1. A physical manipulative interaction system comprising: a physical manipulative sensor device, comprising: one or more hardware-based sensors configured to detect physical manipulatives within a physical environment; a processing unit comprising one or more processors; and memory coupled with and readable by the processing unit and storing therein a set of instructions which, when executed by the processing unit, causes the physical manipulative sensor device to: detect at least one of: a position of, a movement of, or a user interaction with, a first physical manipulative within the physical environment; determine at least one of: an updated physical position, an updated physical orientation, an updated physical configuration, or an updated physical relationship of the first physical manipulative, based on the at least one of the detected position, movement, or user interaction with the first physical manipulative within the physical environment; store data identifying the at least one of the determined updated physical position, updated physical orientation, updated physical configuration, or updated physical relationship of the first physical manipulative; and transmit, to one or more user computing devices, data identifying the at least one of the determined updated physical position, the updated physical orientation, the updated physical configuration, or the updated physical relationship of the first physical manipulative; and one or more user computing devices, each user computing device comprising: a graphical display screen configured to render a set of virtual manipulatives in a virtual environment; a processing unit comprising one or more processors; and memory coupled with and readable by the processing unit and storing therein a set of instructions which, when executed by the processing unit, causes the user computing device to: output, to the graphical display screen, a rendering of one or more virtual manipulatives, including at least a first virtual manipulative corresponding to the first physical manipulative within the physical environment; receive the data identifying the at least one of the determined updated physical position, the updated physical orientation, the updated physical configuration, or the updated physical relationship of the first physical manipulative; and update, via the graphical display screen, the rendering of the first virtual manipulative based on the received data corresponding to the first physical manipulative.