A new experimental technique has been applied to measure absolute scattering cross sections for electron impact excitation of the n = 2, 3 states of helium at near-threshold energies. The experimental results are compared with predictions from recent state-of-the-art theoretical calculations. The calculations are performed using the R-matrix with pseudostates, B-spline R-matrix, and the convergent close-coupling methods. Generally, very good agreement is found between the experiment and the three theories.