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...View metadata citation and similar papers at core ac uk brought to you by provided texas a amp m repository knowing mathematics for teaching case study of teacher responses students errors difficulties in equivalent fractions dissertation meixia ding submitted the office graduate studies university partial fulfillment requirements degree doctor philosophy august major subject curriculum instruction approved co chairs committee gerald kulm yeping li members donald allen mary margaret capraro radhika viruru head department dennie smith iii abstract s nanjing advisory dr goal this is align teachers mathematical knowledge mkt with their classroom reduce complexity while keeping connection between learning i focused on student tred an eye cognitive gains as assessment effects research used qualitative paradigm videos concerning from six were observed triangulated tests personal interviews data collection analysis went through naturalistic inquiry process results indicated that great differe...