When my Mom died last summer, all of her great-grandchildren were at the funeral and the interment. In fact at the interment, each of the grandchildren came forward and placed a yellow rose on the casket.
Their ages ranged from 5 years to 14 years.
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My first funeral was the funeral of my grandmother. I was six years old. I remember nothing of it.
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My personal belief is that in our culture we have an unhealthy fear or disdain of death. One of the ways this disdain is manifest is the feeling that children need to be protected from matters regarding death.
If you believe that death is simply a normal component of existence on earth I can't think of a single reason why children should be shielded from it.
I'm not saying one should be blase about someone's passing; mourning is necessary and needful, nor am I referring to violent or sudden tragic deaths. Those are situations that need to be handled with understanding and care.
But with a "normal" death, after a time of illness and especially of an elderly relative, I think the children should absolutely be involved in whatever memorial or funeral arrangements are conducted by and for friends and loved ones. Because if you don't do so, you are inevitably sending a message that death is scary and fearful and something to be dreaded and awful.
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I should also add that DW's side of the family does not believe in embalming, caskets, funerals, etc. I am fully with them on that matter. We have memorial services. We have small gatherings where we manage the ashes in whatever ways have been decided.
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[added note re young children at services]:
To me the question of children at funeral situations is really a matter of how well they might be able to sit still or behave during the event. I don't think it's a good idea to take a four-year old child to a one-hour funeral service, where they will have no awareness of what is going on and where it will be almost impossible for them to sit still for an hour. Or, if they do attend, it should be like a church service where space is available on the rear or side and a parent and child can make a quick and easy exit if necessary.
But that is a matter of being courteous to other attendees, and not a matter of shielding the children from the experience.
As I think back more on my mother's funeral, I remember that my nieces and nephews with small children made child care arrangements for the funeral service, then they brought the children to the cemetery for the internment. At the interment they remained in the back, circulating away from the service as needed, up to the point at the end of the service when the roses were laid on the casket.