The Number of Plagues in Egypt

There is a Tannaitic dispute in the Pesach Haggada regarding the number of plagues that were inflicted on the Egyptians. Is this merely an informative question, or is it a fundamental question regarding the number of plagues and its significance? Where does the "ten" come from regarding the ten plagues? How does the book of Psalms count and describe the plagues? Why are the plagues divided into groups of three? Is there a natural connection between the second and third plagues?