This paper discusses how concepts and procedural skills in problem-solving tasks, as well as affects and emotions, can be subjected to meaningful measurement (MM), based on a multisource model of learning and a constructivist information-processing theory of knowing. MM refers to the quantitative measurement of conceptual and procedural knowledge with qualitative interpretations that should be rooted in a theory of knowing, model of difficult learning, classroom realities, and educational objectives as intended in the programs of study. Knowledge of the problem and search spaces of learning tasks, cognitive and affective schemes, alternative conceptions, and cognitive and procedural barriers contribute to an informed understanding of measurement of the process of development of pertinent cognitive and affective structures and their linkages. Metaphors of pigtails, bamboo stems, and competence ladders are heuristics used to describe these structures and linkages. Quantitative requirements of measurement are elaborated, and associated methodology is described, including focus group interviews, network and latent trait analyses, and dual scaling. Examples based on empirical data are presented. The progression of competence and affective schemes, affordability of problem tasks, conformity of test responses with conceptual and measurement models, simultaneity of conceptualization of a measure, and requirements of specific objectivity are hallmarks of MM. An agenda for a research program is also presented. Six figures and four tables illustrate the discussion. A 54-item list of references is included. (SLD)