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The purpose of the CSA was to examine the types ofconnections prospective middle grades teachers’ makebetween various mathematical concepts, definitions, andproblems. Participants were asked to complete a repeatedsingle criterion open card sort and closed card sort(Fincher & Tenenberg, 2005; Rugg & McGeorge, 2005).In the closed card sort, five particular pairs were chosenbased on national recommendations (CBMS, 2001;NCTM, 2000, 2006) for what middle school teachers andstudents should know and be able to do. The cards chosenwere also influenced by content from the reform middleschool curriculum textbook series Connected Mathematics2: Grade 6, 7, and 8 (Lappan, Fey, Fitzgerald, Friel, &Phillips, 2006) and three university mathematicians.For the open card sort, participants sorted the cardsbased on a single criterion: their perceived notion of howthe statements on the cards were connected. Theresearcher developed a protocol of interview questionsfor both the open and closed card sorts that focused onstudents’ mathematical connections. The design of the
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