Canuto and Mazzitelli have proposed an alternative theory to the standard Mixing Length Theory for the treatment of turbulent convection in stars. In this study, we explore the effects of the new treatment of convection on the 0.9, 0.8, 0.7, 0.6 and 0.5 M. stars during the pre-main sequence evolution. Two different cases, with and without an adjustable parameter in the mixing length expression, are applied to the evolution of the Sun starting from the Hayashi track to the present position. We then compare the zero-age-main sequence models of low mass stars obtained with the same input physics, the same code but with different treatments of turbulent convection. We also compare the models with the observed properties of some stars in the same mass range.