Experimental Studies of Belief Dependence of Observations and of Resistance to Conceptual Change

Natural scientists were invited to evaluate a rediscovery-based written manual for teaching high school science and math. The first session refamiliarized participants with the concepts this experiment presupposed, reinforced the legitimacy of the instructional setup, and fostered tolerance for unconventional mathematical formulas. The session also used a cylinder for a hands-on confirmation that the two ways of measuring the volume of geometrical solids-theoretical (through length measurements and the use of a formula) and experimental (through capacity measurements)-yield similar values. In the second individual session, an artificial clash was created: Participants were given an incorrect theoretical formula that ted them to believe that spheres are 50% larger than they are. They were then asked to compare expectations created by this formula to their own capacity measurements of two actual 10-cm and 20-cm spheres. The discrepancies between theoretical and experimental volumes frequently led to doubt, discomfort, adjustment of measurements, and ad hoc explanations. They rarely ted to the abandonment of belief in the false formula. Based on these experimental results, several stages in the process of conceptual change are proposed, including discomfort, ad hoc explanations, adjustment of observations and measurements to fit expectations, doubt, vacillation, and- finally-conceptual shift.