Schemes for the use of contracted basis functions in algebraic variational electron scattering calculations are presented. These schemes are tested by computing partial cross sections for the scattering of electrons by atomic hydrogen for several contracted and uncontracted basis sets. The results indicate that the use of contracted functions is an effective means of circumventing lengthy algebraic computations without much loss of accuracy. One contraction scheme provides a method intermediate in accuracy and volume of computations required between the distorted wave method and the close coupling method. Another provides a method intermediate in accuracy and volume of computations required between an M-channel close coupling calculation and an (M + M′)-channel close coupling calculation where M′ is the number of channels in which the number of contracted functions is insufficient for convergence.