Jonathan Martinez had Williams syndrome, a rare disorder characterized by learning delays, mild-to-moderate intellectual disabilities and heart problems, according to Dale Marsden, superintendent of the San Bernardino City Unified School District.
But affected children also have "extraordinary gifts," including a passion for music and an extremely friendly personality, an expert said.
"By all accounts, Jonathan Martinez was a happy child," Marsden said at a news conference.
A classmate, Jeffrey Imbriani, 7, said he used to talk and play soccer with Jonathan.
"I know him because one day he just walked up to me and said, 'Can we be friends?' and I said, 'Yeah,' and we've been friends ever since," he told The Associated Press.
Jeffrey said students got out of their chairs and ran outside with their teacher when they heard gunshots.
"I thought they were firecrackers but then the police started coming and then I realized it was gunshots," he said.
He found out about Jonathan's death when he got home and listened to the news.
"I just felt sad," Jeffrey said. "I will think of him as a very best friend."
Jonathan died at a hospital after being shot Monday in his classroom by the estranged husband of his teacher, Karen Smith, who also was killed. The gunman, Cedric Anderson, then fatally shot himself.
A 9-year-old classmate also struck by gunfire in stable condition, was in good spirits and watching cartoons at a hospital, Marsden said. That boy, whose name was not been released, was expected to recover.
The superintendent said the Martinez family wanted to honor Jonathan's memory by getting the word out about Williams syndrome.
It affects about 25,000 people in the United States, according to Terry Monkaba, executive director of the Williams Syndrome Association.
Children with the syndrome can have learning disabilities and heart problems akin to hardening of the arteries, frequently requiring surgery. As they age, people with the disorder also can suffer from kidney and gastrointestinal disorders, anxiety and depression, Monkaba said.
Children with Williams syndrome can be "overly friendly and endearing," Monkaba said. "They prefer to see ... the glass as half-full rather than half-empty. They look for joy. They love people."
If more people were like those with Williams syndrome, "there wouldn't be the kind of anger that led that man yesterday to shoot his wife and two children besides. That just wouldn't happen," she said.
Hundreds of people attended a candlelight vigil for the victims Tuesday evening at North Park Elementary. The school will remain closed until April 16, Marsden said.
The Martinez family has set up a crowdfunding website requesting donations to help with funeral expenses.