Schenecker's daughter, Calyx, was found in an upstairs bedroom, and Beau was found in an SUV in the garage, police spokeswoman McElroy said.
Both had been shot with a .38-caliber pistol that police believe had been bought five days earlier, according to police.
Schenecker wrote a detailed notes planning the murder and after the murders occurred, she wrote detailed notes describing the crimes, McElroy said.
"It's hard to believe that a mother authored the notes because it's very methodical, non-emotional description of the murder of two innocent children, of her own children. Whe she's describing it, it's just a very matter of fact, devoid of emotion, matter," McElroy said.
At the time of her arrest and confession, Schenecker was not remorseful, McElroy said.
In court today, wearing a burgundy jumpsuit with the words "inmate" written across it, Schenecker did not speak, although she appeared emotional.
Her husband, Col. Parker Schenecker, did not attend the hearing. He is not staying at his home. Public Information Officer McElroy said that it does not appear Col. Schenecker will be supporting his wife through her trial.
Judge Heinrich said the court will request the appointment of doctors for a mental evaluation of Schenecker.
Brad Garrett, a former FBI profiler and special agent who's now an ABC News consultant, said, "In situations where women kill their children ... about 80 percent of the time, it's driven by some mental illness issue ... and what happens is women become so depressed, they believe they can't go on in life and in some situations, they believe that it's better that the children not go on without them there, so they kill the children, then kill themselves."
Schenecker reportedly intended to kill herself, police said. She had left a note detailing why she'd killed her children and her plan to commit suicide, police said.
Former FBI profiler Garrett said it will be difficult for Schenecker to use an insanity defense.
"In her case, it appears this is a very pre-mediated murder," Garrett said. "The government can clearly show, well, this woman thought through this. She went and bought a gun, she kills her son at one location, she drives home and kills her daughter at another location. Clearly, [that is] someone who is thinking logically at least about what they're going to do and how they are going to do it."
At Calyx's high school today, the principal asked for a moment of silence, the Tampa Tribune reported. Several students wore Harry Potter clothing for the teen girl who loved the books and movies, the newspaper said.
Schenecker's children were described as star athletes and students, according to friends and family of Schenecker.
A Facebook group memorializing the siblings has been visited by over 7000 people."These were special children," John Pisco, a family friend, told ABC News. "The reason why so many people are affected in our community is they've touched a lot of people's lives."
"Obviously, teens are going to say things to their parents, they aren't going to get along sometimes but that? I never saw her once speak wrong to either one of her parents," Calyx's track coach said. "One of the parents was always at a meet, you know, whether it was a dad or mom, someone was always there."