Single parents face a different sort of dating landscape than those without children. When you hold someone else's well-being in your hands, this has to factor into who you choose to enhance your own well being. Different aspects of individuals must be examined in order to ensure the possibility of a good family when there is a family already established (as opposed to situations where family is only in theory).
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If you've just become a single parent then there's no need to launch yourself immediately into a new relationship (rebounds rarely work out anyway), but getting into the mindset that dating is unnecessary, your kids are the only thing that matter, is not a good idea either. If you spend a year talking only to your five year old then you might end up thinking of using the restroom as “going to potty” and suddenly start seeing the merits of having ice cream for breakfast. Furthermore, if you start to define yourself too much by your role as a parent it can have a way of spilling over into your relationships (in the form of “mothering” or being overly protective and controlling of your partner) so let your grief die down somewhat, and then start meeting new people.
Seek out someone responsible. Responsibility is a trait to look for in a partner for anyone, but it is especially important for the single parent. There can be no future for your relationship if your partner isn't willing to carry his or her own weight. This isn't to say that you should push the parenting role onto people you date soon after meeting them or becoming involved with them, because you shouldn't, but realistically you need to be looking for stable people with their feet on the ground. There are people out there who don't mind the idea of trying to prey on single parents as a means of taking advantage of vulnerability while potentially getting to date someone a bit out of their league or use someone as a benefactor, as well as people who may not have ill-intentions but don't have any real concern for your children or circumstances and just want to date you because you're attractive. Dating only people around your own age or older will weed out some of these undesirables.
Dating other single parents has advantages and drawbacks. Relatability is something that can help to get all relationships off on the right foot, and no one can relate to your situation more than someone who shares your situation. For those who don't have any children, the notion of being a parent can be a distant and sort of imaginary thing. Some might find you attractive, love your personality, and think that having a role in your child's life would be a worthwhile endeavor, but on realizing what parenthood really entails might come to realize that they underestimated the reality of it all. This isn't an issue at all when dating other single parents; they understand. If your child is old enough to be in school then parent-teacher conferences and the like can be a very good way to meet responsible single parents like yourself. On the other hand you need to always be realistic about what you are willing to take on in terms of responsibility. Sometimes adding more children into your life for the sake of dating a good person is just not very practical. This is a personal decision and depends on circumstances, but you cannot expect any more from anyone than what you offer them.
When you're on a date don't make the conversation center around your kids. There's no need to pretend as if they aren't a part of your life, but this should not be the center of discussion when first becoming acquainted with someone. Parenthood is certainly a part of who you are, but on first dates you should be trying to help a person get to know you; not your children.
When you begin dating someone new, have a talk with your children. Older kids may already have a pretty firm understanding about your situation, but you should still give them the courtesy of letting them know that you may be becoming serious with someone soon. Some kids won't be too hip on the idea (particularly if there's an estranged relationship with the other parent) but just explain to them that you deserve companionship and dating is an important part of an adult's life. Don't talk about new moms or dads or potentially remarrying or anything like that; just be straight forward about the fact that you're dating someone (and not just out spending time with friends etc.). At this point your children may have some questions, which you should answer, but you don't need to turn it into an epic discussion (if the “birds and bees” talk hasn't happened yet, this is not a good time to try to bring it up). Children who are used to having a single parent often need to be eased into the notion of having that parent be connected closely with someone besides themselves. Be honest, but don't overwhelm them.
Being a single parent presents you with enough challenges all by itself; throwing a dating life into the mix can sometimes seem pretty daunting and unachievable. Chances are though that the inner strength that you have already developed and called upon in order to provide a life for you and your children is a quality that will be viewed as attractive and endearing by many people. So just be yourself, don't sweat rejection (remember people without kids have to deal with that too), get out there and let someone make you happy.