Often there are three kinds of homicide although the grading of homicide offenses actually differs quite a bit from jurisdiction to jurisdiction and often there are special statutes specifically covering deaths caused by child abuse and neglect.
The most serious form of criminal homicide is intentional murder which is often called "murder" in English.
A less serious form of criminal homicide involves reckless conduct or conduct in a sudden spurt of rage. This is often called "manslaughter" although the terminology in English varies much more for this offense. This is still a very serious offense typically on a par with forcible rape or aggravated assault or attempted murder.
A less serious form still is criminally negligent homicide which involves "gross negligence" or neglect. When children are involved, it is often classified as "child abuse" or "child neglect" and frequently is punished more harshly than criminally negligent homicide directed at a stranger. This would typically be a middling to low grade felony.
Even if criminal charges are not justified, often a teacher in this situation might lose a license or have a teaching license suspended for a period of time.
The teacher might also be subject to civil liability in a wrongful death lawsuit brought by the mother. In England, the standard of liability would probably be "negligence" although sometimes negligence is presumed when a third party is caring for a child as a substitute parent. In most of continental Europe there would generally be liability if the teacher was "at fault" although the doctrine that goes into establishing if someone was "at fault" would be rather involved and wouldn't be entirely uniform from country to country.
In a modern setting, the fact that the kid got sick in these circumstances, per se, would probably not amount to even civil negligence or fault.
The key factor for civil and criminal liability would be whether the teacher took medically appropriate steps to address the illness, and there would be liability of some kind if the teacher failed to do so when it should have been apparent that treatment was necessary.
Indeed, failing to seek appropriate care when it was obvious that it was necessary and the care would have made a difference, might very well even constitute criminal child neglect, criminal negligence, or give rise to civil liability. But, since the story focuses on how the boy got sick and not what the teacher did or did not do to treat the boy's illness, we don't know enough to determine the teacher's civil or criminal liability.