To resolve the fundamental question of how the mammalian neocortex learns to create complex hierarchical representations, two main competing theories that intersect ideas from neuroscience and machine learning are currently debated. The first theory draws inspiration from artificial neural networks, suggesting the brain approximates error backpropagation (BP), where neurons adjust synapses to minimize a backpropagated error. The second approach, target learning (TL), proposes that neurons learn by reducing feedback needed to achieve desired activity patterns. While both theories are computationally sound, decisive biological evidence for either one is lacking. To address this gap, we began by modeling the membrane potential and calcium dynamics of individual pyramidal neuron synapses and employed a molecular-scale calcium-dependent plasticity rule detailing how synaptic calcium levels affect plasticity [Graupner \& Brunel (2012)]. We extended our synaptic model with somatic and apical dendritic compartments, integrating intracellular processes that influence synaptic dynamics and plasticity. We implement somatodendritic coupling via backpropagating action potentials, dendritic calcium spikes, and bursting. Together, these mechanisms supervise plasticity at basal synapses by relating inputs arriving at the apical dendrite. To validate our model we next performed in vitro electrophysiology experiments in L5 pyramidal neurons of the mouse neocortex. To finally answer which of the two learning algorithm better explains cortical learning, we use our pyramidal neuron model and in vitro results to form hypotheses of the BP and TL algorithms that we test on in vivo data from the mouse lateral visual cortex [Nguyen et al. (2024)]. Our analysis reveals that, consistent with our in vitro results, in vivo population activity more closely matches TL predictions than BP. In conclusion, our findings represent a significant advancement in understanding biological learning systems, highlighting a fundamental difference from current artificial neural networks and providing new insights into cortical information processing.