A strict construction of the Constitution is one way of interpreting the Constitution. People who believe in a strict construction of the Constitution believe we can do only what the Constitution specifically says we can do. There would be no stretching the meaning of the Constitution with this view of it. We can do only what the Constitution specifically says we can do.
Thomas Jefferson and James Madison were two people who supported a strict view of the Constitution. People who were concerned the federal government would have too much power generally supported a strict view. By utilizing a strict view, the federal government and those who wanted a strong federal government would find it much more difficult to expand the powers of the federal government. Thomas Jefferson and James Madison wanted a weaker federal government. Many people in the Democratic-Republican Party also supported a strict view of the Constitution because they, too, wanted to limit the power of the federal government.
Considering how much the world has changed since the Constitution was written, it would be interesting to see how we would have functioned if we followed a strict view of the Constitution throughout our history. Even Thomas Jefferson was tested with his views when he had to decide if we should make the Louisiana Purchase. There is nothing written in the Constitution about the President agreeing to buy land. Jefferson eventually agreed to make the Louisiana Purchase even though the deal went against his views of how to interpret the Constitution.