How much 'emergency fund' saving do you set aside as a teacher?

Just been sorting out some of my finances and was curious as to how other teachers manage this. Financial advice given in most places is to set aside 3-6 months expenses as an emergency fund in case of job loss, etc.

As a teacher am I crazy to think it's better to keep the emergency fund lower and put more into longer term savings, etc? I feel like if I lost my job for some reason, I can't even imagine why, it wouldn't take long to get a new one. Surely one of the perks of our profession - job security and lots of employment opportunities? Though I appreciate this isn't the same for every subject... I teach maths!