Perhaps it is a very silly question...

Hallo Christian,

that's not at all a silly question! Cost of damaged devices to electronics industry due to ESD is billions of dollars every year. ESD is one major cause for failure of chips. And even if ESD events have taken place with stress well below destruction level, performance of chip can be heavily degraded. I think here for instance of high precision operational amplifiers showing very low offset voltage.
And even if after an ESD event chip seems to be ok, chip can be pre-damaged now, showing a failure in some weeks or months!

I'm questioning myself if DS1232 is also sensitive to ESD.

Yes, it's also sensitive to ESD. All modern chips are sensitive to ESD, unless special protection schemes on die are used, like with MAX232E, e.g. Even discrete transistors, diodes and resistors are sensitive to ESD!!

How easy is to burn some DS1232 without taking precautions?

Very easy!! Even simply removing chip from packing, or pulling off the socket can result in total destruction. Yes, even moving a heavily charged-up poly bag in close distance to chip, without needing to touch it directly (!), can result in a destructed chip.

When a device as DS1232 does not warns about ESD should i asume it is very sensitive or i can handle with my bare hands?

This warning is placed somewhere else in your databook, I guess... And whether you can handle it with bare hands depends on situation: Are you charged up and will touching the chip cause a discharge running through the chip? Then, no! If you are charged, then only coming close to chip even without directly touching it can already destroy the chip. In this case the strong electro-statical field causes separation of charge directly on chip by 'influencing'.

Many people think, that ESD is only a problem, when chip is directly touched by a charged object. But also strong electro-statical fields resulting from charged objects can destroy the chip, without any need for directly touching.

Here are some examples showing what potential differencies are involved with ESD events:

Walking across carpet:           35,000V
Walking across vinyl tile:       12,000V
Working at bench:                 6,000V
Poly bag picked up from bench:   20,000V
Chair with urethan foam:         18,000V

This table is valid for 10-20%RH. With much higher relative humidity, namely 65-90%, no more than about 1,500V is to be expected. You see, relative humidity plays an elementary role with ESD!!

If you remember now, that todays chips are only protected against discharges from about 2,000V to 4,000V, then it's clear, that this 'ESD protection' is only capable to make the chips robust against ESD involved with normal handling procedures, and only in combination with additional measures to limit the potential differencies!

So, how to behave now with your DS1232?
It's always important to decrease the potential difference between you (who wants to touch the DS1232) and the chip to as little values as possible. But not by direct touching, of course, but by indirect:
Assume the DS1232 is soldered into a PCB containing a solid ground plane, which is connected to safety earth. Then, you must touch something that is at same potential as safety earth, but far away from DS1232.
If PCB does not have any connection to safety earth, then discharging you at something that is connected to safety earth will also help. After this 'coarse-discharge' you should touch some point of solid ground plane of PCB. Only after this 'fine-discharge' you may touch the DS1232 directly.
But if you, on the other hand, walk across the room, go to DS1232 and touch it directly without pre-discharging you, then there's a high probability of destroying the DS1232, especially if relative humidity is rather low!

Same procedure if you want to pull off a chip from antistatic foam or packing: First coarse-discharge you at something connected to safety earth. This could be some part of earthed house installation. Then, fine-discharge you by touching the antistatic bag or foam, and only then, touch the chip directly, if needed.

Unfortunately, even after such a total discharge, electro-static charge and potentials can again develop, when handling with isolating materials. Think of the poly bag, for instance: If you pick up the poly bag from work bench thousands of volts are generated. The same, if you move in your chair, made of urethan foam. So, the only way to be totally protected against damage resulting from ESD events, is to provide a permanent discharge path, which allows a permanent equalization of any developed electro-static charge. This can only be done by the help of personnel grounded wrist strap, which connects each user to the same potential as ground plane of PCB, via high ohmic resistances (for safety purpose!).

So, tell every student, who wants to touch the DS1232, that he first must pre-discharge himself, as mentioned above. And it's wise to additionally provide personnel grounded wrist straps for everyone who wants to touch the DS1232.

Kai