolutely were mindful that they were being watched, were making history, and, that future generations of Americans - you - would be looking back and judging them. Their writings and the writings of their contemporaries make that clear.
The Federalist Papers were, of course, advocating the ratification of the new constitution. But, even more importantly, they serve as a first-person primary resource for our interpretation of the constitution. They outlined both the philosophy and motivation of the system of government they were proposing. There is little doubt, simply by the way they are written and the points they repeatedly and painstakingly address, that their intent was to shape future interpretations of their baby. To that end, it is generally agreed that no analysis by later historians matches the incredible depth and breadth of the political science masterpiece contained in the essays of the Federalist Papers. Read the Federalist Papers directly; they are available to you. You do not have to rely on someone else's interpretation of them.
Students of American Government cannot fully grasp, I don't think, the reasoning that went into our constitution unless they read and study the Federalist Papers of Hamilton, Jay and Madison. Especially read Madison's essays and you will come away with a new appreciation of the then-groundbreaking concepts that have been mimicked by dozens of governments over the years.
(Then click on the red "Federalist 29" to enlarge it.)
[Next: The problems with the Articles of Confederation, how the new constitution would remedy those problems, and an explanation of the concept of Federalism. Please don't shy away; this will be fun!]