Answer:

An investigation involves the explanation, analysis and generalization of a mathematical problem.

For example, a student investigated the problem:
How many squares are there on a chessboard ?
First the student realized it could be interpreted to obtain an answer other than 64. She then simplified the problem by starting with small chessboards (1 by1, 2 by 2 etc.). From these special cases a pattern emerged and a conjecture was made. She then went on to prove the conjecture and was able to generalise it to obtain a formula for the number of squares on an n by n board. Other problems then suggested themselves, for example,
How many rectangles are there on a chessboard ?
Can the problem be extended to three dimension ?