  The method for quantization of constrained theories that was suggested
originally by Faddeev and Jackiw along with later modifications is discussed.
The particular emphasis of this paper is to show how it is simple to implement
their method within the path integral framework using the natural geometric
structure that their method utilizes. The procedure is exemplified with the
analysis of two models: a quantum mechanical particle constrained to a surface
(of which the hypersphere is a special case), and a quantized Schr\"odinger
field interacting with a quantized vector field for both the massive and the
massless cases. The results are shown to agree with what is found using the
Dirac method for constrained path integrals. We comment on a previous path
integral analysis of the Faddeev-Jackiw method. We also discuss why a previous
criticism of the Faddeev-Jackiw method is unfounded and why suggested
modifications of their method are unnecessary.
