Two different analysis techniques for mapping ionospheric total electron content (TEC) are compared. The first technique approximates the ionospheric electron concentration as a thin shell at a fixed altitude. In this case, slant TEC observations are converted into vertical TEC values using a mapping function and interpolated across a grid. Other slant TEC values are then calculated from the vertical TEC grid using another mapping function. The second technique applies an advanced tomographic algorithm to invert the slant TEC observations into a time-evolving three-dimensional grid of electron concentration. Either slant or vertical TEC can then be extracted from the electron concentration images without the need for a mapping function. Results based on both simulated and experimental data are presented. The results indicate that the inversion offers improvements over a thin shell in the mapping of TEC at middle latitudes.