for each function field multiple zeta value (defined by thakur), we construct a t-module with an attached logarithmic vector such that a specific coordinate of the logarithmic vector is a rational multiple of that multiple zeta value. we then show that the other coordinates of this logarithmic vector contain hyperderivatives of a deformation of these multiple zeta values, which we call t-motivic multiple zeta values. this allows us to give a logarithmic expression for monomials of multiple zeta values. joint work with chieh-yu chang and yoshinori mishiba.