The two students who were struck by gunfire were standing behind Smith, the police chief said.
"By all accounts, Jonathan Martinez was a happy child", he told reporters.
Jonathan died shortly after being flown to Loma Linda University Medical Center. Jonathan did not make it to the operating room before dying, hospital officials said.
Police say the couple, both 53, married in January and separated in the middle of March. "The real Cedric came out", Irma Skyes, 80, told New York Daily News. "He had told other ministers and bishops, my mother, his sister and other friends that he is going to kill me", she said in the document. He went to her classroom and "without saying anything" shot her with a large-calibre revolver, Mr Burguan said.
The police chief also said a note believed to be from Anderson had been found that talked about needing closure and feeling disrespected.
He said Anderson had faced a weapons charge, and those involving domestic violence and theft from 1982 to 2013. "In none of those cases was a conviction", he added. He was born with a rare genetic condition called William's Syndrome, which reportedly leads to mild intellectual and developmental delays and causes heart problems.
Students at North Park Elementary School which has around 500 students between kindergarten and sixth grade were transported to a nearby campus, where they were "being well cared for, having snacks, playing games and watching a Disney movie", the police department tweeted. "Our hearts are broken". "This is truly tragic".
Details on what exactly transpired before the shooting were not revealed, however the two were estranged before Anderson entered her classroom Monday and opened fire.More news: Arkansas' multiple execution plan in limbo after rulings
There is no indication that the gun was visible upon the suspect's arrival to the school, Maass said.
Burguan said security footage shows Anderson at first tried to enter through other doors, which were locked.
Smith has been identified by authorities as one of the people shot by Cedric Anderson, identified as her estranged husband, as she taught a special education class at North Park Elementary School in San Bernardino, Calif., Monday, April 10, 2017.
After Smith ended the relationship and moved out of the home to live with her adult children, Burguan said, "he had been making efforts to have her come back home". Dozens of police officers responded and the students were held for hours while the school was searched.
Madden said police had received reports of the shooting at the school shortly before 10:30 a.m., and officers responded within minutes. "We've rose from the ashes before and we know our community can and will do it once more".
"My heart and prayers go out to the victims of this disgusting act and to all students and members of the North Park Elementary School community".
Grief counselors were on hand Tuesday to support students, parents and staff. "I ask everyone to join me in keeping all the victims and those impacted in your prayers".
San Bernardino was the site of one of the nation's worst terror attacks in December 2015.