We present experimental and theoretical results for the electron-impact-induced ionization of ground-state helium atoms. Using a high-sensitivity toroidal electron spectrometer, we measured cross-section ratios for transitions leading to the first three excited states of the residual helium ion relative to the transition leaving the ion in the ground state. Measurements were performed for both symmetric- and asymmetric-energy-sharing kinematics. By presenting results as a ratio, a direct comparison can be made between theoretical and experimental predictions without recourse to normalization. The experimental data are compared to theoretical predictions employing various first-order models and a second-order hybrid distorted-wave + convergent R matrix with pseudostates (close-coupling) approach. All the first-order models fail in predicting even the approximate size of the cross-section ratios. The second-order calculations are found to describe the experimental data for asymmetric-energy-sharing with reasonable fidelity, although significant disparities are evident for the symmetric-energy-sharing cases. These comparisons demonstrate the need for further theoretical developments, in which all four charged particles are treated on an equal footing