Has the sea level changed?

What you're referring to is called eustatic change. And sea levels have changed throughout history. Your mother's anecdotal evidence that it hasn't changed may be dependent on where she lives geographically. Personally, on the coast line that I live on in the north east of England, there is anecdotal evidence that the sea levels have risen. The part that geology plays in this is very important too. Having a coast that is vulnerable to the sea, ie - the rocks are very soft (such as bolder clay/glacial til) and the geological profile of the coast. Discordant coast lines are more vulnerable that concordant ones (google these if you're interested).

Globally there is evidence that sea levels are rising, and land masses and either increasing in height, or decreasing (isostatic change). A small island located east of Indonesia, near Fiji, called Tuvalu, is experiencing the problems from this eustatic change, it's likely to be the first island to be lost to the sea in modern day society.

London is another place vulnerable. During the pleistocene era, approximately 7-10,000 years ago, the glaciers covered Scotland, pushing down the land mass from the sheer weight, this in turn pushing up the south of England, like a see-saw. Now the glaciers are gone London is sinking again - isostatic change. And with eustatic change it's at more risk of the river Thames flooding. The same problem is happening in Vienna and other places globally.

As someone said in another post, it's the melting of land ice that poses the real threat. Often this ice hold stores of methane and other greenhouse gasses, as the ice melts and they're released it will add to the greenhouse effect and aid global warming, further increasing land ice melt. It is quite a complex issue, but I hope I've shone some light on it for you.

At present most of the ice that has melted was already floating in the ocean (Ross Ice shelf, North Pole, etc). This does not affect the sea level. So total sea level rise has been very slight. But, it opens the way for ice on land to slide into the ocean from Antarctica, Greenland, etc. This will cause the ocean to rise, not by inches but by feet. As the oceans rise it will help lift ice off of Greenland and Antarctica, speeding up the process.

However, ask your mother about storms and storm surge? The real issue of sea level rise becomes most apparent at that time. This is why hurricanes become that much more damaging.

There is perceived and then there is imperceptible sea level change.

When there are "groins" or partitions on the beach which extend down the water, one side of the groin gets depleted of sand and the other side gets more (carried by the currents). There are people who have used the former side as evidence for sea level rise while conveniently not mentioning the sand mound on the other side of the groin.

So sometimes "sea level rise" is not so much an effect of melting caps as cultural/anthropogenic factors.

Quick, quick changes in sea level happens when there are quick, quick tectonic movements. Like an island slipping into the Pacific because of an earthquake.

But mostly, sea level rise is localized and mostly depends on your tectonic setting. It is imperceptible.

At one place it goes down ,in another place it comes near the sea shore.There are three reasons for it. One is melting of ice,another one is too much evaporation of sea water ,the third one is shift under crust in ocean base .The high tide and low tides are only temporary .