I disagree fundamentally with your text author that all derivatives become parenchyma cells and then mature into the other two cell types. But then, I disagree completely with the author on almost all of his summary of parenchyma cells. These cells are the biochemistry machines of the plant. They are alive at maturity and are specialized in any number of structural and biochemical ways. Other than support functions, this cell type is the basis for all plant function.
Parenchyma cells have thin primary walls and highly functional cytoplasm.
The cells are alive at maturity and are responsible for a wide range of biochemical processes. For example, other than xylem in vascular bundles, the leaf is composed of parenchyma cells. Some, as in the epidermis, are specialized for light penetration, regulating gas exchange, or anti-herbivory physiology. Other cells, as in the mesophyll, are specialized for photosynthesis or phloem loading. Collenchyma Cells Collenchyma cells are also alive at maturity and have only a primary wall.