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Context: At present, we lack a common understanding of both the process of cognition in living organisms and the construction of knowledge in embodied, embedded cognizing agents in general, including future artifactual cognitive agents under development, such as cognitive robots and softbots. Purpose: This paper aims to show how the info-computational approach (IC) can reinforce constructivist ideas about the nature of cognition and knowledge and, conversely, how constructivist insights (such as that the process of cognition is the process of life) can inspire new models of computing. Method: The info-computational constructive framework is presented for the modeling of cognitive processes in cognizing agents. Parallels are drawn with other constructivist approaches to cognition and knowledge generation. We describe how cognition as a process of life itself functions based on info-computation and how the process of knowledge generation proceeds through interactions with the environment and among agents. Results: Cognition and knowledge generation in a cognizing agent is understood as interaction with the world (potential information), which by processes of natural computation becomes actual information. That actual information after integration becomes knowledge for the agent. Heinz von Foerster is identified as a precursor of natural computing, in particular bio computing. Implications: IC provides a framework for unified study of cognition in living organisms (from the simplest ones, such as bacteria, to the most complex ones) as well as in artifactual cognitive systems. Constructivist content: It supports the constructivist view that knowledge is actively constructed by cognizing agents and shared in a process of social cognition. IC argues that this process can be modeled as info-computation.