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Here is a breakdown of each proposal:
Extreme Risk Protection Orders, also known as Red Flag Laws or Gun Violence Protection Orders: These laws allow family members and law enforcement to ask the courts to order temporary removal of firearms from someone who may be a danger to themselves or others. Senate President Larry Obhof, R-Medina, and House Speaker Cliff Rosenberger, R-Clarksville, said this week that they're willing to consider red flag legislation in Ohio.
Five states have such laws and another 18 are considering them, according to Everytown.org, a gun control group. Some 42-percent of mass shooters exhibited concerning behavior before their crimes, according to the Brady Campaign, another gun control group.
Advocates for Red Flag laws also say they can be used to prevent suicides. In 2016, 924 Ohioans died by suicide using firearms. Nationwide, roughly half of suicides are carried out using firearms.
Domestic violence offenders: Kasich wants Ohio law to mirror federal law, which bars anyone convicted of domestic violence or subject of a domestic violence protection order from buying or possessing a gun. Police in Ohio receive some 65,000 domestic violence calls a year, with about 35,000 leading to criminal charges.
Background Check System: Local clerks of courts are responsible for uploading conviction and sentencing records to the Ohio Bureau of Criminal Investigation and Identification, which then sends it to the National Instant Criminal Background Check System. But records show that several courts across Ohio have failed to upload data in a timely manner, leaving open the chance that convicted felons ineligible to buy guns will pass background checks. Kasich wants local officials to comply with the existing mandates.
"Straw-man" purchases: Kasich wants Ohio law to mirror federal law, which prohibits purchases by third parties, except as a gift. Current state law only blocks such purchases if the straw-man should have known the purchaser is prohibited from buying or possessing a gun. Federal authorities brought charges against a man who is accused of buying a gun for Quinten L. Smith, who allegedly shot and killed two Westerville police officers last month during a domestic disturbance call.
Prohibit the sale of armor-piercing ammunition: The governor wants state law to ban this ammo, which police see as a threat.
Prohibit bump stocks: Kasich wants Ohio law to reflect restrictions being pursued by the Trump administration against devices that are used to convert semi-automatic weapons to fire like automatic guns.
Ohio is not immune to school shootings.
In February 2016, 15-year-old Austin Hancock opened fire at Madison Jr./Sr. High School in Butler County, injuring four students. In February 2012, 17-year-old T.J. Lane killed three students and injured two others in a shooting at Chardon High School.
Kasich, who visited Chardon after the shooting, expressed support for existing Ohio law that allows local school boards to authorize school personnel to carry guns at work.
“If teachers don’t want to do it, that’s fine but there will be some in every school district who will say ‘This is something I want to do for these students.’ That doesn’t mean that if somebody doesn’t want do it that they don’t care about the students,” Kasich said.
Three large public employee unions — Ohio Fraternal Order of Police, Ohio Education Association and Ohio Federation of Teachers — oppose arming teachers as a method of addressing gun violence.
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Also on Thursday, Kasich signed into law a bill sponsored by state Rep. Wes Retherford, R-Hamilton, that will allow paramedics assigned to SWAT teams to carry firearms on the job for self-defense.
Related: Ohio paramedics working with SWAT teams could carry weapons
Student-led demonstrations are pushing lawmakers in Florida, other states and Congress to make changes. Demonstrations are planned in Ohio and nationwide for March 14, March 24 and April 20. Student involvement in Ohio “would be helpful,” Kasich said.
“I think we’re seeing a new era of activism, a new era of citizenship. And there are people now who are engaged saying we should do something who have never said anything before. Those young students down in Florida, they’re just remarkable people and they’re touching everybody in the country,” Kasich said.