The purpose of this study was to examine the ways that teachers use Connected Classroom Technology (CCT) to potentially support achievement on translation problems that require moving between algebraic representations. Four mathematics classrooms were chosen based on their gain scores on pre- and post-test Algebraic translation problems. Two classrooms with the highest and the lowest gain scores were chosen among the classrooms with pre-test scores that were below 50%. This study used video-recorded observational data and found that teachers in effective classrooms created environments wherein students used multiple representations simultaneously and translated between representations through discussion. In contrast, teachers in less effective classrooms fostered environments wherein students used representations independently and missed opportunities to translate representations through discussion. [For the complete proceedings, see ED583608.]
In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.
The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. These objects were introduced and studied in [2],[7] and [14]. Some examples to illustrate these geometric information in practice are given. A classification of unital C*-algebras by noncommutative CW complexes and the modified Morse functions on them is the main object of this work., 18 pages
Published
2011
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