The intrusion of pseudoscience into science classrooms is a problem in science education today. This paper discusses the implications of constructivist pedagogy, which relies on the notions of viability and inter-subjectivity, in a context favourable to the acceptance of pseudoscience. Examples from written statements illustrate how prospective science teachers in Turkey readily accept pseudoscientific explanations of the origin of species. Constructivist pedagogy underestimates, if not ignores, the difficulty of holding rational discussions in the presence of pseudoscientific or absolute beliefs. Moreover, it gives a higher priority to learners' exposure to alternative constructions through social negotiation than to furthering their appreciation of science. Under these circumstances, self-confirmation and social pressure to accept existing pseudoscientific beliefs may be unanticipated consequences of social negotiation. Considering the aim of science education to foster an appreciation of science, the implications of constructivist pedagogy are, or should be, of great concern to science educators.