There is no publicly available, independently verified evidence confirming that the Israeli army directly targeted a kindergarten in Gaza while children were inside.
The Israeli army launched a direct strike on a kindergarten in Gaza while children were inside.

FactVerify
Source: factverify.com
Key Evidence
Available live updates and summaries describe extensive Israeli strikes in Gaza but do not specify attacks on kindergartens or confirm the presence of children during such strikes. No authoritative source in the provided results confirms this particular incident.
What the Evidence Shows
The claim asserts a specific and serious event: that the Israeli military launched a direct strike on a kindergarten in Gaza with children present. The search results and available sources provide general information about ongoing Israeli military operations and airstrikes in Gaza, including heavy bombardment and ground assaults in various neighborhoods.
However, none of the sources explicitly confirm or provide verified details about a direct strike on a kindergarten with children inside. Given the highly sensitive and contested nature of reporting from conflict zones like Gaza, initial reports can be incomplete or subject to propaganda from multiple sides. Independent verification from credible international organizations or multiple corroborated eyewitness accounts would be necessary to substantiate such a claim.
Without such evidence, the claim remains unverified and cannot be confirmed as true or false at this time.