The possessive particle 的 is often dropped when I see an expression like this, especially when referring to a family member (such as in this case). Which is more natural in casual conversation and are both correct by grammatical standards?
In Chinese, when you are talking about family, close friends (我朋友) or a group that you are part of (for example 我班), you don't use 的. They are both grammatically correct, but it is more natural to skip it.
In casual conversation, you can even drop the second 妈 in most cases. So you can just say 我妈 without any problems. In fact, it sounds even more natural.
的 in Chinese is a bit complicated. It may get dropped in different situations. Here are some examples for you:
我（的）妈妈是个老师- sometimes can be dropped
我妈妈的同学是个老师- better be dropped
我妈妈同学是个老师- not so good, not recommended
“那是谁的手机” “我妈妈的。”- should be always dropped
If you wish to put emphasis on possession, then you should keep 的.
Aw Qirui Guo's Example:
“那是谁的手机” whos phone is that
“我妈妈的” my mother's
Be careful to say 妈妈 and not just 妈 here, especially if the owner of the phone is someone else's mother...haha.
我妈 sounds relative more mature and probably more common
我妈妈 sounds more cutesy and can sound a bit childish, but more polite
(These are relative comparisons. Their difference is not very big.)
We drop 的 in any structure where the relationship can be clearly inferred. It also serves to highlight the relation there.
我媽媽 我朋友 我孩子
and so on.
As a rule of thumb, "don't do it if you have to rethink". As a note, dropping it is a no-brainer for familial and personal relations.
If there is another 的 to follow immediately, eg 我妈妈的，我朋友的, then definitely no 的 after 我, otherwise it is mouthful. If there isn't, then it's usually ok to say 我的妈妈.
btw 我的妈呀 is idiom meaning OMG, don't drop 的
Other answers are right, but I will note that 的 is not only usually dropped for personal relationships, but any situation where 1. indicating the possessor is needed; 2. the possessed object is unique up to each person.
1. 我房间里没有暖气 2. 我国今年经济增长率为百分之十二
In case where two nouns are understood to have a close personal relationship, or when the first noun or pronoun belongs to a group indicated by the second noun, 的 is often not needed.
(Resources: Chinese textbook)
It will sound casual when you drop 的. And just one thing that I found interesting is that you can say 我媽媽 or 我媽, but you can't say 我的媽 or 我的哥. It needs to be double when you add 的.
Well, please be aware that 妈 and 妈妈 are ofen used by someone self, 妈妈 especially 母亲 is used for other people's mother.
And 妈, 妈妈 and 母亲 is using from natural to formal.
爸爸，你看到我妈在哪里了吗？Hey Daddy, Do you know where is mummy？
汤姆，这是我妈妈. Tom, this is my mum/mother.
杰克，你妈妈身体好些了吗？Jack, do your mother feel better in these days?
杰瑞，请问您母亲叫什么名字？Jerry, may I have your mother's name?
我的妈妈：for those at the elementary school age
我妈妈：for those at the junior high age
我妈：for those at the senior high age