Prosecutors say Yoselyn Ortega, 55, stabbed herself in the neck after killing 6-year-old Lulu and 2-year-old Leo Krim in the bathroom of their family's home on the Upper West Side in October 2012.
Prosecutors are hoping to prove Ortega was coherent and made a conscious decision to kill the children.
Her attorney is expected to use an insanity defense.
Ortega faces a possible sentence of life behind bars. She is currently being held without bail.
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