Over four decades of conceptual change studies in education have been based on the assumption that learners come to science classrooms with functionally fixated intuitive ideas. However, it is largely ignored that such pre-instructional conceptions are probabilistic, reflecting some aspects of an idiosyncratic sampling of their experiences and intuitive decision-making. This mixed-method study foregrounds the probabilistic aspect of international students' intuitive-to-counterintuitive conceptions when learning pendulum motion. The probability here is rooted in a moving neural time average in the mind for characterizing these students' cognitive processes (sampling and decision-making) and learning processes (resampling and making a new decision). To sharpen the said focus, we would argue that a new taxonomy of physics concepts is needed to save the mathematical identification of the isochrony of pendulum motion. To connect the mathematical core-based taxonomy with reality, we conducted an experimental study and interviewed students to characterize these students' reaction time and error rates in matching the period of a visually presented pendulum, which embodied its mathematical identity: T = 2[pi][square root of]l/g. The reaction times and error rates data have converged on the probabilistic aspects of the students' active learning mechanisms in their mind. The pedagogical implications of such a probabilistic cognitive mechanism have also been discussed.