The event in Massachusetts in 1786-7 that led to the Constitutional Convention is Shays’ Rebellion. This rebellion led to the Constitutional Convention because it helped make conservatives worry that the country had too much democracy under the Articles of Confederation and was headed in a bad direction.
In 1786, Massachusetts was trying to pay off a large debt and so it imposed many taxes, most of which fell on people who were not rich. Many farmers were paying about a third of their income in taxes. At the same time, an economic slump was making it very hard for people to repay their debts. Because so many people were in debt and so many were losing their property when they could not pay, a movement sprang up that tried to use force to prevent courts from meeting and foreclosing on properties. The state legislature responded by passing some laws to try to give the rebels some of what they wanted.
Conservative elites around the country were worried by this. They felt that it showed that America was becoming too democratic and was allowing for mob rule. George Washington (who was, of course, not president at this time) said that the country was moving towards anarchy. Conservatives came to believe that a new constitution was needed, one that would limit democracy to some degree and increase the power of the national government (which was seen as somewhat less responsive to the people than state governments).