We introduce the Progression of Early Computational Thinking (PECT) Model, a framework for understanding and assessing computational thinking in the primary grades (Grades 1 to 6). The model synthesizes measurable evidence from student work with broader, more abstract coding design patterns, which are then mapped onto computational thinking concepts.We present the results of a pilot-test study of the PECT Model in order to demonstrate its potential efficacy in detecting both differences in computational thinking among students of various ages as well as any clear overall progressions in increasing computational sophistication. Results of this sort are vital for establishing research-based and age-appropriate curricula for students in the primary grades, i.e., developing non-trivial, challenging but not overly daunting lesson plans that utilize the cognitive development stage of each grade level most effectively.
We investigate the existence and properties of uniform lattices in Lie groups and use these results to prove that, in dimension 5, there are exactly seven connected and simply connected contact Lie groups with uniform lattices, all of which are solvable. Issues of symplectic boundaries are explored, as well. It is also shown that the special affine group has no uniform lattice. 1 *
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