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Barabási‐Albert and small‐world networks. In this model, the order‐disorder phase transition of the order parameter is well defined on small‐world networks. We calculate the value of the critical temperature Tc for several values of rewiring probability p of the directed small‐world network. For directed small‐world networks we obtained a second‐order phase transition for p = 0.2 and first‐order phase transition for p = 0.8. On directed Barabási‐Albert we show that phase transition do not exist for Ising model with spin S = 1, 3/2 and 2.

This manuscript describes the findings of an examination of 21 pre-service teachers and one literacy course instructor within the context of a program focused on urban teacher preparation. Using inductive thematic analysis of multiple data sources, the research team identified three themes. First, general agreement existed amongst the pre-service teachers that Barack Obama’s 2008 election was a critical, important moment in U.S. history with consistent rationales for why they should include information about President Obama’s life and work as part of the curriculum, especially for African American students. This theme comprised three trends: the importance of teaching civics, the historical importance of the first African American president, and the importance of President Obama as a role model. Second, pre-service teachers enacted and responded to barriers to teaching critical literacy about the Obama presidency. This second theme also comprised three trends: a reluctance to detract from President Obama’s positive image, an unease in teaching politics, and the references to developmental issues related to the ages of the kindergarten children they taught. Third, inconsistencies occurred amongst pre-service teachers’ understandings of critical literacy.