Cerebellar parallel fiber (PF)-Purkinje cell (PC) synapses can undergo postsynaptically expressed long-term depression (LTD) or long-term potentiation (LTP) depending on whether or not the climbing fiber (CF) input is coactivated during tetanization. Here, we show that modifications of the postsynaptic calcium load using the calcium chelator BAPTA or photolytic calcium uncaging result in a reversal of the expected polarity of synaptic gain change. At higher concentrations, BAPTA blocks PF-LTP. These data indicate that PF-LTD requires a higher calcium threshold amplitude than PF-LTP induction and suggest that CF activity acts as a polarity switch by providing dendritic calcium transients. Moreover, previous CF-LTD induction changes the relative PF-LTD versus -LTP induction probability. These findings suggest that bidirectional cerebellar learning is governed by a calcium threshold rule operating "inverse" to the mechanism previously described at other glutamatergic synapses (BCM rule) and that the LTD/LTP induction probability is under heterosynaptic climbing fiber control.