The case for veridical out-of-body experiences (OBEs) reported in near-death experiences might be strengthened by accounts of well-documented veridical OBEs not occurring near death. However, such accounts are not easily found in the literature, particularly accounts involving events seen at great distances from the percipient. In this article, I seek to mitigate this paucity of literature using my collection of dream journal OBE cases. Out of 3,395 records contained in the database as of June 15, 2012, 226 had demonstrated veridicality. This group divides into examples of precognition, after-death communications, and OBEs. Of the OBEs, 92 are veridical. The documentation involved is stronger than is normally encountered in spontaneous cases, because it is made prior to confirmation attempts, all confirmations are contemporaneous, and the number of verified records is large relative to the total number of similar cases in the literature. This database shows that NDE-related veridical OBEs share important characteristics of veridical OBEs that are not part of an NDE. Because the OBEs are similar, but the conditions are not, skeptical arguments that depend on specific physical characteristics of the NDE-such as the use of drugs and extreme physical distress-are weakened. Other arguments against purported psi elements found in veridical OBEs are substantially weakened by the cases presented in this article.
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It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
