Jonathan and his teacher, 53-year-old Karen Elaine Smith, were shot by Smith's estranged husband, 53-year-old Cedric Anderson.
Jonathan and another student, 9, were rushed to an area hospital. Jonathan died before making it to surgery, while the 9-year-old was reported to be in stable condition. The 9-year-old boy was said to be recovering and even watching cartoons on Tuesday, officials said. His identity was not released.
Police said the children shot were not targeted and were likely struck by accident.
MORE: Details emerge about gunman in San Bernardino school shooting
The shooting happened in a North Park Elementary School special needs classroom that included students from grades 1-4. At the time, the room held 15 students, one teacher and two adult aides.
Jonathan's family set up a GoFundMe account for funeral expenses. To donate, visit https://www.gofundme.com/jonathan-our-family-angel-ngeljonathan.
Jonathan's family wants people to know he was a happy child, born with a genetic condition known as Williams syndrome and had survived heart surgery.
Williams syndrome is a rare disorder characterized by learning delays, mild intellectual disability and heart problems, district superintendent Dale Marsden said. Children with Williams tend to be social, friendly and endearing.
VIDEO: Community mourns victims of San Bernardino school shooting
Members of the community, including students and parents of North Park Elementary as well as other schools, gathered at the corner of North Park's campus on Tuesday, saying prayers, sharing hugs and dropping off flowers, toys and candles.
Gina Corrales has three daughters - all three were at North Park on the day of the shooting.
Corrales said one of her daughters told her that when the gunshots rang out, her teacher threw a desk in front of the door and stacked chairs on top. Another daughter told Corrales that her teacher did the same thing, even tying a belt around the door to lock it. The students were on the ground, praying.
Many parents said they are struggling with how and what to tell their children.
MORE: How adults, children can cope with trauma
"School is still school. Everything will be safe there," said parent Jamil Morrow. "It's just hard to break it down for him."
The incident is hard even for adults to understand.
Also, the fact that the gunman got on campus by following standard visitor procedures has some parents wondering if more security is needed.
"More security? It's an elementary school. I hope that we don't have to do that," Corrales said.
VIDEO: Support available for those coping with trauma after school shooting
The San Bernardino City Unified School District has set up support services at Del Vallejo Middle School on Lynwood Drive in San Bernardino so parents and students who need help coping with Monday's traumatic experience can receive aid from counselors.
"I saw SWAT come into my classroom and telling us to put our hands up," said Christian Flores, a 10-year-old student at North Park Elementary. "I just didn't want to die."
Christian was in a nearby classroom when shots were fired and police rushed in, evacuating Christian and his terrified classmates.
"I just got into my car. It's was really hard. It's even hard to talk to you about it right now, because I relive that emotion of not being able to get to my son," said Frank Flores, Christian's father.
Christian and his father decided to take advantage of the support services at Del Vallejo Middle School.
"Just get this past us and just hopefully this doesn't scar him later in life," Frank Flores said.
Therapy dogs were also on hand at Del Vallejo to provide comfort and encouragement.
The services at Del Vallejo will be available to the community on Tuesday and Wednesday.